HEAT TRANSFER THROUGH MOIST FABRICS
by
Anna M. Schneider
A thesis submitted for the degree of Doctor of
Philosophy in the School of Physics, the University of New South Wales.
January, 1987 BXiVZ^IIY OF N.S.W.
2 0 JUN 1988
LIBRARY I hereby declare that this submission is my own work and that# to the best to my knowlege and belief, it contains no material which to a substantial extent has been accepted for the award of any other degree or diploma of a university or other institute of higher learning, except where due acknowlegement is made in the text.
Anna M. Schneider ACKNOWLEDGEMENTS
I would like to thank my supervisors,
Prof. H. J. Goldsmid and Dr. B. N. Hoschke for their guidance and comments and in particular Dr. Hoschke for help and advice during the course of this project. In addition, I would like to acknowledge the assistance of
Dr. B. V. Holcombe in the design and construction of experimental apparatus, Mr. I. M. Stuart in the development of the theory and Dr. R. N. Baulch in the construction of electronic components.
I would also like to thank the Wool Research Trust
Fund for a Junior Research Fellowship and the C.S.I.R.O.
Division of Textile Physics for providing the facilities which enabled me to do my research. ABSTRACT
The aim of this study was to investigate the effect of fabric moisture content, and the form in which it is present, on the effective thermal conductivity of textile materials.
Thermal conductivity is important in characterizing the thermal comfort properties of textiles. Due to the lack of suitable measurement methods, very little is known about the thermal conductivity of moist fabrics.
A transient heat flow apparatus has been specially developed which allows very rapid determinations of conductivity (less than 100 s per sample). This is needed with wet fabrics as moisture is redistributed during the test. The samples tested were made of four fibre types, of different water sorption properties,
(wool, cotton, porous acrylic and polypropylene).
Four regions could be distinguished in the conductivity vs regain curves. The first is characteristic of absorbent fibres and ranges from zero regain to 15 % for wool and 10 % for cotton. The conductivity is low, and almost independent of regain.
The second region starts at zero regain for the non-absorbent fibres, polypropylene and porous acrylic) and extends to saturation regain. In this region the
conductivity rises sharply to a value about double that of dry fabric. The third region extends to about 200 %
regain. Here the conductivity increases slowly. The
fourth region is above 200 % where there is a further
steep increase. From 0 % to 100 % regain, the range of practical significance to clothing comfort, wool had the
lowest thermal conductivity of the four fibre types.
The conductivity of moist fabrics was found to depend on whether the water was absorbed into the
fibre polymer, retained in micropores within the fibre
structure , or held as free water between fibres and yarns .
It was found that the effective thermal
conductivity has three components which correspond to the three modes of heat transfer in operation during the tests. These are conduction, radiation, and the evaporation, diffusion and condensation of water. It was also found that the evaporation and condensation process
is responsible for the characteristic shape of the
conductivity curves.
In this thesis the conductivity of moist fabrics has been investigated experimentally and a theory has been developed to help explain the results. A simple model has been developed which explains the influence of
fabric geometrical structure and fibre sorption properties on the three modes of heat transfer. This work has given an understanding of the role of moisture in the conductivity of fabrics. GLOSSARY OF TEXTILE TERMS <67>
Brushed fabric
A fabric which has one or both surfaces raised by brushing .
Cover Factor
A number that indicates the extent to which the area of a knitted fabric is covered by the yarn: it is also an indication of the relative looseness or tightness of the knitting . cover factor = ^coun^(tex)____ _ loop length (cm)
Cuprammonium Rayon
The fibre regenerated from a solution of cellulose in
cuprammonium hydroxide . Double knit fabric
A fabric with two interconnected layers, which can be made of different fibre types.
Filament Yarn
A yarn composed of one or more filaments (a fibre of indefinite length) that run the whole length of the yarn .
Flannel
An all-wool fabric of plain weave with a soft handle.
Interlock
A double weft knit fabric. Man-made Fibres
Ail fibres manufactured by man as distinct from those
which occur naturally.
Packing factor
A ratio of the volume of fibre present in a fabric to
the total volume of the fabric.
Plated fabric
A fabric with two yarns of different kind, (usually
knitted in such a way that only one of these yarns
is visible on one face of the fabric and the other on
the other face).
Regain
The weight of moisture present in a textile material
expressed as a percentage of the oven-dry weight of
the material. Saturation regain
Regain of a fabric, which contains the maximum
amount of absorbed water.
Spun yarns
A yarn that consists of fibres of regular or
irregular length, usually bound together by twist.
Taffeta
A plain-weave, closely woven, smooth and crisp fabric
produced from filament yarns .
Tex
The direct decimal system based on metric units for
describing the linear density (mass per unit length)
°f fibres; the name tex is usually used for the
combination 'grams per kilometre'. Twist
The number of turns per unit length of yarn.
Warp
Threads lengthways in a fabric as woven.
Weft
Threads widthways in a fabric as woven. TABLE OF CONTENTS
1. Introduction 1 2. Outline of experimental arrangement 26 3. Theoretical analysis of the transient method 29
4. Preliminary experiments 40
5. Development of new apparatus 47
6. Performance of the dynamic conductivity
tester 60
7. Description of samples and their preparation for testing 69 8. Results and discussion 80 9. Analysis of results 91 10. Conclusions 114 Literature cited 122 Published papers -1-
1. INTRODUCTION
One of the most important functions of clothing is to provide thermal comfort to the wearer. Thermal comfort can be defined as "the condition of mind which expresses satisfaction with the thermal environment" <1>.
Clothing plays a very important role in the relationship that exists between the wearer, clothing and environment because it is the factor which can be adapted to meet varying requirements. Clothing should give comfort over a broad range of changing climatic conditions and under different kinds of physical activity. It must ensure adequate insulation in order to keep the body temperature constant within narrow limits, that is, to protect the wearer from getting cold. On the other hand, under physical strain or in a hot environment it must be possible for the body heat to be dissipated by the evaporation of perspiration, otherwise overheating occurs. Good moisture transport and absorption properties will ensure that, even when the wearer is perspiring, the feeling of dampness is avoided. After sweating has stopped, the garment should feel comfortably dry and act again as protection against cold. To assess the comfort level provided by clothing a very complex analysis is required, which takes into account various factors such as the dry insulation value of textile materials, resistance to moisture transfer, specific heat and effective thermal conductivity of -2- moist or wet fabric. Knowledge of these parameters enables a description of the phenomena of heat and moisture transfer from the skin to the environment-. In this thesis one of these factors, the effective thermal conductivity of moist and wet fabrics, is studied.
The thermal conductivity of a fabric is an important factor characterising its insulating properties. It is defined as the ratio of the rate of heat flow per unit area normal to the face of the fabric to the temperature gradient between the two faces of the fabric. It is expressed in W/(K.m). In a dry textile material, which is a complex structure of fibres and air entrapped within it, heat transfer takes place by conduction through air and fibres, by radiation and by forced convection through the pores of the fabric. So when we speak of effective thermal conductivity of fabrics we really mean a heat transfer coefficient where heat is transferred by all these modes. In the case of moist or wet fabrics there is additionally transfer of heat due to evaporation and condensation of moisture.
It has been found <2-7> for common apparel textiles that the thermal resistance (inverse of thermal conductance) of a dry fabric is proportional to the fabric thickness regardless of the fibre from which it is made, with the exception of cotton which is a highly conductive fibre. A fabric immobilizes a layer of air -3- and it is this air which offers most resistance to heat
flow.
Fabrics made of wool are commonly considered as
"warm", but tests on dry or conditioned wool fabrics do not show any superiority in the insulating value of wool as a function of fabric thickness compared with other
fibre types. The main advantage of wool is that, due to its fibre mechanical properties, it makes up to light
fabrics of bulky structure. The common opinion that wool is warmer and more comfortable to wear than other
fibre types cannot be therefore proved by a simple conductivity test on dry or conditioned fabrics. The wearer's perception of warmth may also be influenced by the fabric/skin contact. Wool fabrics generally make little direct contact with the skin, because of the hairy nature of the fabric surface. Garments worn during moderate to heavy activity are not usually in the dry state because of sweating.
The total heat loss from the skin consists of two parts: the heat loss by evaporation and the heat loss by other means (conduction, convection, radiation). Even under normal conditions, for instance while sitting and resting, heat loss by evaporation takes place in the form of insensible perspiration and accounts for about
15 % of the total heat loss through the skin <8>. This form of heat loss is enhanced by sweating when the skin -4- becomes covered by a film of water. Water from the skin gets into the fabric and changes its thermal properties. An example of that is post exercise chill. When a fabric gets wet, its effective thermal conductivity increases. After exercise, as the body stops producing heat, post exercise chill takes place. Even insensible perspiration can introduce water into the clothing under environmental conditions of low temperature but high relative humidity <9>. Condensation of water can occur depending on the temperature gradient across the fabric and the distribution of resistance of the fabric to water vapour transfer. Clothing can also get wet for instance from rain penetration. It is therefore useful to measure the effective thermal conductivity of fabrics when they contain different amounts of water, in order to detect any differences in thermal performance caused by the fibre type from which the fabric is made.
To reveal differences in thermal properties of fibres, transient thermal effects caused by absorption or desorption of moisture by textile materials have been investigated <10>. The experiments showed higher heat losses from moist wool than from nylon during drying out on a guarded hot plate. The authors concluded that nylon, as a non-absorbent fibre, is more suitable for wear when sweating occurs due to activity. However, experiments of this type do not simulate real conditions -5-
accurately enough to draw final conclusions about clothing design and choice of the right fibre type.
Attempts have been made <11/12> to construct mathematical models to explain transient thermal effects
in clothing. Although the use of computers enables the construction of complicated models in which combined
heat and water-vapour transport through multi-layered clothing systems are considered, several simplifing
assumptions are made. One of them is that each clothing
layer is characterized by a thermal conductivity which
is not influenced by the presence of absorbed or liquid water. The reason for such an assumption is that there are no reliable data on effective thermal conductivity of fabrics as a function of fabric regain. Although the authors claim that the results obtained from experiments on a sweating hot plate <13> agree generally quite well with the predictions obtained from the model, several discrepancies were also observed. These probably could be avoided if reliable thermal properties of the textiles were used. Therefore, a need arises for measurements of the effective thermal conductivity of textile fabrics containing water.
Currently scientific information, related to thermal insulation and moisture transmission properties of fabrics, is being used in the development of new products or as a basis for consumer advertising. The —6 — types of products which compete with existing wool products are claimed to have equal or superior properties with regard to warmth or to the transfer of perspiration. One such product is Dunova <14>, an acrylic fibre of porous structure that can absorb considerable amounts of water into its capillary system. It has similar water retention value to cotton and wool
(30 % - 40 %) and can, therefore, absorb perspiration very well. It is also claimed that Dunova quickly feels dry and warm again after perspiring, because its drying time is short. Other tests show that Dunova has a high wetting rate (wicking) but only very low absorption of humidity, which also increases its wearing comfort. In this work, tests on the effective thermal conductivity of Dunova fabrics containing water have been conducted to check its performance in other than standard testing conditions.
Not much information is available on the conductivity of moist or wet fabrics. The reason for the scarcity of information on the effective thermal conductivity of wet fabrics is the lack of reliable methods to measure this property. Standard methods <15,16> of determining the thermal conductivity are based on equilibrium conditions and therefore require a considerable measurement time. This is not tolerable for measurements on moist fabrics as considerable moisture transport will occur during the experiment. -7-
A steady state technique for measurement of the thermal conductivity of moist porous materials was, for instance, applied by Woodside and Cliffe <17> who performed their tests on wet sand of 24 % regain, sealed in containers to prevent water content changes and placed between hot and cold plates. The actual measurements were conducted only after the cycle of evaporation near the hot plate and condensation near the cold plate reached equilibrium. A moisture content gradient is set up in this condition and liquid moisture returns to the hot side by capillary forces. The distribution of moisture in that state is far from what it was in the original conditions and, therefore, the value of the measured conductivity does not apply to natural conditions. It was found that the measured conductivity increases with the decrease in the applied temperature difference between the hot and cold plates because of the moisture redistribution in the sample.
Because of such problems, attempts have been made to characterize properties of wet fabrics in some other ways than by specifying thermal conductivity.
Measurements of thermal conductivity have been restricted to samples with low regains where steady state methods could be used. -8-
The steady state technique was for instance used by Staff <18> to measure conductivity of textiles at low regains. She obtained a linear relationship between conductivity and moisture content of fabrics.
Fink <19> commented on the lack of reliable data on the conductivity of materials containing moisture and pointed out that existing data are inaccurate due to water transport during measurements. Because the effect of moisture movement decreases with decreasing moisture content, he conducted experiments using a steady state hot plate technique on low moisture content samples. The samples were conditioned for several days in air of 53 % relative humidity at room temperature. His results show that the conductivities of conditioned fabrics were only 10 % higher than those of dry fabrics .
Baxter <20> also measured the conductivity of moist fabrics by a steady state technique for low regains. A double plate method was used. The tests were conducted for a very low (0.7 %) and medium (10 %) regain. He noticed that the effect of moisture depends on the density of the fabric. At low densities, the effect of moisture could hardly be detected owing to the small part played by the fibres and also, at low temperatures, the conductivity of air is negligibly altered by increase in the relative humidity. For higher densities -9-
the conductivity increased linearly with increasing
regain.
Black and Matthew <21> measured "the insulating
value" of wet fabrics using the katathermometer covered with a wet cloth. "The insulating value" was expressed
as a ratio of the times required to cool the katathermometer from a given temperature to another temperature with the cloth covering it and without. Two kinds of experiments were conducted: one using a dry cloth and another using a wet clo.th. Because, in the case of a wet fabric, heat transfer took place not only by conduction, convection and radiation but also by evaporation of water into the air and, therefore, was higher than in the case of dry fabrics, it was concluded that "the insulating value" of wet fabrics is lower than that of dry fabrics.
Buzanov and Sukharev <22> developed an apparatus for the measurement of the thermal resistance of wet fabrics. They expressed it in terms of the rate of cooling of a heated block. Movement of clothing could be simulated and experiments were conducted at various moisture contents of the fabrics, by placing the equipment in an air conditioned chamber at various relative humidities.
Similar measurements were conducted by Pratt, Fonseca -10- and Woodcock <10>. The aim was to determine which fibre type (wool or polyamide) is more suitable to wear in conditions of variable physical activity when sweating occurs. Samples of fabrics, conditioned at high and low relative humidities were placed on a guarded hot plate. The rate of heat loss from the plate was measured as a function of time until the steady state was reached.
The rate of heat loss from the plate was in this case a measure of the insulating value of the fabric. As might be expected, the rate of heat flow for fabrics conditioned at high humidities was higher than for fabrics conditioned at low humidities. That effect was especially pronounced in the first 30 minutes. Because the heat loss for a wool fabric was higher than for a polyamide fabric, it was concluded that a non-absorbent fibre like polyamide is more suitable in the case of variable physical activity. Unfortunately, the results are not presented in terms of thermal conductivity and, therefore, it is difficult to compare the obtained data. There is a lack of detailed description of samples and it is therefore difficult to draw final conclusions about the performance of the two fibre types as far as comfort in clothing is concern.
Spencer-Smith studied transient effects in moist or wet fabrics in a series of papers <23, 24, 25,26> . He investigated the buffering effect in hygroscopic and hydrophobic fibres <23>. The apparatus he used was a -11- sweating hot plate. For hygroscopic fibres, the heat loss from the hot plate was very high in the first moments after introducing water into the fabric. Then the heat loss decreased slowly to reach the steady state. In the case of hydrophobic fibres, there was little increase in heat loss after water was released from the surface of the hot plate and after that the steady state was reached very quickly. However the heat loss in steady state was higher for hydrophobic fibres than for hygroscopic ones.
Behmann <27> conducted experiments both on a hot plate and on human subjects, measuring heat loss through two kinds of fabrics, wool and polyamide, at various moisture contents. In both the objective and subjective tests he obtained higher heat losses for the polyamide fabric than for the wool one. This result contradicts that of Pratt et al. <10>.
Another approach to the problem of measuring effective thermal conductivity of wet fabrics is the use of transient methods. A double plate apparatus utilizing measurements in transient heat flow conditions was first developed by Fitch <28> for measurements on semiconductors. The apparatus is now available on the market as the Cenco-Fitch apparatus and is used as a standard method for measuring the thermal conductivity of leather <29>. The specimen is placed between two -12- metal blocks, one at a constant temperature, higher than ambient, the other of uncontrolled temperature, initially equal to ambient. After that moment, the temperature of the second block starts to rise. The heat flowing through the specimen per unit time is approximately equal to the heat received by the block of uncontrolled temperature, which can be measured by recording the changing temperature of the block. If the area and the thickness of the specimen, and the heat capacity of the block of uncontrolled temperature, as well as the temperature of the other block, are known, the thermal conductivity of the specimen can be calculated.
Schwartz <30> measured the effective conductivity of dry fabrics using the same method. In his apparatus the heat source was a copper block heated by a calorimeter vessel containing fluid maintained at a constant temperature, higher than that of the surroundings. The heat sink was another copper block, insulated on all sides but the top. The distance between the two blocks was adjusted so that the required pressure or no pressure could be applied to the sample. A simplified method of calculation of the thermal conductivity is described in the paper. Although the author claims that no adverse conditions such as heat losses disturb the measurements in the first 10 to 15 minutes this seems improbable because of heat losses into the insulation. -13-
Ioffe and Ioffe <31> used the same principle for measurements of the thermal conductivity of semiconductors. The temperature of one of the copper blocks was kept constant at 0°C by immersing it in an ice-water mixture. To minimize possible errors of the method they took into account the heat capacity of the sample while calculating the conductivity. The first several seconds of measurements were ignored while a uniform gradient was established in the sample. The block of variable temperature was additionally equipped with a thermal guard, in the form of a cylinder, in order to reduce heat losses and thus minimize the main source of error. A detailed theoretical analysis of the method and an estimation of errors was conducted by
Kaganov <32>.
Another type of apparatus based on transient heat transfer measurements was constructed by Niven <33>. It was a single plate apparatus and employed a guard in the form of a box around the plate of variable temperature.
The heat sink was ambient air of constant temperature.
To measure the effective thermal conductivity the apparatus required special calibration. The main sources of error in this arrangement lay in the calibration of the apparatus, the variations in room temperature (which was supposed to be kept constant), and in the heat losses which occurred despite the -14- existence of a simple thermal guard. The author claimed that the main advantage of the apparatus was its simplicity.
Hollies and Bogaty <34> measured the effective thermal conductivity of moist fabrics using a modified
Cenco-Fitch apparatus. The constant temperature plate could be kept at a temperature as low as -10°C. The distance between the heat sink and the heat source was adjustable to test fabrics under various pressures. The authors investigated the influence of fibre arrangement under different pressures. They derived an expression for the effective thermal conductivity as a function of the volume fraction of water in the fibre-air-water mixture. A source of error in the experimental arrangement was heat losses or gains into the control plate, as no thermal guard was applied.
Kawabata <35> developed an apparatus, called
Thermo-Labo, based on the same principle as the Cenco-Fitch apparatus, for measurements of the effective thermal conductivity of fabrics. The heat sink of constant temperature is a box with water flowing through it. The heat source is a copper plate heated to a temperature above ambient and insulated from the top.
The sample is placed on the heat sink and covered with a copper plate. The temperature fall of the copper plate is recorded and the thermal conductivity can be -15- calculated. Unfortunately with this arrangement, when the temperature of the control plate decreases in time, no simple thermal guard can be applied. The control plate is insulated instead. The heat losses from the control plate are the main source of error in the measured conductivity. Another disadvantage of the apparatus is that there is no adjustment of the distance between the heat source and the heat sink, so the copper plate rests with its weight on the sample.
In fact, all the measurements are made under a pressure of 12500 Pa which greatly exceeds pressures occurring in practical applications of fabrics.
This apparatus was first used by Yoneda and Kawabata to measure the effective thermal conductivity of conditioned fabrics <36>. Then measurements were made on wet fabrics by Yoneda et al.<37>. The aim of these measurements was to study the effect of fibre type, blend in the yarn, yarn structure and density on the conductivity of fabrics at various regains. The results showed that the conductivity increases with increasing regain. The graphs of conductivity as a function of regain are of sigmoidal shape. Out of the three groups of samples, cellosic fibre, man-made fibre and wool, wool shows the lowest values of conductivity. With the blended wool/polyester yarns the conductivity of the fabrics increased with the increase of content of polyester for the same regain. This can be due to the -16- increase of the amount of free water, compared with absorbed water, with the increase of the ratio of polyester. The effects of the yarn structure and density were also observed. At the same regain, fabrics made of spun yarn had larger values of conductivity compared to that of fabrics made of filament yarns.
Also the conductivity increases with increasing yarn density. Experiments conducted on knitted fabrics show a large maximum conductivity because their maximum regains are large.
Naka and Kamata presented two transient methods for measurement of the effective thermal conductivity of wet fabrics. The first one <38> was a line heater method. A heater in the form of a thin wire is introduced into the sample together with two thermocouples at known distances from the wire. The temperature perturbation can be measured as a function of time and from that the conductivity can be calculated, if the specific heat and density of the sample are known. The method is suitable for measurements on wet samples because it introduces only a small temperature gradient in the sample and takes only short times. In this way the evaporation of water is avoided. The disadvantage of the method in its application to fabrics is that the samples at the time of measurements are in a state which is very different from when they are in wear. The sample has to consist of several layers of fabric placed one over another and -17- enclosed in a polyethylene bag to keep the regain constant. The conductivity was measured normal to the fabric surface and parallel to the warps on flannel, cuprammonium rayon, cotton and polyester fabrics. The relationship between the thermal conductivity as a function of volumetric fraction of water was found to be quadratic when tests were carried out normal to the fabric surface and linear when parallel to the warps with almost no effect of fibre type. As the regain approached 100 %, the conductivity of the samples approached the conductivity of water. A geometrical model has been developed to predict the conductivity of wet fabrics. It includes such factors as the conductivity of saturated air, swollen fibre, and water.
The other transient method presented by Naka and Kamata used a plane heat source <39>. A specimen was placed between a semi-infinite standard sample and a metal plate heater which was kept at a constant temperature. From the known thermal properties of the standard sample, the thermal properties of a fabric can be estimated by measuring the temperature at the contact surface of the fabric and the standard sample. The fabric specimen has to consist of several layers of fabric. Although the method is rapid, and therefore suitable for measurements on wet fabrics, only conditioned fabric (polyester taffeta) tests were presented in the paper. -18-
Suzuki, Sato and Ohira measured the effective thermal conductivity of wet fabrics by another transient method <40>. Their periodic heat source was an air-conditioned chamber with variable temperature. The measured property was thermal diffusivity from which thermal conductivity was estimated. The necessary specific heat and density of the wet sample were calculated from the densities and specific heats of air, water and fibre of the mixture. The diffusivity obtained was constant regardless of the water content of the fabric and, therefore, the calculated conductivity was increasing with increasing water content. The samples for testing consisted of several layers of fabric placed one over another and compressed.
Suzuki and Ohira <41> developed also a model for predicting the effective thermal conductivity of wet fabrics. This is a geometrical model and involves such factors as the conductivity of the fibre, the content of air in the fabric, the regain, and the swelling and shrinkage caused by water. Although good agreement was found between their calculated and experimental results, their conditions of testing always involved the high compression needed in their technique. These conditions are not applicable to clothing in wear. -19-
Salivon at al. <42> studied the effective thermal conductivity of wool fabrics of various regains. The measurements were conducted by a transient method developed by Volkenshtein <43>. In this method the sample is placed between a heat source of constant temperature and a heat sink of known thermal properties.
The temperature at the surface where the sample and the heat sink are in contact is measured as a function of time. The range of regains studied was 0 % - 75 %. The results were presented graphically. From the graph it can be seen that the conductivity decreases steadily with decreasing regain till the regain reaches its saturation value (30 % - 32 %), then the decrease becomes very steep because of the rapidly diminishing water bridges between the fibres. After the stage is reached when most of the absorbed moisture is removed, the conductivity stays almost constant, regardless of the moisture content. Two fabrics were studied: one made of 100 % wool, the second one consisting of 92 % wool. Their structure was similar and their densities also almost equal. The conductivity vs regain curves of the two fabrics were parallel to each other and the value of the conductivity of the 100 % wool fabric was approximately 10 % lower than that of the blended one. -20-
Another transient method suitable for measurements on porous materials containing water was developed by
Eckert and Pfender <44> . They used it for measurements of the effective thermal conductivity of moist soils. A
cylindrical arrangement was used and the apparatus consisted of two concentric circular tubes with the soil
sample in the annular space between the tubes. The
measurements were conducted for a wide range of
temperatures and moisture contents. The conductivity was found to depend little on temperature, especially for low moisture contents, but was strongly dependent on the moisture content. Because the time required to run the test is rather long (over one hour), phase changes take place, and the conductivity is measured under conditions of combined heat and mass transfer.
The theoretical analysis of the experimental results obtained by Eckert and Pfender <44> was conducted by Dinulescu and Eckert <45>. The model predicts moisture
distribution in the sample of the porous material as a
function of time. The time in which steady state moisture distribution conditions are reached can be also predicted.
Crow <46> developed a theoretical model for predictions of the effective thermal conductivity of -21- layers of fabrics containing water. The factors considered were the conductivities of fibre, dry air, water vapour and water or ice. The model took account of whether the heat flow took place parallel or perpendicular to the yarns. As a result the effective thermal conductivity could be read from the graph for combinations of variables, including the diffusion of water vapour .
Krischer <47> developed a model for the calculation of the effective thermal conductivity of non-absorbent moist porous materials. He took into account the energy transfer both by conduction, which in the case of the presence of water is increased by the formation of water bridges, and by diffusion of water vapour under a temperature gradient. The conduction takes place through the solid phase, air and water, and the equivalent conductivity is calculated for all three phases based on a geometrical model. The solid phase is composed of parallel and perpendicular arrangements with respect to the direction of the heat flow and the ratio of these two arrangements has to be found empirically. The ratio can be calculated if the thermal conductivity of the material in both dry and completely saturated states is known.
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For temperatures higher than 59°C, the conductivity is higher than that of water for low moisture contents and rises with increasing water content to reach a maximum at about 50 % saturation water content. Some of the experimental results of different authors for measurements of the effective thermal conductivity of fabrics are presented in Figs.l and 2. Cotton and wool fabrics are presented on the graphs because most of the available information concerns these two fibre types. For cotton, the highest value of the conductivity was -23- obtained by Suzuki, Sato and Ohira <40>. The rise in conductivity is very steep as soon as the water is introduced into the sample. Values obtained by Kawabata <35> on Thermo-Labo are considerably lower and the conductivity is almost constant in the region from 0 % - 10 % regain. Then there is a steep increase in conductivity with increase of moisture content. The measurements were conducted under a pressure of 12500 Pa. The model developed by Kawabata <35> does not explain this characteristic shape of the conductivity vs regain curve as it is based on a simple additive theory. The theoretical curve presented in the graph is based on the assumption that the conductivity of a wet fabric consists of two components: conductivity of dry fabric and conductivity of water contained in this fabric. Although the measurements by Yoneda <37> were also conducted on Thermo-Labo apparatus, he obtained slightly lower values of conductivity than Kawabata. His measurements were done over a wide regain range (up to 200 % regain) but very low regains (below 5 %) were not tested. The conductivity rises sharply as soon as water is introduced into the sample, until approximately saturation regain is reached, and then changes slowly with water content. Hollies and Bogaty <34> tested a cotton fabric at two -24- regains only: 11 % and 23 %. They obtained lower values than any other workers. They developed an additive theory for the calculation of the thermal conductivity of wet fabrics. According to the theory, the thermal conductivity of wet fabrics could be calculated by adding the conductivity of dry fabric multiplied by volume fraction of dry fabric, and the conductivity of water multiplied by its volume fraction. To obtain agreement of the theory with experimental results an "effective thermal conductivity" of water was used which was lower than the normal conductivity of water. For wool fabrics the highest values of conductivity were obtained by Salivon et al. <42> in the regions of regain above saturation. However, the conductivity for lower regains was considerably lower and stayed approximately constant in the regions of regains from 0 % - 10 %. Then a steep increase occured. Suzuki, Sato and Ohira <40> obtained an almost straight line for the relationship, conductivity vs regain, but the rise of conductivity was much slower than in the case of the cotton fabric . Baxter <20> and Hollies and Bogaty <34> tested only low regains and they also obtained a linear relationship for conductivity as a function of regain, although there is a variation in the magnitude of the values. The -25- curve for wool <34> was lower than that for cotton and both agreed with the ones derived from the theory. Yoneda's curves for wool are similar in shape to those for cotton but the rise in conductivity with moisture content is less steep and the value of the conductivity of wool is much lower for the whole range of regains. Both for cotton and for wool, large discrepancies in the thermal conductivities measured by different authors can be observed. The reasons could be: the variation of the temperature gradient applied when measuring heat flow which has resulted in the variation of the diffusion component of the effective conductivity, the various pressures under which fabrics were compressed during tests and the variations in uniformity of moisture distribution in samples. Also the boundary conditions varied in different tests, depending on whether a double or single plate apparatus was used or whether a single layer of fabric or multiple layers were tested. Another source of variation is that samples, even if made of the same fibre type, varied in construction. Also, in most of the methods presented, heat losses caused substantial errors in the measured conductivity. -26- 2. OUTLINE OF EXPERIMENTAL ARRANGEMENT As demonstated above in Chapter 1, transient methods are superior to steady state methods for measurements of the effective thermal conductivity of porous materials containing water. For measurements on wet fabrics, a transient technique utilizing a heat source of constant temperature and a heat sink of uncontrolled temperature has been developed. A sample is placed between the heat source and the heat sink and the rate of heat flow, proportional to the rate of change of heat sink temperature, as well as the temperature difference across the sample, are observed as a function of time. Knowing the heat capacity of the heat sink and its area (this is the area through which energy transfer takes place), and the thickness of the sample, the effective thermal conductivity of the sample can be calculated. This method was used for measurements of the conductivity of various semiconductors <31> when the conductance of the sample was low enough so that the heat flow between the heat source and the heat sink did not take place too rapidly. If the temperature of the heat sink reached the temperature of the heat source too quickly, a sufficient number of measurements could not be taken. On the other hand, if the conductance was too -27- low, changes in the heat sink temperature were too slow to be recorded with the desired accuracy. Of course, the range could be extended towards either lower or higher conductance. In the first case, the heat sink should be of large heat capacity to slow down the temperature rise in the heat sink as desired, in the second case it should be as thin as practically possible. The most suitable arrangement in the case of fabrics is when the heat sink and the heat source are two flat copper plates. The heat capacity of the heat sink (and therefore its mass) has to be chosen carefully to obtain a sufficient rate of change of its temperature during the test to enable it to be recorded with sufficient accuracy. However the heat capacity of the heat sink must not be too small because, as it will be shown later, it is important that the heat capacity of the heat sink is much larger than the heat capacity of the sample. a It is advisable that the area of the sample and therefore of the' heat sink and the heat source are large, to reduce edge effects. This also results in more accurate data as fabrics are not homogeneous materials. At the moment that a fabric is placed between the heat source and the heat sink plates, heat starts to flow from the heat source through the fabric to the heat -28- sink. In the first few moments, most of the heat flowing from the heat source is used to heat up the sample. For the case of dry fabrics, this period does not take long because of the small heat capacity of fabrics. After a short time, an almost uniform temperature gradient is established in the sample and most of the heat flowing from the heat source is used to heat up the heat sink. Only in that period, after a uniform gradient is established in the sample, can readings be used for calculation of the thermal conductivity. This condition sets limits on the heat capacity of samples which are to be tested. If the samples are of high heat capacity, this initial period is long. Also, it is required that the ratio of the heat capacity of the sample to that of the heat sink be less than one, otherwise the uniform temperature gradient across the sample is not established. In the case of a slightly non-linear temperature profile the conductivity can still be accurately established by introducing a correction factor, as shown later. On the other hand, the duration of measurements is limited because at the moment at which the temperatures of the heat sink and heat source become almost equal, even a small error in the measurement of the temperature difference introduces a large error to the calculated conductivity. A ABOVE (T) AMBIENT TEMPERATURE METHOD METHOD TRANSIENT FOR TEST. SINK SOURCE ARRANGEMENT SAMPLE HEAT HEAT CONDUCTIVITY EXPERIMENTAL A 3. d (X) 30NV1SI0 O FIG. -29- I 3. THEORETCAL ANALYSIS OF THE TRANSIENT METHOD 3.1 Introduction A short theoretical analysis of this method was presented by Kaganov <32> . A more detailed analysis is given below. It is supposed that the sample is originally in thermal equilibrium at the ambient temperature. The face x = 6 is then subjected to a heat source which is T C above ambient, as shown in Fig.3. Then the only heat flow into the sample is from the heat source and the only heat losses from the sample are into the heat sink. Heat exchanges from the side surfaces are negligible and are assumed to be zero. It is assumed that there are no heat losses from the heat sink to the surroundings. 3.2 Approximations to the temperature distribution The distribution of the temperature above ambient through the sample can be described <48> by the equation T (x,t) = QO . Tj [1 -I B . sin (v . (1 - x/6)).e~mn ] ....( 1 ) n - i n n -30- where B = 1 / (^ v + { sin 2v ) ....(2) n w n 4 n and Here v are the roots of n cot v=v/B ....(4) For n>1 , v ~n7T + «/n7T — n+ i M where 6 = s/s x = distance through sample from heat sink face (m), 5 = the thickness of the sample (m), t = the time elapsed from the start of the test (s), s = the thermal heat capacity of the sample in contact with the sink (J/K), sj = the thermal heat capacity of the heat sink (J/K), a = the thermal diffusivity of the sample (m2/s), = k/(pc ' ) , Here k = the thermal conductivity of the sample (W / (m. K) ) t 3 p = the density of the sample (kg/m ), c*= the specific heat of the sample (j/(kg.K)) -31- From equation ( 1 ) it follows that the temperature drop in the sample, A T , is given by the series expansion -m t AT T r - T - T . I B sin v . e n ..( 5 ) x = 6 x = o i n= o n n Because of the exponential factors this series converges quickly. Some time after the beginning of the experiment all the terms in the series become negligibly small relative to the first. From this time on A T is approximated by a single term AT - T j . B j . sinv x . e-™1 11 . Differentiating with respect to t we get dT2 = - dAT =. Rij . Tj . . sin . e 1 dt "dF where T2 is the variable temperature of the heat sink. So dT2 / AT ~ m . dt 1 From equation ( 3 ) with n = 1 H2/ at- av,2 / 62 , where from equation ( 4 ) cot vi Vi / 6 . -32- From the definition of the thermal diffusivity a we obtain for the thermal conductivity k the expression dT2 k / AT . 6 .sj / (A. Vi2 ) . . . . ( 6 ) dt where A = the area of the sample in contact with the sink. 3.3 Approximations to the roots of cot v = v / 6 . In this equation we can substitute cot v by its series expansion <49>. Thus 1 / v - v/3 - v 3 / 4 5 + 0(v ) = v/3 or v2 .( 1 -*-6/3 ) = 6 - 33 / 45 + 0 ( 6"). The absolute error in the approximation v2 = 6/d + 6/3) --- ( 7 ) 3 is therefore less than 6 /45 - 2 2 3.4 Errors in v induced by approximation v =6/(1 + 6/3) 2 In the table are listed values of v calculated from cot v = v /6 and from the approximation, equation ( 7 ). -33- The absolute and the relative errors are also listed 6 lies in the range 0.1 < 0 < 0.9. ERROR TABLE 2 6 V eqn ( 7 ) Abs. Error Rel. Error . 1 0.096754 0.096774 -0.000020 0.00021 .3 0.272266 0.272727 -0.000461 0.0017 .5 0.426763 0.428571 -0.001808 0.0042 .7 0.563337 0.567568 -0.004231 0.0075 .9 0.684591 0.692308 -0.007717 0.011 2 3.5 Conductivity with v replaced by its approximation As can be seen in the table this replacement can be made with an error of 1.1 % or less for S < 0.9. Substituting for Vj by equation ( 7 ) with 0 = — the s i conductivity is given by k = ^t2/ AT * (6/A) * (Sl + s/3) --- ( 8 } The conductivity of the fabric sample can be evaluated using this equation. The following must be known : the thickness of the sample, 6 ; the heat capacity of the heat sink, Sj ; the heat capacity of the sample, s; and the area of the heat sink, A. The rate of -34- rise of the heat sink temperature divided by the temperature difference between the heat source and the heat sink, dT2 /AT dt can be measured by the transient method. In the treatment of Ioffe and Ioffe <31> no term such as s/3 appears. This term arises from the proper accounting for the boundary condition at the heat sink which leads to the equation for v , cot v = v/B and therefore to roots v such that v2 ~ 3/(1 + 6/3). 3.6. Estimation of Time when Single Term Approximation Applies: Analytic Method The ratio R , defined as dT2 . dt ' can be expressed as a ratio of two series by using equation ( 5 ) for AT and its derivative with respect to the time t for the time derivative of T2. Neglecting all the terms except the first ones in this ratio of series introduces a small error in the -35- calculated conductivity. This error diminishes rapidly as the time elapsed since the beginning of the experiment increases. Kaganov did not present such an analysis of errors in his treatment of Ioffe and Ioffe's experimental method. However, he estimated the time after which this approximation can be introduced. It will now be shown how to estimate this time. As described above the ratio R can be expressed as the ratio of two series m,. T . B,.sinv . exp (-m t) + ... R 1 J- . ■ 1______1______!------( 9 ) T . B[ . sinv j . exp (-n^t) + ... mj <1 - G, + • • • ) ---( 10) (1 - F, + ... ) Here we have taken as a factor the leading term in each series. So from equation ( 5 ) which defines the terms in the series, m 2 G i = Fi , ---( 11 ) Fx = (sinv2 . B2 / sinvj . Bj ) exp (- (m2 - mj) .t) ...( 12 ) -36- Using the formulae for B^ and given in equations (2) and ( 3 ) and the approximation, equation ( 7 ) for Vi , we obtain 2 ______i______B i ✓ bn +3/3) (1 + sin2(1+3/3) ) •••*( 13 ) 2/6 (1+6/3)' --- ( 14 ) ^ ( 1 +6/2tt + sin (26/tt) / 2tt) sinvi = sin/6/(1+6/3) --- ( 15 ) sinv2 = - sin (6/tt) ....( 16 ) m2-mi = (tt2_ 6/3) . a/62. --- ( 17 ) Forming F and approximating sin£/£ by 1 , for a number of values of £ , we obtain the estimates F j - 2 6 / tt 2 . exp ( — 7T2 . a . t/62) --- ( 18 ) 2 G,- 2 . exp (- tt " . a . t/6 ). --- ( 19 ) -37- For n 2. 2 v>^ are approximated by V ~ nTT + 3/ TT - n --- ( 20 ) n * So sin v has sign (-) for 6 < tt . This is n well outside the range (0.0<3<0.9) . So the terms of both the series are alternating in sign and because of the exponential factors are strictly decreasing. Having these properties the series are convergent and the sums o f the series to successive terms define maximum and minimum values of the respective sums. So from equation ( 9 ) the true value of the ratio R ( R^_ say) , has upper and lower bounds as defined by the inequality 1 -G < R --- ( 21 ) i t If we approximate to Rt by the value R = 1 then -G < R, - R < F / ( 1 -F ) i t e i i As G > F , i i ' lRt " Re I < Gi ~ 2 exp (- tt 2 . a . t/fi*). ....( 22 ) So, for the error to be negligible, 62. £n 2 t > > ______--- ( 23 ) 2 a 7T (x) aoau3 BAiitnau -38- This inequality is Kaganov's result. The evaluation of relative error in the calculated conductivity as a function of time is shown in Fig.4. 7. Variation of the Single Term Approximation Error with Time: Computer Technique The above estimate of the time elapsed for negligible error is very conservative. Its advantage is its simplicity. The conservative nature of the estimate comes from the upper and lower bounds taken for the ratio of the sums of the two series. The first two terms only are considered. If, say, the first ten terms were considered for each sum, the upper and lower bounds would be much closer to one, but the expressions for these bounds are complicated. To obtain a more accurate estimate of this time, the calculations required were done on a computer. The conductivity is first calculated from equation ( 8 ) in which the ratio of the sums of the two series is approximated by the ratio of their first two terms. This conductivity is then compared with that obtained when the sums of the series are approximated by the sums of their first 50 terms. This latter value is taken here to be an "accurate" evaluation of conductivity. o o ro FUNCTION A AS TECHNIQUE. o o CNI CONDUCTIVITY COMPUTER BY CALCULATED OBTAINED IN ERROR SAMPLES o o RELATIVE DIFFERENT OF FOR TIME OF ESTIMATION 3 . FIG. (%) «o«y3 3Ai±*ri3u 0 ' r 300 9*0 9*0 1 / c. 1 fr *0 Z '0 0*0 FIG.6. TEMPERATURE DISTRIBUTION AS A FUNCTION OF TIME IN A S*¥-1PLE OF THICKNESS 1 .5 mm, CONDUCTIVITY 48.0 rr*4/(m .K) ^ ID HEAT CAPACITY 8 .0 J/K. THICKNESS . CD OF O J/K 26 SAMPLE A IN CAPACITY TIME HEAT OF AND -o \ X FUNCTION A mW/(m.K) AS 37.0 DISTRIBUTION CONDUCTIVITY rwn, 4 .3 TEMPERATURE o 7 . o FIG. » Z 1/ 1 -39- The results of these calculations are shown in Fig.5. This shows the relative error in the calculated conductivity for samples of different diffusivities and thicknesses. It can be seen that for thin, dry, fabric samples, the error becomes negligible in times as short as 10 s, because of their low heat capacity (see sample 1). In the case of thick and wet fabric samples this time is extended to about 100 s (see sample 3). Curve 4 in Fig.5 presents a case of a sample of a different nature to a textile fabric. It is very thick, of high heat capacity and it has a low conductivity. Here the time to obtain a small error can extend substantially, in this case to about 300 s. In this analysis it was assumed that the heat capacity of the heat sink was 163 J/K. The reason for this variation in times for different samples is that the time to establish a uniform temperature gradient across the sample depends on the diffusivity and the thickness of the sample. The temperature profiles in samples 1 and 2 from Fig.5, at times : Is, 10 s, 100 s, 500 s, are shown in Figs.6 and 7 respectively. As can be seen, in sample 1 a uniform gradient is already established after 10 s, while for sample 2 it takes 100 s. >- \- ►H LU z> _J h* Q_ O ZD 3 Q § O _l LJ I H U MI> h" 0 u L- Ll. UJ LJ 1 h- CD z a; ZD (ft CL METHOD. CL OL TRANSIENT z HI cn BY h- CL oo LU < CD X CO M L_ -40- 4. PRELIMINARY EXPERIMENTS Preliminary experiments, using a simplified experimental technique, were conducted to demonstrate the utility of the above described method to measure the conductivity of dry or wet fabrics. An existing laboratory hot plate was used as a heat source. The surface area of the hot plate was 310 mm * 310 mm and the temperature was controlled, so that it could be held approximately constant during the test. The heat sink was a copper plate of an area 150 mm * 150 mm and thickness 1.2 mm. Copper was chosen as the heat sink material because of its good thermal conductivity and high heat capacity. The heat sink was insulated against heat losses from the top with 100 mm thick foam. The experimental arrangement, which is similar to that of Kawabata1s Thermo-Labo <35>, is presented in Fig. 8. The temperature of the hot plate was measured by a copper/copper-nickel thermocouple embedded in its surface. The heat sink temperature was measured by the same kind of thermocouple attached to its upper surface. -41- Because of the good thermal conductivity of copper it was assumed that the temperature of the upper surface of the thin copper plate was equal to the temperature of the bottom surface. The reference point of both thermocouples was a big copper block kept in an air-conditioned room at a constant temperature. The reason for setting the reference point at room temperature instead of, for example, using an ice-water mixture was that the differences between the measured temperatures and the reference point temperature were reduced and could be more accurately recorded, as voltages, by a chart recorder. The chart recorder was set at 0.5 mV full scale for measurements of the heat sink temperature recording and 1.0 mV full scale for the heat source temperature recording. The most suitable chart speed was found to be 60 cm/minute. During the test the samples were compressed by the weight of the heat sink copper plate and insulating foam having a total mass of 390 g. The exerted pressure was therefore 170 Pa. -42- The experiments were conducted on two kinds of © samples, a Thinsulate type M (a non-woven batting of extremely fine polyolefin fibers of very good insulating properties, produced by 3M <50>) of thickness 1.6 mm and a cotton fabric of thickness 0.6 mm. The thickness measurements were obtained using a "Shirley" thickness gauge at a pressure of 170 Pa. The Thinsulate and the cotton were both tested after conditioning in standard conditions (21 °C, 65 % relative humidity) and additionally the cotton fabric was tested at 111 % regain. The heat capacities of the conditioned Thinsulate (12 J/K) and the conditioned cotton fabric (5 J/K), as well as the wet cotton fabric (25 J/K), were much lower than the heat capacity of the heat sink (97 J/K). The heat capacities of the samples were calculated from their packing factors and specific heat capacities of the fibre they are made of. The output voltages of the heat sink and heat source thermocouples were recorded for the whole period of the -43- test, then data extracted from the graph at 10 s intervals was used to calculate the thermal conductivity for each data point using the following expression: s 6 T' - T" k. = ------1 * ------2 2 ——----- — A . At (T \ - T'2 ) + < T" - T"2 ) 2 where At is time period between readings = 10 s. Symbols ’ and " at heat sink and heat source temperatures mean that the reading is taken at the start and at the end of a 10 s period. Because the temperature of the heat source is not ideally constant during the test, an average temperature from the start and end of the 10 s period is taken as the temperature of the heat source. The same is done to calculate the mean temperature of the heat sink. It will be noticed that the term (l/3)*s has been omitted in the above equation, compared to the eq.8. The reason for that is that heat transfer during measurements by the above transient method is of two kinds; one is heat transfer by conduction, and the other by evaporation and condensation of water. (This -44- phenomena of coupled heat and mass transfer is discussed in detail in Chapter 9). In that way, the measured "conductivity" is not due to pure conduction and eq.8 cannot be used without introducing some error. When the above equation is used, the calculated value represents heat flux to the heat sink divided by the temperature difference between the heat sink and the heat source. This coefficient is related to thermal conductivity and from now on when the term effective thermal conductivity is used it means that it was calculated according to the above equation. For conditioned or dry samples the effective thermal conductivity calculated as above is equal to the actual thermal conductivity (including heat transfer from radiation) as the term containing the heat capacity of the sample can be omitted as being small. Conversion from the voltage output from the thermocouples into the temperature was performed according to the expression: \r ( 1485 + 0.17 * voltage) 2 - 38.55 temperature = ------0.085 which was based on tables <51> for electromotive force as a function of temperature for copper/copper-nickel thermocouples. Voltage is expressed in volts and BY OBTAINED APPARATUS. THINSULATE® METHOD CONDITIONED OF TRANSIENT SIMPLIFIED CONDUCTIVITY THE ON THERhV^L EFFECTIVE MEASUREMENTS 9 . FIG. (Orw)/MW) AlIAIlOnONOO “!VWa3H± 3AI103J33 OBTAINED OBTAINED FABRIC APPARATUS. COTTON METHOD CONDITIONED TRANSIENT OF SIMPLIFIED THE CONDUCTIVITY ON THERMAL MEASUREMENTS BY EFFECTIVE 10. FIG. (orw)/Mw) AiiAiionaNoo ivnushi 3ai_lo3jj3 09 TEST N o. SYMBOL r-t OS (Nl ((X*UJ)/M*JJ) CO 10 LO Ofr A l I A I l O n a N O O OS 3VWy3H± 02 3AI133JJ3 01 0 o h- CL OC U z LJ H LJ FIG.11. EFFECT IVE THERMAL CONDUCTIVITY OF WET COTTON FABRIC (REGAIN 111 %) OBTAINED BY MEASUREMENTS ON THE SIMPLIFIED TRANSIENT METHOD APPARATUS. -45- temperature in degrees Celsius. For each type of sample (conditioned Thinsulate, conditioned cotton, wet cotton) tests were repeated six times and the results are presented in Figs. 9, 10 and 11. The effective thermal conductivity is plotted as a function of the temperature difference between the heat sink and the ambient air. In this way it is possible to obtain a common "zero starting point" for all the tests. Additionally the temperatures of the heat sink and the heat source as a function of time are plotted in Fig.12. (Data from the test No.1 for conditioned cotton). As can be seen from Figs. 9, 10 and 11, the value of the resultant effective conductivity decreases with time. The reason for this is that the calculations are based on the measurement of the heat gain of the heat sink. Because its temperature rises above the ambient temperature, heat losses from the heat sink always occur during the tests, even if insulation is applied to the heat sink. It is therefore necessary to extrapolate the conductivity to the zero point, which is obtained as an intercept of the linear regression line of all the o Ln CM TIME. OF o o CM FUNCTIONS AS o SINK 10 HEAT AND w 3 H-t E-* o SOURCE CD HEAT OF o L0 TEMPERATURES 1 2 . FIG. o (Do) 3HfUVa3dH3J. -46- points obtained from the tests with the conductivity axis. The values of conductivity acquired in this way are as follows: 30.5 mW/(m.K) for conditioned Thinsulate, 37.5 mW/(m.K) for the conditioned cotton and 49.0 raW/(m.K) for the wet cotton fabric of 111 % regain. It is evident that the values of the conductivity for the conditioned fabrics are not very realistic. However, the method showed differences between the fibre types and the value of the conductivity of cotton is correctly higher than that of Thinsulate. Even more significant is the difference between the conductivity of the conditioned and wet cotton fabric where the increase in value is 30 %. The method proved, therefore, to be sensitive enough for studying effects of water on the effective thermal conductivity of fabrics. To obtain more reliable results it was necessary to eliminate the main source of errors in the method, namely heat losses from the heat sink. It was also necessary to make improvements to the heat source to obtain less variation in the heat source temperature during the test than in the original arrangement (Fig. 12) and to provide for adjustment of the distance between the heat sink and the heat source to correspond to sample thickness under the desired pressure. -47- 5. DEVELOPMENT OF NEW APPARATUS To overcome the forementioned deficiencies in the simple transient method, a new apparatus has been designed and constructed. To reduce the drop in the temperature of the hot plate, which has a disturbing effect on the uniformity of the temperature gradient accross the sample, its heat capacity has been increased by placing a 4 mm thick, 310 mm * 310 mm copper plate on top of it. Later tests revealed that the increase in the heat capacity was still not sufficient and another copper plate of the same thickness was added. Good thermal contact between the plates was ensured by filling the gaps between the plates with a silicone heat sink compound (Dow Corning ® 340). The new heat sink consists of a 1 mm thick copper plate, thermally guarded from the sides and the top. A copper ring of the same thickness as the heat sink plate is applied at the sides. During the test the temperature of the ring rises in the same way as the temperature of the heat sink and, therefore, heat losses from the sides of the heat sink are avoided. The heat sink plate is held in place by a countersunk plastic spacer and if necessary it can be removed and exchanged with a -48- different plate, for instance of different thickness to change the rate of temperature rise of the heat sink. The top thermal guard is a plate heater of an area covering both the area of the heat sink and its guard ring and is electronically controlled to follow the temperature of the heat sink. It consists of two parts: a bakelite plate 310mm * 310 mm with a resistance wire wound on its bottom side and an aluminium plate of the same area and of 1 mm thickness. The wiring consists of four 7.5 m long pieces of wire of resistance 9.35 ohm/m connected in parallel. The aluminium plate is pressed tightly to the wired side of the bakelite plate and ensures that the heat produced in the wires is evenly distributed over the whole area of the guard. To guarantee a good thermal contact between the wires and the aluminium plate, a heat sink compound was applied between the aluminium and the bakelite plate. The aluminium plate is thin enough to obtain quick response from the guard heater. The output of the heater is about 365 W which makes it possible to obtain a rate of temperature rise of about 0.6°C/s. The aluminium side of the heater faces the heat sink. A 2 mm air gap is left between the guard heater and the heat sink to prevent heat conduction between the two when momentary differences in the temperatures of the guard and the heat sink occur. The separation is maintained by 2 mm -49- thick bakelite spacers. The heater is insulated from the top with 60 mm thick rigid polyurethane foam to reduce heat losses. This is covered on the top with a 2 mm thick aluminium plate to protect the foam from structural damage. The heat sink plate, guard ring, guard heater plate and insulating foam are held together by screws which are insulated from the test plate by plastic spacers. The heat sink assembly rests on three micrometer adjusters which are attached to the top aluminium plate so that the distance between the source and the sink plates can be adjusted to correspond to fabric thickness . ITT M51W thermistors embedded in the heat sink plate and attached to the surface of the guard heater aluminium plate and a YS144032 thermistor embedded at the surface of the heat source plate are the temperature sensors. They have been calibrated with the help of copper/copper-nickel type T thermocouples made of very thin wire, with their junctions placed in close -50- proximity to the thermistors. The advantage of using thermistors over thermocouples as temperature sensors is that their change of voltage output as a function of temperature is higher than in case of thermocouples and can, therefore, be more easily logged by the computer. The ITT thermistors are specially designed to be attached to flat surfaces as the thermistor bead sits on a flat, thin disc. The thermistor is insulated from the ambient air with a thin layer of glass covering the bead and cannot therefore be affected by humidity of the air (coming for instance from water evaporating from a sample). The very small mass of the thermistor (0.05 g) ensures quick response. Conduction through the thermistor leads is minimized as they are made of a very thin platinum wire. The YSI thermistor used in the heat source is of slightly larger mass but the response time in this case is not important as the heat source temperature remains almost steady during the test. The heat sink thermistor is embedded in the middle of the heat sink plate. It is completely sealed there with Araldite ® epoxy resin so that good heat transfer conditions from the plate to the thermistor are ensured. The heat source thermistor is placed in the middle of FIG.13. TRANSIENT THERMAL CONDUCTIVITY TESTER. -51- the plate near its surface in the similar way. The guard heater thermistor is glued directly to the aluminium plate surface. The heat sink thermocouple, for practical reasons, was first soldered to a small copper plug, which was then pressed into a hole in the heat sink plate. The procedure with the heat source thermocouple was similar. The guard heater thermocouple was first soldered to a thin copper disc which was then glued to the aluminium plate surface. The leads of the heat source plate thermocouple and thermistor are buried in a groove along the plate and lead to a measuring device. The leads of the thermocouple and thermistor of the guard heater and the heat sink pass up through a hole in the guard heater insulation to the measuring device. The basic construction of the apparatus is presented in Fig.13. An additional part to the apparatus is a box with cold water circulating through it. On its upper plate, which is made of aluminium, the heat sink assembly is placed after a test in order to cool it quickly. In this way experiments can be repeated rapidly. The water is fed to the box from a controlled temperature water bath. AO 521 AD 580 3K3 15 V >— 14 •001 pF AD 521 |-nJTJ"Lr->+70V 1RF530 6800 J? FIG.15 A. THE ELECTRONIC CONTROL SYSTEM FOR THE TRANSIENT CONDUCTIVITY TESTER. HEAT SINK AND GUARD HEATER SECTION. RT1 = HEAT SINK THERMISTOR, RT2 = GUARD HEATER THERMISTOR AD 521 C<4 LT» > + > __ ° nz **r CL ro a ) +- o E CL LO V > FIG.15 B. THE ELECTRONIC CONTROL SYSTEM FOR THE TRANSIENT CONDUCTIVITY TESTER. HEAT SOURCE SECTION. RT3 = HEAT SOURCE THERMISTOR -52- The electronic control system of the tester fulfils two functions: 1. transmits the measured temperatures (as voltage) from the temperature sensors to the computer to be recorded there, 2. controls the temperature of the guard heater so that it follows the temperature of the heat sink during tests. The basic structure of the control system is presented in Fig.14. The detailed schematics of the electronics is shown in Figs.15 a and b. The thermistors of the heat sink and the guard heater are incorporated in a common bridge. There are three outputs from this bridge. The first one is the voltage output at the point between a resistor and the heat sink thermistor and gives temperature in terms of voltage of the heat sink. This voltage is compared with a constant voltage which is generated by a voltage divider. By changing the resistance in this voltage divider the output can be varied according to requirements. This output is amplified and sent to the computer. Calibration is necessary to find the relationship between the voltage registered by the computer and the actual temperature of the heat sink. -53- Before the calibration, adjustment of the reference voltage and the gain of the amplifier has to be carried out. Because the voltage input to the computer must lie in the range -10 V to +10 V, it is convenient to adjust it in such a way that the assumed lowest heat sink temperature (about 20°C) corresponds to about -9 V and the highest (about 60°C) corresponds to +9 V. This is done in stages . In the first stage, when the system is maintained approximately at the mean temperature between the lowest and the highest, the resistance of the variable resistor of the voltage divider is adjusted in such a way that the reference voltage is equal to the voltage output of the bridge and, therefore, the input to the amplifier is equal to zero. Then the heat sink is brought to a temperature of about 20°C and the gain of the amplifier is adjusted in such a way that the voltage going into the computer is about -9 V. It is then checked that the voltage recorded by the computer, when the heat sink is at its highest temperature, is around +9 V. All the above adjustments are conducted in the steady state. The system is brought to the required temperature by placing it on the "water box" of variable temperature controlled by the water bath controller. o _ LD THERMISTOR. SINK HEAT THE _ O FOR POINTS CALIBRATION 16. FIG. TTTTTTT ITITT [ I I I I I I I I I'T T T 09 OS Ofr 0£ 03 Oo> 33nXVa3dH3X -54- After that, the actual calibration of the thermistor can be conducted. The voltage output of the thermistor is recorded by the computer and the temperature from the thermocouple is recorded at the same time. The reference point for the thermocouples is a water-ice mixture and voltage readings are made using a voltmeter (3465B Hewlet Packard Digital Multimeter, reading with accuracy to 0.001 mV). This procedure is repeated for various temperatures in the range 19°C - 50°C. The heat sink plate is brought to the desired temperature by placing it on the "water box". Based on the points obtained, a four term polynomial is constructed as a curve of the best fit (least squares method). The function is almost linear. The calibration points are presented in Fig. 16. The polynomial is of the form: temp = 36.99+1.798 * V + 0.0036338 * V2 + 0.000995 * V3 where temp is the temperature output of the thermocouple in degrees Celsius and V is voltage output from the thermistor in volts recorded by the computer. The copper/copper-nickel thermocouples used for the calibration of the thermistors were themselves calibrated first against a Leeds and Northrup 8926 -55- General Purpose Platinum Resistance Thermometer used with a Leeds and Northrup 8078 Portable Precision Temperature Bridge. The accuracy of the thermometer was improved from 0.35°C to 0.02°C by having it calibrated by CSIRO National Measurement Laboratory. The calibration of the thermocouple was performed in a stirred water bath. An ice-water mixture was used as a reference point. Both the thermocouple and the thermometer were immersed in the water and readings of the voltage output of the thermocouple and resistance of the thermometer were taken at various temperatures in the range from 12°C to 57°C. A four term polynomial was derived as a curve of the best fit for conversion from voltage output of the thermocouple in volts into temperature in degrees Celsius. The second kind of output of the bridge containing the heat sink and guard heater thermistors is the output at the point between the resistor in the second arm of the bridge and the guard heater thermistor. The same procedure as for the heat sink thermistor was used to calibrate the guard heater thermistor. The calibration curve obtained is a three term polynomial given by: temp = 31.31 + 1.802 * V + 0.0093151 * V2 where temp is the temperature in degrees Celsius and V o THERMISTOR. HEATER GUARD THE FOR POINTS CALIBRATION 17. FIG. (Do) 3HfUVH3dW3.I -56- is voltage recorded by the computer. The calibration points are presented in Fig.17. The third kind of output from the bridge is used for controlling the tracking of the heat sink temperature by the guard heater temperature. The voltage difference, at the points where thermistors are connected to the bridge is read, and amplified by an amplifier. It is then transmitted to the guard heater controller. This is a proportional contoller which switches the heater on when the temperature of the heat sink is higher than the temperature of the guard heater. The amplifier has a variable offset adjustable by a variable resistor and, therefore, the adjustment of the tracking system is possible. The adjustment of the tracking system is done in the steady state. The heat sink and guard heater are brought to the same temperature by leaving them for a considerable time in an air-conditioned room of steady temperature. Then the offset of the amplifier is adjusted in such a way that the heater is switched off but a minimal rise in the heat sink temperature would cause it to switch on. The indication of the heater being on is that a LED connected to it lights up. Next, the performance of the tracking system is o o HEAT HEATER READABLE. THE GUARD AND o o DRAWING K> THE (2) THE TIME. HEATER MAKE OF TO C GUARD 0 lA o - 1.5 O w FUNCTION (1), CM 2; A ►-» BY h AS SINK TEST HEAT A DOWNWARDS THE o OF DURING o SHIFTED (3) IS SOURCE TEMPERATURE CURVE 18. FIG. o (Do) 3anJ,Vd3dW31 -57- checked in a situation when the temperature of the heat sink rises with time. A computer program has been written to record the outputs from the heat sink and guard heater thermistors as temperatures in degrees Celsius as functions of time. After the heat sink assembly is placed on the heat source the temperature of the heat sink begins to rise and the temperatures of the heat sink and the guard heater are recorded. It is desirable that the heater temperature follows closely the heat sink tmperature. When#after the test, the temperatures were plotted as functions of time (Fig.18, please note that the "guard heater curve" is shifted downwards by 1.5°C to make it possible to distinguish it from the "heat sink curve") it was noticed that some "hunting" takes place in the curve of heater temperature vs time. This has, however, negligible effect on the "thermal guarding" of the heat sink because of the insulating air gap between the heat sink and the guard heater plates. In order to measure the temperature of the heat source a separate bridge, containing the heat source thermistor was built. The other arm of the bridge is used as a voltage divider with a variable resistance to enable variations in the reference voltage to be made. The calibration of the heat source thermistor was conducted in the similar way as for the case of the heat o THERMISTOR. SOURCE HEAT o < THE FOR POINTS CALIBRATION 19. FIG. Till (D0) 3Hn«LVH3dW3J. > o + QC W Eh < W X Q X < ZD CD W X O > X X r? cn x w x o X o IN CD *-t X Ov o * 6 > > LD > Ln O SYSTEM. Ln CONTROL ON THE TO SUPPLY LL. zx POWER 21. FIG. CNJ uo -58- sink and guard heater thermistors, but for a higher range of temperatures. The obtained calibration curve is : temp = 42.92 + 2.886 * V + 0.12344 * V2 + 0.0061774 *V3 where temp is temperature of the heat source in degrees Celsius and V is voltage from the thermistor in volts recorded by the computer. The calibration points are presented in Fig.19. The power supply to the guard heater and the tracking control system are presented in Figs. 20 and 21. The data from a test is automatically stored in a file in the computer. During a test, readings of the voltage outputs from the heat sink, heat source and guard heater thermistors are recorded in a file at approximately every 8s, as well as the time at which each reading was taken with an accuracy 1/50 of a second. Then the voltages are converted to temperatures in degrees Celsius using the calibration functions. Next the term, rate of temperature rise of the heat sink divided by the difference of heat sink and source temperatures, is calculated for each 8 s period. The value corresponding to the mean temperature between the heat source and sink, 40°C, is chosen as a basis for -59- calculating the conductivity, since this quantity is temperature dependent. In practice, a mean value of several points around the temperature 40°C is calculated because of some scatter in the data as a function of time. Then, given the thickness of the sample, the conductivity is found. (N| U O U UJ HEAT THE if) Ci BETWEEN PLATE. ALIGNMENT OF SOURCE HEAT THE DETERMINATION AND 22. FIG. 6. PERFORMANCE OF THE TRANSIENT CONDUCTIVITY TESTER The next step in the development of the transient conductivity tester was to check the contact resistance between the heat sink and source plates. This was done in the following way. Resistances of layers of fabrics were measured and plotted as a function of thickness and a linear regression line was calculated. (Fig. 22). Theoretically, the regression line should pass through the origin. If this does not happen, it means that there is some displacement between the heat sink plate and the heat source plate even when micrometers are set to zero. This can happen when the two plates are not perfectly flat or when the distances of temperature sensors from the surfaces of the plates are not negligible. Another possible reason could be that heat transfer through the fabric takes place not only by conduction but also by radiation, which is not proportional to the distance. The displacement obtained here is equal to -0.03 mm and therefore is negligible compared to fabric thicknesses, so that the effect of contact resistance may be neglected for calculations of the thermal conductivity. The data from the contact resistance test is given in Table 1. Before each test, fabrics were conditioned in the standard atmosphere (21°C, 65 % relative humidity) and thickness was measured before the test according to -61- Australian Standard AS 1587-1973 at a pressure 10 Pa. Fabrics which were to be tested in multilayers were conditioned in that state and the thickness measurement was taken of the multilayer assembly, as it differs from the sum of thicknesses of separate layers, due to the pressure exerted by one layer resting upon another. Ten separate tests were made for each sample arrangement and the mean value was calculated. The scatter about the regression line is very small with the correlation coefficient being 0.9998. The repeatability of the obtained values is good for a typical fabric thickness. An example is given in Table 2. However, the scatter increases when samples are very thin or very thick (example in Table 3 A and B). This effect can be attributed to the fact that the optimum accuracy of data recording is obtained for a certain rate of change of temperature of the heat sink, which is dependent on the fabric thickness (in the conditioned state), or that slight maladjustment of the control of the tracking of heat sink temperature by the guard heater may become pronounced in situations when very small or very high output of the heater is required. Also, with very small thicknesses, small -62- inaccuracies in the adjustment of the distance between the hot and cold plates of the apparatus, both in the guarded hot plate and transient conductivity test, can cause a large error in the measured thermal resistance. Then the performance of the transient tester was checked against a steady state method. A series of tests was conducted in order to compare the values of the effective thermal conductivity obtained by the transient method and with a guarded hot plate with a controlled cold plate arrangement which maintains a constant temperature gradient across the sample. This apparatus was developed in the C.S.I.R.O. Division of Textile Physics laboratory. The gradient across the sample was chosen such that it reproduced the gradient used in transient method conductivity tests. The tests were performed on conditioned fabrics. Thickness measurements were carried out before tests and the same thickness value was used for both tests. The results are presented in Table 4. The samples are described in Tables 5, 6 and 7 with the exception of cu5 and w4, which are commercial fabrics and no detailed data is available for them. All the rest of the fabrics are chosen from a "library" of fabrics of known properties. Generally good agreement was obtained except for the case when the fabric thickness was very small (cu5, thickness 0.79 mm). This can be due to the reasons -63- discussed before, when commenting on the scatter in the thermal resistance results for very thin or very thick fabrics. In the case of w4, with a four layer arrangement, the measured conductivity was larger than for a one layer assembly because of the compressed state of fabrics in multilayer assemblies. In each fibre group (wool, polypropylene, cotton, acrylic) the conductivity of the denser fabrics (w33, p21, c45, a9) was higher than for the less dense fabrics (w36, pl9, c38, al), because fibre is more conductive than air. Generally, for the "library" fabrics, the values of conductivity measured by the steady state method are slightly larger than these measured by the transient method (except for the cotton sample c45). This effect can be attributed to some inaccuracy in the adjustment of the hot and cold plate spacing in the case of one or both methods, or to some calibration inaccuracies (for instance there may be a slight error in the calibration of temperature sensors in the case of both methods or in the adjustment of the tracking of the temperature of the heat sink by the guard in the case of the transient method). -64- Table 1 Resistance of layers of fabrics as a function of thickness. fabric no. of thickness mean code layers resistance mm (m2.K)/W 1 0.79 0.0205 2 1.39 0.0355 cu5 3 2.02 0.0450 4 2.66 0.0650 5 3.31 0.0800 1 3.38 0.0850 w4 2 6.09 0.1530 3 8.66 0.2100 4 11.16 0.2740 cu5 - cotton, single jersey w4 wool melton -65- Table 2 Experimental data from 10 tests of resistance of four layer cotton fabric assembly, cu5, thickness = 2.66 mm test no. resistance relative difference from mean value (m2.K)/W % 1 0.065 0.0 2 0.065 0.0 3 0.065 0.0 4 0.065 0.0 5 0.065 0.0 6 0.064 -1.5 7 0.065 0.0 8 0.066 + 1.5 9 0.064 -1.5 10 0.064 -1.5 Mean 0.065 -66- Table 3 A Experimental data from 10 tests of resistance of four layer wool fabric assembly, w4, thickness = 11.16 mm test no resistance relative difference from mean value (m .K)/W 0.255 -6.9 0.287 +4.7 0.287 +4.7 0.287 +4.7 0.287 +4.7 0.242 -11.7 0.265 -3.3 0.265 -3.3 0.276 +0.7 0.287 +4.7 Mean 0.274 -67- Table 3 B Experimental data from 10 tests of resistance of thin cotton fabric, cu5, thickness = 0.79 mm test no. resistance relative difference from mean value (m2.K)/W % 1 0.020 -2.4 2 0.020 -2.4 3 0.021 +2.4 4 0.022 + 7.3 5 0.020 -2.4 6 0.022 + 7.3 7 0.021 +2.4 8 0.019 -7.3 9 0.020 -2.4 10 0.020 -2.4 Mean 0.0205 -68- Table 4 Comparison of thermal conductivity results from tests using steady-state and transient methods. steady-state guarded hot transient method test plate test fabric thick. resist. conduct. resist. conduct. rel. differen code of resistance compared to steady state value mm (m2.K)/W mW/(m.K) (m2.K)/W mW/(m.K) % cu5 0.79 0.017 46.5 0.021 57.6 +25.5 w4 308 0.089 58.0 0.085 59.8 -4.5 w4,4 layers 11.16 0.287 38.9 0.274 40.7 -4.5 w56 2.56 0.065 40.6 0.066 58.6 +4.8 2.86 0.069 41.4 0.073 39.2 +5-7 p19 2.35 0.046 51.1 0.053 44-3 + 15-2 p21 2.45 0.047 52.1 0.051 48.1 +8.5 LT\ 00 c38 2.33 0.045 • 0.051 45.8 + 13-3 c45 2.27 0.058 59-7 0.057 61.2 -2.6 a1 2.28 0.052 43.8 0.056 40.5 +7.8 a9 2.25 0.046 48.9 0.047 47-9 +2.2 -69- 7. DESCRIPTION OF SAMPLES AND THEIR PREPARATION FOR TESTING Samples were chosen from a "library" of fabrics of known properties. The list of samples used for testing and details of their properties are given in Tables 5, 6 and 7. The vapour resistance (a measure of the water vapour permeability of a fabric expressed in terms of the thickness of a layer of still air which would have an equivalent permeability) was tested by the control dish method ( Canadian Standard Textile Test Method, Method 49-1977). Mass per unit area was tested according to Australian Standard AS 1587-1973, thickness according to Australian Standard AS 1587-1973, using a foot area 2 of 50 cm and a head pressure of 10 Pa. The thickness was measured when fabrics were in the conditioned state and this was the distance at which the heat sink and heat source plates were kept for the experiments for the whole range of regain. Though such an approach introduces some error into the value of measured conductivity (as fabrics generally reduce in thickness when wet <52>), it was convenient ini terms of experimental procedure and for further theoretical analysis. Velocity of wicking of water was tested according to German Standard DIN 53 924. The test was carried out with distilled water containing 0.1 g/1 wetting agent, Lissapol TNXP, a non-ionic alkyl aryl -70- polyether alcohol manufactured by ICI. The test apparatus consists of a base plate with levelling screws, a dish containing water, a holder for samples and measuring rods with millimeter divisions attached in the vertical position to the holder. Samples are pieces of fabric of 250 mm length and 30 mm width taken in both warp and weft direction. They are attached to the holder at one end and immersed in the water at the other end, so that 15 mm is under water. At the moment of immersion, the rising height of the water is observed as a function of time. The mean of wicking rate obtained in 5 tests is calculated. The desired water content was obtained by drying wetted specimens. Distilled water, with the addition of the wetting agent Lissapol in the amount of 0.1 g/l, was used. Approximately 10 minutes was allowed after drying for the specimen to reach uniform moisture distribution. Tests were conducted for the range of regains 0 % - 300 % . The regain was determined before the test by weighing the sample before the test. It was calculated according to the expression: weight of wet sample - weight of dry sample regain weight of dry sample -71- The weight of the dry sample was determined after drying to constant mass in an oven at 105°C according to Australian Standard AS 2001.2.2 - 1978. In the case of polypropylene a temperature 50°C was used. After each test, the water which condensed on the heat sink during the test was blotted off with a paper tissue and the difference in weight of the tissue after and before the operation was measured. That gave the weight of water which condensed on the heat sink during the conductivity test. This amount is dependent on the regain and, for instance, for polypropylene fabric pl9, with a regain based on weight before the test of 228 %, the amount of water condensed on the sink was 2.33 g, which is 6.3 % of the initial water content of the sample (oven-dry mass of the sample is 16.31 g); for regain 70 % the amount of evaporated water was 1.87 g (this is 16.4 % of the initial water content); and for regain 17 % it was 1.47 g (53.0 % of the initial water content). Of course the rate of condensation is not constant during the test mainly because of the rising temperature of the heat sink. -72- The samples are of four fibre types having different water sorption properties: porous acrylic, polypropylene, wool and cotton. Porous acrylic is strongly wicking (as seen from Table 7, it has the highest velocity of soaking of water of all fibre types) and absorbs water very well. However, water is not absorbed in the polymer (the polymer absorbs less than 6 % at saturation, Table 8) but imbibed in micropores of the fibre by capillary action. After centrifuging the regain of porous acrylic is 30 % - 40 % <14,54> and no swelling occurs as in the case of wool or cotton. Polypropylene is non-absorbing (0.1 % regain at 90 % rh) and does not wick pure distilled water in the test for wicking rate according to German Standard DIN 53 924. However the wicking rate of water with Lissapol was quite high (higher than cotton, Table 7). Wool absorbs moisture very well (35 % regain at saturation) and does not wick. Because of its moisture sorption properties wool has a very high heat of wetting which causes a "buffering effect" in clothing. Cotton also absorbs moisture well and wicks water rather well. -73- The fabrics were of similar thickness. In each fibre type group, a fabric of low packing factor (al, pl9, w36, c38) and one of high packing factor value (a9, p21, w33, c45) were chosen to enable investigation of the influence of packing factor on the conductivity of wet fabrics . In each fibre type group, a brushed fabric was also tested. The properties of brushed fabrics are presented in Tables 9 and 10. These properties were derived based on the assumption <56> that a fabric consists of three layers: the core which is incompressible over the pressure range 200-500000 Pa and two outer, compressible layers. The values in Tables 9 and 10 are only approximate as it was assumed that knitted fabrics behave in a similar way to the woven ones when compressed and that the distribution of fibres in the outer layers of fabrics is random. It was possible to obtain separate data for the two outer layers (the brushed one and the non-brushed one) by first doing measurements on the non-brushed version of the fabric and then on the brushed version. The data in Tables 9 and 10 apply to conditioned fabrics only and properties of the structure most probably change when fabrics contain water. The pressures applied for measurements of the core thickness were 200 Pa and 5000 Pa. All fabrics were of the same construction: knitted interlock. -74- Table 5 Fibre and yarn parameters. fibre parameters yarn parameters fabric fibre type diameter tex twist diameter code (i .e. pm g/km) turns/m mm al porous 19.6 25 502 0.26 a9 acrylic 19.6 25 502 0.26 a9B 19.6 25 502 pl9 poly 19.5 18 643 0.18 p21 propylene 19.5 25 540 0.22 p2 IB 19.5 25 540 w33 wool 20.6 30 626 0.16 w36 20.6 18 852 0.14 w33B 20.6 30 626 c38 cotton 13.0 24 671 0.21 c45 13.0 30 874 0.15 c45B 13.0 30 874 -75- Table 6 Fabric parameters fabric cover thickness mass per unit area packing construction code factor factor at standard oven conditions dried 2 mm g/ra a1 11.1 2.28 275 261 0.102 a9 14.1 2.25 342 328 0.127 knitted a9B 14.1 2.30 339 318 0.123 interlock, P19 12.6 2.35 279 278 0.130 letter B p21 14.1 2.45 326 326 0.146 refers to p21 B 14.1 2.59 327 325 0.139 brushed w33 14-1 2.86 363 297 0.085 fabrics w36 14.1 2.56 279 237 0.074 w53B 14.1 3.62 357 303 0.067 c38 11.1 2.33 264 237 0.068 c45 14.1 2.27 376 342 0.099 c45B 14.1 2.34 388 341 0.100 -76- Table 7 Physical properties of fabrics fabric water wicking rate,clistance after code vapour 10s|30s|60s|300s 10s|30s|60s|300s resistance warp direction weft direction mm mr al 3.53 29 48 63 115 25 39 49 81 a9 4.05 30 49 67 119 27 41 55 97 a9B 3.84 26 49 66 118 25 52 58 99 pl9 3.75 16 28 37 64 15 25 34 57 p21 3.89 14 26 35 57 14 22 30 45 p2 IB 3.97 16 25 34 50 12 21 29 44 w33 4.01 4 7 10 16 2 4 6 15 w36 3.63 4 8 10 18 3 5 7 12 w33B 4.77 3 6 9 15 2 3 5 11 c38 2.99 6 11 15 27 7 14 20 37 c45 3.37 3 6 9 18 4 7 11 19 c45B 3.44 3 5 9 18 2 4 7 14 -77- Table 8 Fibre properties <7,53>54,55> polyester acrylic polyprop. wool cotton specific gravity 1.38 1.17 0.91 1.32 1.54 thermal conductivity, 140.0 200.0 170.0 190.0 460.0 mW/(m.K) regain at '50% rh, % 0.18 0.8 0.0 7-84 3.8 50% rh, % 0.3 1-4 0.04 11.50 5-5 90% rh, % 0.55 3-5 0.1 22.2 12.8 saturation, % 6.0 35.0 25-0 heat of wetting, negligible 60.0 17.0 kJ/kg specific heat, 1 .88 1 *51 2.18 1.36 1 -34 kj/(kg.K) -78- Table 9 Thicknesses of the layers in brushed fabrics. fabric total thickness of thickness of thickness of code thick. outer core brushed non-brushed layer layer as percen. as percen. as percen. of total of total of total thickness thickness thickness mm mm % mm % mm % a9B 2.50 0.45 19.6 1.33 57.8 0.52 22.6 p21 B 2.59 0.45 17.4 1.57 60.6 0.57 22.0 C\J w33B 3-62 0.68 18.8 1.62 44.8 36.4 c45B 2.34 0.40 17.1 1.52 65-0 0.42 17.9 -79- Table 10 Mass and packing factor of layers in brushed fabrics. fabric total mass per unit area packing factor code mass as percentage of total per mass per unit area nni t area outer core brushed outer core brushed non- layer non- layer brushed brushed layer layer g/m2 g/m2 g/m2 g/m2 a9B 339 21 295 23 0.040 0.190 0.039 p21B 327 16 290 21 0.039 0.203 0.040 w33B 357 40 265 52 0.045 0.124 0.030 c45B 388 27 304 57 0.044 0.130 0.088 REGAIN. OF FUNCTION ((X-Ui)/Mui) AiLIAIiLDfidNOD 'IVWHSHJ, 3AII.03333 REGAIN. OF FUNCTION < Ol-ui)/MU1) AiLIAIiLDnQNOD GVWaSHJ, 3AIJ.03333 REGAIN. OF FUNCTION WOOL FABRICS FOUR OF . o POLYPROPYLENE, > w OC J < cl ACRYLIC, CONDUCTIVITIES ui O' O=> >•CL J E-. o o o o CL CL 2 U POROUS THERMAL TYPES, EFFECTIVE FIBRE OF COTTON. DIFFERENT OF COMPARISON AND 27. FIG. 0S2 00S OSt 001 OS 0 8. RESULTS AND DISCUSSION The results of tests of effective thermal conductivity as a function of water regain on porous acrylic (al)# polypropylene (pl9), wool (w36) and cotton (c38) fabrics of low packing factors are presented in Figs. 23, 24, 25 and 26. In order to compare different fibre types the results are also presented on a common graph in Fig.27. The conductivity of moist fabrics depends on the way in which water is contained in the fabric, eg. absorbed into the fibre polymer, retained in micropores within the fibre structure or as free water between fibres and yarns. Polypropylene, which does not absorb water, shows a rapid increase in conductivity as soon as water is present and with further increase in water content the conductivity increases slowly up to 200 % regain. In the range of regains 200 % - 300 % the conductivity rise is steeper. For porous acrylic, the conductivity rose steeply with regain from oven dry to saturation regain and then increased slowly with further increase in water content. The saturation regain is about 30% when the fabric is centrifuged. For the tests the required water content was obtained by conditioning the fabrics from the wet -81- side, so 30 % regain appears to be the relevant saturation value and not 6 % which is obtained by conditioning fabrics at 95 % rh. However, attempts have been made to obtain the required range of regains by conditioning from the dry side. For regains 0 % - 6 % this was done by conditioning the fabrics at certain air humidities. To obtain regains 0 % - 300 % the fabric was placed on a wet surface and then left for a certain time in order to get uniform distribution of moisture. However, the values of measured conductivity as a function of regain for samples conditioned from the dry side were the same as for samples conditioned from the wet side. The reason is that as soon as water comes in contact with the fabric it is transported by wicking into the micropores of the fibres to be absorbed there. Between the saturation regain and 200 %, the conductivity of porous acrylic rises slowly with increasing regain and, further, a slightly steeper increase takes place for regains above 200 %. The wool fabric showed a low conductivity, almost independent of regain in the region between oven dry and approximately 15%. In this region, water is strongly bound to the fibre <57> which is observed also when measuring electrical conductivity of wool fibres as a function of regain. Between 15 % regain and 33 % o o a9, FABRIC, ACRYLIC POROUS A OF CONDUCTIVITY REGAIN. OF THERMAL FUNCTION A EFFECTIVE AS 28. FIG . osz: 003 osr ooi os o (OTUO/M01) AJ.I AIiLDOGNOO 1VWM3H.I 3AII03333 REGAIN. OF FUNCTION OF FUNCTION OF FUNCTION <(>I-ui)/mui) AJ.IAIlLDHONOD TVWM3HJ. 3AIJ.D3333 -82- (saturation regain) the conductivity rose sharply to a conductivity value almost double that of dry fabric. From saturation regain to 200 % the conductivity changes slowly with water content. From 200 % to 300 % regain, the rise of conductivity with water content is steeper. The behaviour of cotton is similar to that of wool. The low conductivity region is for regains 0 % - 10 %. Between 10 % and 25 % (saturation regain) the conductivity rises steeply and then levels off. A further rise takes place in the region of regains 200 % - 300 %. Wool had the lowest thermal conductivity of the four fibre types for the range of regains 0 % - 200 %. However, it is the performance of fibres in the region 0 % - 100 % regain that is really important, as regains of clothing even after heavy exercise do not exceed 100 %. A further series of tests has been performed on porous acrylic (a9), polypropylene (p21), wool (w33) and cotton (c45) fabrics of high packing factors. The results are presented in Figs. 28, 29, 30 and 31. The shape of the curves remained essentially the same as for the low packing factor samples and the only effect of the increased packing factor is the increased FABRIC POLYESTER/COTTON A OF . bu8 CONDUCTIVITY FACE, ONE THERMAL ON EFFECTIVE BRUSHED 32. FIG. OSl ( OT«i> /M«> AJ,IAIJ.DnaNOD 1VWH3HJ. 3AIJ.03333 -83- conductivity throughout the range of regains studied. In the case of dry fabrics, the increased conductivity is caused by the increased ratio of well conducting fibre to air, which has insulating properties, in the fibre-air mixture. In the case of wet fabrics, fabrics of higher packing factors contained more water for the same regain and this may be the cause of the increase in the conductivity for fabrics of higher packing factor. Next the influence of fabric surface structure on the effective thermal conductivity as a function of regain was investigated by testing fabrics brushed at one face. The first series of tests was conducted on a brushed polyester/cotton fabric, interlock knit, code bu8. The ratio of polyester to cotton is 65/35. The thickness is 3.87 mm measured under a pressure of 10 Pa and the mass 2 per unit area is 227 g/m . The thickness of the incompressible core is 2.23 mm and the total thickness of the outer layers is 1.64 mm. Unfortunately separate data for the brushed and non-brushed layers could not be obtained because a non-brushed version of bu8 was not available. The properties of cotton and polyester are listed in Table 8. The results are presented in Fig.32 for both cases when the brushed side rests against the heat sink and when it rests against the heat source. -84- The effective thermal conductivity is evidently higher for the brushed fabric with the brushed face at the heat sink than with the brushed face against the heat source. The explanation for this is that, with the brushed side against the heat source and the smooth side against the heat sink, the insulating layer of air with the small amount of fibre (brushed layer) and of water attached to it is placed against the hot face. This can cause slowing down of the evaporation process from the hot face and, therefore, the measured conductivity is less than in the case when the smooth face is placed against the heat source. With the smooth face against the heat source most of the fibre, and therefore water, is concentrated at the hot face and the heat from the heat source is easily conducted through the wet fabric and used to evaporate water from the hot face. Also, because of the low concentration of fibre at the heat sink face (brushed side), the water vapour diffuses more easily to condense on the heat sink. The difference in conductivity of the two arrangements (brushed side against the heat sink and brushed side against heat source) is large because of the difference in fibre concentration between the smooth face and the brushed U-l O NO FABRIC ACRYLIC O O CM POROUS A OF if (2—) < U w cc a9B. CONDUCTIVITY FACE, o o ONE THERMAL ON BRUSHED EFFECTIVE 33. FIG. o OSS 003 OSI 001 OS 0 < (M-rot/MUl) AilAIiDnaNOO 1VMM3H1 3AIID3333 o FABRIC POLYPROPYLENE A OF p21B. CONDUCTIVITY FACE, ONE THERMAL ON EFFECTIVE BRUSHED 34. FIG. osz ooz: ost oo r os o ( <»•«!) /M<“ > AXIAIiDnaNOD 3VWH3HJ, 3AIJ,33333 o FABRIC WOOL A OF w33B. CONDUCTIVITY FACE, ONE THERMAL ON EFFECTIVE BRUSHED 35. FIG. 00Z os r oo r OS 0 ( (X /Mui) AiiAiionaNoo 1VWH3HJ, 3AII.D3333 o o NO FABRIC COTTON A OF c45B. CONDUCTIVITY FACE, ONE THERMAL ON EFFECTIVE BRUSHED 36. FIG. ( (M-ui)/mui) AlLIAIlLDCKINOD 3YWH3HJ, 3AIJ03333 -85- face in the fabric. Also, the difference between the thicknesses of the two sides seems to be large, although as mentioned before, no quantitative data is available to show the difference between the brushed side and the smooth side. Similar tests were conducted on the brushed library fabrics: a9B, p21B, w33B, c45B, the unbrushed versions of which (a9, p21, w33, c45) had already been tested. The results are presented in Figs. 33, 34, 35, 36. In the case of brushed library fabrics the difference between the two arrangements, brushed side against the heat sink and against the heat source, is not as large as in the case of bu8 because they are "less brushed" than bu8. As seen from Table 9 the difference between the thicknesss of the brushed and smooth faces for the acrylic (a9B) and the cotton (c45B) fabrics is very small. The largest difference between the two faces occurs for the wool fabric (w33B). However, the effect of the arrangement (brushed side at the heat sink or at the heat source) can be seen in all the presented graphs. No difference occurs in the regions of low regain and the conductivity of the dry or conditioned fabric is the same for both arrangements. Compared with the non-brushed version of the same fabric, the conductivity for dry or conditioned fabric is lower because of the lower packing factor. The difference in o o KNIT DOUBLE w < PLATED, in w A a o OF . < cc o J bu7 o o FABRIC, CONDUCTIVITY THERMAL EFFECTIVE WOOL/POLYPROPYLENE 37. FIG. oss oos as t oot os o (ornn/Mo) AiiAixonaNOD 3vwh3h.i 3AIX03333 -86- conductivity in the two arrangements is comparatively small in the case of the cotton fabric (c45B), because of the small difference between the brushed and the non-brushed side and probably because wet cotton fibres do not maintain their dry state brushed structure. The difference between the faces is also small for the acrylic fabric which results in a small difference in conductivities for the two arrangements. The difference in conductivities for the two arrangements is largest for the wool fabric because of the large differences in thickness of the two faces and also because the brushed layer has a very low packing factor (Table 10). Wool also maintains the brushed structure when wet. The difference disappears in the case of all fibre types for high regains, when the brushed structure is no longer maintained. Next, tests have been performed on a plated, double knit modified pique wool/polypropylene fabric, code bu7. The thickness of the fabric is 2.75 mm, mass per unit area 298 g/m . The thermal conductivity has been measured as a function of regain for two arrangements: wool layer against the heat sink and polypropylene layer against the heat sink. The results are presented in Fig. 37. Except for very low regains (up to about 20 %) and very high regains (above 200 %) the conductivity for the arrangement with the polypropylene layer against the -87- heat source is higher than with wool layer against the heat source. This effect is due to the fact that with the wool against the heat source there is less water available for evaporation at the hot face than when polypropylene rests against the heat source. For regains up to 10 %, the conductivity is approximately constant regardless of water content and arrangement, that is the fabric behaves like a wool fabric. Most probably, in the case of the wool layer at the heat source, the plated fabric behaves very similarly to a wool fabric because evaporation takes place from the hot face. In the case when polypropylene rests on the heat source the behaviour described above is probably due to the fact that, for this low water content, even if water evaporates easily from the hot face, it becomes partly absorbed by the upper wool layer and only part of it condenses on the heat sink. However, the conductivity does not remain constant up to 15 % regain as in the case of pure wool fabrics because, above 10 % regain, the wool layer with the vapour absorbed from the polypropylene layer stops absorbing any more vapour (the wool layer probably reaches then 15 % regain). To make sure that the measured conductivity was not affected by the fact that most of the water might have been gathered -88- during the conditioning period in the lower layer, the fabrics were tested after they were conditioned both with the polypropylene face down and up. No difference in conductivity due to the method of conditioning was detected . From these results a conclusion can be drawn which may appear to be in contrast with what has been found by other researchers. It has been maintained so far that double layer fabrics made of a layer of absorbent fabric and another layer of non-absorbent wicking fabric are most suitable clothing for active sportswear, when they are worn with the non-absorbent layer next to the skin. This is because, when sweat is generated, it is wicked away by the non-absorbent layer and stored in the absorbent layer, leaving the non-absorbent layer, and thus the skin, dry. However, the results of the above experiments show that when such clothing gets thoroughly wet, for instance from rain or very heavy perspiration, it gives better insulation if worn with the absorbent layer next to the skin. In such a case, an absorbent layer feels "drier" than a non-absorbent layer, in which all the water present is "free" water and therefore feels "wet" as well as cold, because of rapid evaporation. This does not contradict the fact that a double layer fabric is most comfortable if worn with the non-absorbent layer next to the skin, if moderate -89- exercise is performed and a moderate rate of sweating takes place, but shows that this arrangement is not the most comfortable in all situations when the garment is meant for active outdoor sports. In order to compare the behaviour of fabrics with that of another porous material, tests were also performed on a polyurethane foam. The thickness of the foam, at a pressure of 10 Pa is 3.3 mm, mass per unit 2 area, 49 g/m . The properties of polyurethane are as follows <55>: specific gravity: 1.31 thermal conductivity, mW/(m.K): 146.0 regain at 65% rh, % : 1.2 heat of wetting: negligible specific heat, kj/(kg.K): 1.89 The above properties are very similar to those of non-absorbent textile fibres, but the geometrical structure of the material is very different from that of textile fabrics. It does not consist of fibres but has the form of a sponge. The distribution of the solid fraction is random, which is different from fabrics where fibres are spun in yarns and, therefore, are oriented in certain directions. Its mass per unit area is very low and, therefore, its packing factor is very low (0.011 in this case compared with 0.1, which is o o in FOAM. POLYURETHANE OF CONDUCTIVITY THERMAL EFFECTIVE 38. FIG. 0S£ ( (M-ui)/MU1) AI. IA Ilona NOD lYWHSHI, 3AIJ.D3333 -90- approximately typical of a knitted textile fabric). It can hold much more water without dripping and, therefore, conductivity tests were performed for a range of regain 0 % - 1600 %. The results are presented in Fig.38. As can be seen, the conductivity rises rather steeply in the range of regain approximately 0 % - 500 % and then increases slowly with further increase in water content. It can, therefore, be concluded that the shape of the conductivity curve, as a function of regain is of the same form as in the case of non-absorbent textile fabrics, that is, it consists of two distinct parts. The first one takes place, when the conductivity rises steeply with increasing regain and the second one, after certain regain has been reached, when the increase in the conductivity is slow. (In the case of non-absorbent fabrics, another region can be distinguished, where, for regains higher than approximately 200 %, the conductivity starts to rise steeply again, but in the case of the foam the tests were not performed at high enough regains for this behaviour to be observed). The conductivity value of the conditioned foam is 43.4 mW/(m.K). -91- 9. ANALYSIS OF RESULTS The results of tests on the effective thermal conductivity of textile fabrics and foam indicate that the value of conductivity is dependent on regain, but the function of conductivity vs regain is not a linear one. Certain characteristic regions can be distinguished in the conductivity curve. The existence of these regions depends on the sorption properties of the material but not on its geometrical structure. The following analysis of the process of heat and mass transfer during the conductivity tests by the transient method explains the characteristic shape of the conductivity curves as a function of regain for porous materials. During a test, evaporation of water from the sample takes place and the evaporated water condenses continuously on the heat sink, raising its temperature. This can be considered as the first mode of heat transfer by the wet sample. The other modes of heat transfer are by conduction through the mixture of solid fraction (fibre or foam), air and water of which the wet -92- sample consists and by radiation between the heat source, fibres and the heat sink. All these processes interact but for the purpose of simplicity they will be treated separately in this analysis. According to Stuart and Holcombe <59> the contribution of infra-red radiation in fibrous assemblies used for insulating is a significant component in the heat transfer process, even when the temperature difference across the assembly is low. A mathematical model <59> has been developed from which the heat transfer behaviour of fibrous beds may be predicted as a function of conduction and radiation both through the structure and from fibre to fibre. At first the equivalent fibre diameter of the fibrous bed is established, in the following way. The insulating bed is compressed a little at a time and the thermal conductivity is measured at each thickness <60> and plotted as a function of packing factor. At the same time, by using suitable computer programs (Appendix 2 in <61>) it is possible to plot the theoretical, overall (i.e. including conduction and radiation) thermal conductivity against packing factor for various fibre diameters. The experimentally determined plot is compared with the theoretical ones and the equivalent fibre diameter of the bed is established (in practice, even for beds with randomly oriented fibres, for which o o LO U1 E-> tn w E-i > E- t—( > t-i U a 2 o O o u o a 2 t-4 CX r> Q X 2 n tn 2 n < < O u W X X o H 2 »—i FOAM. X o o u. LO E-* < W X < POLYURETHANE E-i O 2 O cn m O t-t u. o oos r ooot ( jUJ/M) xmi J.V3H -93- the model was primarily developed, the equivalent diameter varies from the actual one <62>) . To obtain the equivalent diameter in this way, means that the insulating bed, regardless of its actual geometrical structure, behaves as a fibrous bed of this diameter as far as heat transfer by radiation and conduction is concerned. Such an approach has been undertaken in order to analyse the data obtained from the transient conductivity tests. The first step was to partition the heat flux entering the heat sink into two parts. The total flux was expressed as the sum of radiation flux and the rest (i.e. conductive heat flux and the heat flux from the process of condensation of water on the surface of the heat sink). POLYURETHANE FOAM At first, this approach was used to analyse data obtained for polyurethane foam, because the experimental apparatus available for the determination of the equivalent fibre diameter is most suitable for samples of low packing factor.The total heat flux to the heat sink, calculated for each effective conductivity test, is presented in Fig.39, as a function of regain. The shape of the curve is, naturally, the same as that for 1 5 0 0 CONDUCTIVITY CONDUCTIVITY DURING 00 1 ° RADIATION <*) FROM FOAM. regain SINK HEAT 500 INTO POLYURETHANE ON FLUX TESTS HEAT 40. FIG. 001 ( Z“J/M) xmi iLV3H -94- the effective conductivity curve. As described above, the experimental procedure to determine the equivalent fibre diameter for radiation was followed using an insulating bed of polyurethane foam of initial thickness 50 mm and compressing it 5 mm at a time. The equivalent fibre diameter obtained was 40 urn. By using a suitable computer program <61>, the radiation component of the heat flux was determined for each conductivity test and presented in Fig. 40, as a function of regain. As expected, the magnitude of the radiation heat flux diminishes with regain and, thus, with increasing packing factor. (The water in the sample was assumed to have similar properties to fibre, as far as infra-red radiation was concerned, and was assumed to form uniform layers on the surface of the solid. Thus the equivalent fibre diameter increased with increasing regain.) However, it is not possible to obtain a value of "conductivity" from the radiation process, firstly because the radiation process is not directly dependent on the thickness of the sample, and also, because the radiation flux varies with position across the bed <61>. The radiation flux presented in Fig. 40 is the flux measured at the plane of the heat sink. Subtracting the radiation heat flux from the total heat flux at the heat sink, the heat flux from the processes of evaporation of water, diffusion of water o o LD FOAM. VAPOUR WATER POLYURETHANE OF ON o o o TESTS CONDENSATION o'? 2 I—I FROM o< w CONDUCTIVITY a: SINK HEAT DURING O O LO INTO FLUX CONDUCTION HEAT AND 41. FIG. o 0051 ooor (Zu»/M) xmj J.V3H o o LO 2 O m Fh uj u t- >* t-H t-t u Q 2 O O o U o U 2 I—I a: 0 v: 2 HH 01 2 ►H E-* < < ID W W X OC 2 0 Q M FOAM. CD 01 2 CD U L0 Q 2 O U DC W E- < 2 POLYURETHANE CM U M O (gUi/6) aalVM dO ilNHOWY -95- vapour and condensation, and conduction is obtained. This is presented in Fig.41. This heat flux has to be divided in two parts, the heat flux from conduction, and the heat flux from the evaporation and condensation. The first step is to calculate the heat transfer by the evaporation and condensation process during a test. The amount of water condensed on the heat sink during the test can be calculated as described in the Chapter 7, "Description of Samples and Their Preparation for Testing". This gives the total amount of water condensed on the heat sink during the test (that is during approximately 360 s). Such a calculation has been done for each conductivity test, and the results are presented in Fig.42. (On the graph the water 2 condensed has been calculated in grams per m and presented as a function of regain.) As can be seen, the amount of water condensed rises steeply in the range of regain approximately 0-600 %, and then remains almost constant with further increase of regain. The shape of this curve is therefore very similar to the effective conductivity curve. Next, the total heat gain of the heat sink during the test is calculated from the difference in temperature of the sink at the beginning and end of the test. It is now assumed that the ratio of the heat transferred to the o o DURING VAPOUR WATER o OF o FOAM. CONDENSATION w DC FROM POLYURETHANE SINK ON HEAT TESTS INTO FLUX HEAT CONDUCTIVITY 43. FIG. ooo r <2“/M) xmi J.V3H TESTS CONDUCTIVITY DURING CONDUCTION FROM SINK FOAM. HEAT INTO FLUX POLYURETHANE HEAT ON 4 4 . FIG. 000 1 (z^/M) xmj J.V3H rS x cn in X w o u X o x < DU 2 X o X t-t o Eh X CJ X Q w 2 Eh o in u M X o X Eh X x« w X :r> u Q tn >• X Eh o HH X > X n E- Q u W Eh Q < 2 X O X> U u l-J W < X u Eh >H Eh FOAM. X > o M X 2 u O :=> cn Q M 2 X o < u X X Q o 2 u < POLYURETHANE in Ma X osz ( <>i-Ui)/MUJ) AilAIiDnaNOD TVWM3HJi -96- sink by condensation of water vapour on the sink to the total amount of heat transferred to the sink is constant during the test (this means that the amount of heat transported by the evaporation/condensation process in the sample is assumed to be proportional to the rate of change of the temperature of the heat sink). We thus assume that the total heat flux less the radiation heat flux can be divided into two parts: heat flux due to the heat transfer by conduction through the sample and heat flux due to the evaporation/condensation process. The heat flux due to the evaporation/condensation process is presented in Fig. 43. The heat flux from the conduction process, as the total heat flux less the radiation heat flux less the heat flux from condensation of water vapour on the heat sink is presented in Fig. 44. Heat flux from the conduction process is not constant across the sample <61>, and varies with the position through the sample. However, it is useful to calculate an expression called here "the conductivity due to the conduction process" . It will be represented here by a symbol {K}. It is not exactly equal to the actual, true conductivity of the sample. It is obtained by dividing the heat flux from conduction by the temperature difference across the sample and multiplying it by the thickness of the sample. {k} obtained in this way for the polypropylene foam is presented in Fig. 45. It is FIG.46. MODEL OF POROUS MATERIAL FOR THE PURPOSE OF CALCULATING THERMAL CONDUCTIVITY. F = SOLID, W = WATER, A = AIR, R = VOLUMETRIC RATIO OF SOLID ORIENTED PARALLEL TO DIRECTION OF HEAT FLOW TO THE TOTAL AMOUNT OF SOLID. -97- not a unique property of the sample (i.e. it is not invariant with the position in the sample), as is, for instance, the conductivity calculated from Schuhmeister's formula <63>. However, it is instructive to compare the {K} obtained with Schuhmeister's conductivity. In order to do that, a simple geometrical model, based on Schuhmeister‘s theory <63> but including water as a third component besides air and fibre, has been constructed to predict the conductivity of the foam containing water. It assumes that the solid component is oriented either parallel or perpendicular to the direction of the heat flow and that water is adsorbed on its surface. Because the solid component in the foam is randomly oriented, it can be assumed that one third of the total volume of the solid is oriented parallel to the direction of the heat flow and two thirds perpendicular. Because water is adsorbed on the surface of the foam, it is also assumed that one third of its total volume is in the direction of the heat flow and the rest perpendicular. The model is illustrated in Fig. 46. -98- Accord ing to the model, the expression for the conductivity parallel to the direction of the heat flow is given by: k v,. + k v , + k . par foam foam wat wat air air and the conductivity perpendicular to the direction of the heat flow is given by: per kc + v k , + v . / Vfoam ^ foam wat wat air ' air where k_ , k . and k . are respectively conductivities foam wat air c 2 foam, water and air, Mr , v and v . are respectively volume fractions foam wat air c J of foam, water and air. The total conductivity from conduction of the foam, water and air mixture is expressed as follows: r . k - r ) con par + ( 1 per -99- where r is the volumetric ratio of the solid component directed parallel to the direction of the heat flow to the total volume of foam, water and air mixture. As explained above, r=0.33. The comparison between {K} and Schuhmeister's conductivity is presented in Fig. 45. Schuhmeister's conductivity is presented as a solid line in Fig. 45. As can be seen it is almost a straight line. {K} is also very close to a straight line. However, these "conductivities" need not necessarily equal each other as a function of regain. The reason for that is, that Schuhmeister's model is not an absolutely correct model of the structure of three phase mixtures. In fact superposition of Schuhmeister's models gives a different expression for conductivity from that when the model is used in its simplest form). Yet it is close to being a characteristic of the conducting property of the bed. The main disadvantage of this model is that in practice the isotherms across the conducting sample are not flat planes, as is implied in Schuhmeister's model. By assuming that isotherms are flat discontinuous planes, the conductivity of the sample calculated by Schuhmeister's model is underestimated. At the same time, {K} is an overestimation of the actual -100- conductivity, as a property of an insulating bed, in the region of low regain, because the actual temperature gradient at the position where {K} was calculated is larger than the average temperature gradient across the bed <61>. Because of that, {K} is not a property of the bed, but rather an average conductivity at a certain position in the sample. (The position at which the graph presents {K} is at the plane of the heat sink) . For the region of high regain, this effect disappears <61>. For that region, {K} is an underestimation of the actual conductivity, because part of the heat leaving the heat source does not enter the heat sink, but becomes absorbed by the sample. This effect increases with increasing heat capacity of the sample, i.e. with increasing regain. The physical effects described above are the reasons for discrepancies between the measured conductivity and the values obtained from Schuhmeister's model. However, there should be a reasonable agreement between Schuhmeister's conductivity and {k} that, indeed, can be observed in Fig. 45. The shape of the curve representing the heat flux due to condensation is similar to that of the total water condensed on the heat sink (Fig.42). There is a steep increase in the heat flux as a function of regain in the range of regain 0-600 %, and then the value of the heat flux remains almost constant regardless of the -101- regain. Comparing Fig.43 (heat flux from condensation) with Fig.39 (total heat flux) it becomes clear that it is the heat transfer by evaporation, diffusion and condensation processes that is responsible for the shape of total effective conductivity curve with its characteristic regions, while {K} (Fig.45) is an almost linear function of regain. There is no simple theory available, as in the case of heat transfer by conduction, to explain the shape of the curve for heat flux from condensation. It can be assumed, that in the case of foam, 600 % regain is equivalent to the saturation regain, that is, up to that regain water is strongly bound to the material, or in other words, adsorbed. In fact, water is attached to the material in the form of internal layers <64>, one layer on top of the other, and the number of layers increases with the increasing regain. Also, each subsequent layer is attached less and less strongly to the previous one. This means that, with increasing regain, the binding forces between water and the material decrease, and water evaporates more easily from the material. This seems to be a linear function of regain and explains why, with increasing regain, the amount of water -102- evaporated from the material and condensed on the heat sink increases. From that it also follows that the heat flux due to the evaporation/condensation process increases with increasing regain for the range of regain 0 % - 600 %. When the regain reaches 600 %, free water begins to appear on the surface of the material. The higher the regain, the more water is on the surface. However, the amount of water evaporated during a test, for regains higher than 600 %, remains almost constant, regardless of the regain. It may be that, once free water is available for evaporation, it does not matter how much is available because only a limited amount can be evaporated anyway. The limitation is that the required heat of evaporation has to be transported to the water at the given position and the transfer of heat is controlled by the conductivity of the sample. Though the conductivity increases with increasing regain (Fig.45) the rise is not very steep and does not affect the transfer of heat sufficiently to cause much increase in the amount of evaporated water. Also, the effect of this slight increase in conductivity for the increasing regain is counteracted by the decrease in porosity of the material with increase of water content, which restricts the movement of water vapour towards the heat sink. So, in the region of regain 0-600 %, the rate of AIR AIR B) REGAIN BELOW SATURATION REGAIN. C) REGAIN ABOVE SATURATION REGAIN. (FREE WATER APPEARS ON THE SURFACE OF SOLIDS. IT PARTLY REPLACES SATURATED AIR IN THE PORES.) D> VERY HIGH REGAIN. (WATER DUE TO GRAVITATION IS TRANSPORTED DOWNWARDS. WATER FIG.47. CROSS SECTION OF A NONABSORBENT POROUS MATERIAL AT DIFFERENT REGAINS. -103- evaporation of water is controlled by how strong the binding forces are between water and the foam. In contrast to that, in the region of regain over 600 %, the process of evaporation is controlled by the availability of heat, which is to be used as the heat of evaporation, and the availability of space for the water vapour to diffuse through the sample towards the heat sink. This model is illustrated in Figs.47 a-c. FABRICS A similar analysis can be conducted for a non-absorbent textile fabric, for example polypropylene fabric p21. As before the eguivalent fibre diameter has to be established, in order to estimate the heat flux to the heat sink due to radiation. There were two difficulties in making these measurements. The existing measuring equipment is not very suitable for tests on materials of high packing factor. Also an inconveniently large amount of fabric is required to obtain a sample of suitable thickness to get a reliable equivalent fibre diameter. It followed that it was not possible to conduct separate tests on all the library fabrics. Instead, a woollen fabric of a similar structure to the library fabrics (knitted underwear) has been tested. The results indicate that the equivalent fibre diameter is around 350 pm. From this information it is evident o o TESTS . o CONDUCTIVITY DURING . SINK p21 HEAT FABRIC, INTO . o FLUX HEAT POLYPROPYLENE ON TOTAL 48. FIG. 000 1 (z0J/M) xmi J.V3H o o NO CONDUCTIVITY CONDUCTIVITY O DURING O CM . p21 RADIATION 2 < FROM CD W FABRIC, OC SINK HEAT CD CD INTO POLYPROPYLENE ON FLUX HEAT TESTS 49. FIG. o ( e The procedure follows that was used for the polyurethane foam. The total heat flux to the heat sink is shown in Fig.48 and the shape of the curve is the same as that for the effective conductivity (Fig. 24). The radiation heat flux is presented in Fig. 49. As o CD . pZl AND FABRIC, VAPOUR WATER . O OF POLYPROPYLENE ON TESTS CONDENSATION FROM SINK CONDUCTIVITY HEAT DURING INTO FLUX HEAT CONDUCTION 50. FIG. 0001 000 1 (z m/M) xmj J.V3H o 2 O in inEh w Eh > Eh t-H > t-H UEh Q 2 O U 13 2 l-H O' Q 2 t-H . in Eh p21 < w X 2 o Q FABRIC, w in W2 2Q O u a: w Eh < 2 POLYPROPYLENE in 13 t-H OS 01 0£ OZ 0[ 0 {zm/5) aaiVM JO iLNflOWV o DURING VAPOUR . WATER p21 OF FABRIC, CONDENSATION FROM POLYPROPYLENE SINK ON HEAT TESTS INTO FLUX CONDUCTIVITY HEAT 52. FIG. 0001 000 1 (Z«1/M) xmi J.V3H -105- before, the magnitude of it diminishes with regain. The heat flux from the process of evaporation, diffusion and condensation, and conduction was obtained by subtracting the radiation heat flux from the total heat flux and it is shown in Fig. 50. The total water condensed on the heat sink during tests as a function of regain is presented in Fig.51. Three regions can be distinguished. In the first one, for very low regains, the amount of water condensed on the heat sink rises very steeply with regain. After saturation regain has been reached the amount of water is almost constant, or slightly decreases with regain. For regains higher than 200 %, the amount of condensed water again increases steeply with regain. The heat flux due to the evaporation/diffusion/ condensation process has been calculated and presented in Fig. 52 as a function of regain. As in the case of water condensed on the heat sink, three regions can be distinguished in the graph. In the first region, the conductivity rises steeply with increasing regain. This is because water, which is initially strongly bound to the surface of the fibre, becomes less strongly attached and evaporates more easily. In the second region free water begins to appear on the surface of the fibre. The amount of water evaporated (and therefore the heat flux o o TESTS CONDUCTIVITY DURING CONDUCTION . p21 FROM SINK FABRIC, HEAT INTO FLUX POLYPROPYLENE ON HEAT 53. FIG. D09 r 000 1 (eUi/M) xmj J/V3H o o IK), FOR PROCESS", FORMULA CONDUCTION ^ u TO DUE SCHUHMEISTER FROM . p21 CONDUCTIVITY CALCULATED "THE FABRIC, OF CONDUCTIVTY POLYPROPYLENE COMPARISON AND 54. FIG. os2 002 os r oo r os o (Oi-m/Mui) AiiMionaNoo lywaam -106- from the evaporation/ diffusion/ condensation process) is controlled by the availability of heat for evaporation and availability of space for the water vapour to diffuse through the sample towards the heat sink. When the regain exceeds 200 %, which is in the third region, it was observed that liquid water was present on the heat source even after 360 s of the test. What this means is that the amount of water in the sample was such that some of it was no longer attached to the fibre but was moving, due to gravitation forces downwards, towards the heat source. The amount of this "excess" water increased with increasing regain. Because of the direct contact between water and the heat source, evaporation is much higher in this region compared with the previous region and the heat flux curve rises very steeply with the availability of "excess" water, that is with increasing regain. This phenomenon of water leaking downwards is illustrated in Fig.47 d. Also, as for the polyurethane foam, heat flux due to the conduction process has been calculated and presented in Fig.53 as a function of regain. Subsequently {K} was calculated and it is shown in Fig. 54. The solid line in Fig. 54 is the conductivity calculated according to Schuhmeister's model with the ratio r=0.33, which is a realistic value for fabrics of knitted structure. As for TESTS CONDUCTIVITY DURING SINK HEAT INTO w33. FLUX FABRIC, HEAT WOOL TOTAL ON 55. FIG. 00S5 OOOS OOSI OOOI OOS 0 xmi IV3H o o CONDUCTIVITY CONDUCTIVITY DURING RADIATION FROM w33. SINK HEAT FABRIC, INTO WOOL ON FLUX HEAT TESTS 56. FIG. 001 (giu/M) XmJ IV3H o o w33. VAPOUR FABRIC, WATER WOOL OF ON TESTS CONDENSATION FROM CONDUCTIVITY SINK HEAT DURING INTO FLUX CONDUCTION HEAT AND 57. FIG. 000£ o o 9 r 000 1 (ZUJ/M) xmj J.V3H 300 ON TESTS 200 CONDUCTIVITY DURING (V.) SINK REGAIN HEAT ON w33. 100 CONDENSED FABRIC, WATER WOOL 58. FIG. ( Zw/B) H3XVM JO ilNflOWV o o DURING VAPOUR WATER . o OF w33. CONDENSATION FABRIC, FROM WOOL SINK ON HEAT TESTS INTO FLUX HEAT CONDUCTIVITY 59. FIG. OOOS oo s r 000 1 ( ZUJ/M) xnad J.Y3H -107- the foam, Schuhmeister's conductivity is smaller than {K} in the region of low regain and higher than {K} in the region of high regain. However, there is a reasonable agreement between these two figures as a function of regain. The explanation of the discrepancy was given before, while discussing the results for the foam. In contrast to non-absorbent materials, a wool fabric, w33, has been also analysed in the same way. The total heat flux to the heat sink and the radiation heat flux are presented in Figs. 55 and 56. The shape of the total heat flux curve is the same as that for the effective conductivity (Fig. 25). The shape of the radiation heat flux curve is similar to that for the polypropylene fabric, that is, the radiation heat flux decreases with increasing regain. The heat flux from the process of evaporation, diffusion and condensation of water and the process of conduction is shown in Fig. 57. Water condensed on the heat sink is presented in Fig. 58, the heat flux due to evaporation/ diffusion/ condensation process in Fig. 59. Four regions can be now distinguished in the two graphs. The first region is for regain in the range 0 % - 15 %, where no water evaporates from the sample and none condenses on the heat sink. This is the region where water is very strongly bound to the fibre and it is characteristic SOLID A) DRY STATE AIR INTERNAL WATER SOLID B) WATER IS ABSORBED INTO STRUCTURE OF MATERIAL IN FORM OF INTERNAL LAYERS. INTERNAL WATER SATURATED AIR D) REGAIN ABOVE SATURATION SOLID REGAIN. (FREE WATER APPEARS ON THE SURFACE OF SOLIDS. IT PARTLY FREE WATER REPLACES SATURATED AIR IN THE PORES. ) LAYERS OF ADSORBED WATER SATURATED AIR INTERNAL WATER SOLID DRIPPING E) VERY HIGH REGAIN. _ WATER (WATER DUE TO GRAVITATION*"' IS TRANSPORTED DOWNWARDS.) Y TESTS CONDUCTIVITY DURING CONDUCTION FROM SINK w33. HEAT INTO FABRIC, FLUX WOOL HEAT ON 61. FIG. ooo r ( 2UJ/M) xmi IV3H o o IKI, WOOL FOR PROCESS", FORMULA CONDUCTION TO SCHUHMEISTER DUE FROM CONDUCTIVITY CALCULATED "THE . OF w33 CONDUCTIVTY FABRIC, COMPARISON AND 62. FIG. osz ooz os r oo r os o (<>TUI)/M«*> AJ-IAIvLDnaNOD 1VWM3HJ. -108- only of absorbent fibres. The heat flux due to the evaporation /diffusion/ condensation process in this region is obviously equal to zero. The other regions are similar to those of polypropylene fabric. The second one is from 15 % regain to saturation regain, (33 %), where water evaporated and the heat flux rises steeply with regain. The third one is for regain between saturation regain and 200%, with the heat flux almost constant regardless of regain and the fourth one is for regains higher than 200 %, where the heat flux rises very steeply again. The explanation for the existence of these regions is the same as that for the polypropylene fabric. The illustration of the four regain regions is presented in Figs. 60 a-e. The heat flux due to conduction has been presented as a function of regain in Fig. 61 and {K} in Fig. 62. It can be noticed again, that {K; is a linear function of regain. A similar model to that used for the polypropylene fabric (based on Schuhmeister's theory) has been constructed. However, in the case of wool it was assumed that in the initial region 0-15 % regain water is very strongly bound to the surface of the fibre and does not take part in conduction. The ratio of fibres parallel and perpendicular to the direction of heat flow was assumed to be again 0.33. -109- In contrast to the behaviour of the non-absorbent materials studied above, polyurethane foam and polypropylene textile fabric, the values of {k} are below the values obtained from Schuhmeister's model practically for the whole range of studied regains. This phenomenon can be explained by taking into account that wool fabrics have a much more hairy structure than fabrics made of other fibres. Therefore there may be fewer bridges between the separate fibres in wool fabrics . This includes also the situation when water is present in the fabric and water bridges are formed. Comparing the effective thermal conductivity curves of polypropylene and wool (Figs. 24 and 25), it can be noticed that there are differences in both the shapes of the curves and in the magnitudes of the effective conductivity value. (The effective thermal conductivity for wool is lower than for polypropylene in the region 0 % - 200 % regain.) As was explained above, the evaporation /diffusion/ condensation process is responsible for the shape of the curve. Comparing the curves of the heat flux due to evaporation /diffusion/ condensation process (Figs. 52 and 59), it can be noticed that the main difference in the shape takes place for low regains (up to saturation regain). From that point on, both the magnitude as well as the shape of the heat flux curves are almost the -110- same for both fibres. (The same can be noticed for the curves of water condensed on the heat sink, Figs. 51 and 58.) It seems, then, that sorption properties of fibres are important only up to the saturation regain and after that point both types of fibre behave in a similar way. However, it is the region of low regain (up to 100 % regain) that is important in practice and in this region the effective thermal conductivity is lower for wool than for the polypropylene fabric for the same regain. The two {K} curves (Figs. 54 and 62) for polypropylene and wool are almost parallel but the "wool line" runs below the "polypropylene" one. This explains why the total effective thermal conductivity of wool is generally lower than that for polypropylene not only for low regains, where sorption properties of the fibre affect the total effective thermal conductivity, but also for high regains (up to 200 %). The two fibres analysed above have almost the same critical surface tension of water <65> (wool has slightly higher critical surface tension of water than polypropylene). This property affects the distribution of water along a fibre, which in turn can affect the magnitude of the {K} values as well as evaporation of water from the surface of the fibre. In contrast, cotton <66> has critical surface tension approximately 7 times o o TESTS CONDUCTIVITY DURING SINK HEAT c45. INTO FLUX FABRIC, HEAT COTTON TOTAL ON 63. FIG. 00S£ 000 Z 0001 ooor OOS 0 ( Zui/M) xmj J.V3H o o NO ♦ ♦ CONDUCTIVITY t DURING RADIATION FROM c45. SINK FABRIC, HEAT INTO COTTON ON FLUX HEAT TESTS 64. FIG. (Z“*/M) xmj J.V3H o o AND c45. VAPOUR FABRIC, WATER OF COTTON ON TESTS CONDENSATION FROM SINK CONDUCTIVITY HEAT DURING INTO FLUX HEAT CONDUCTION 65. FIG. 00 01 0001 0001 000 1 000 0 (e^/M) xmi lLV3H o o ON TESTS CONDUCTIVITY DURING SINK HEAT ON c45. FABRIC, CONDENSED COTTON WATER 66. FIG. OS Ot7 0£ OS 01 0 < « UI/S ) H3J.YM 30 TNAOWY o o DURING VAPOUR WATER . o OF c45. CONDENSATION FABRIC, FROM COTTON SINK ON HEAT TESTS INTO FLUX CONDUCTIVITY HEAT 67. FIG. ooor (Z The total heat flux to the heat sink and the radiation heat flux are presented in Figs. 63 and 64. The shape of the total heat flux curve is the same as that for the effective thermal conductivity (Fig. 26) and similar to that of the other absorbent fabric, i.e. w33. However, the magnitude of the heat flux value is much higher for cotton than for wool or polypropylene, for the same regain. The shape of the radiation heat flux curve is the same as that for the two other fabrics and the magnitude of the values is similar. The heat flux from the process of evaporation, diffusion and condensation of water and the process of conduction is shown in Fig. 65. Water condensed on the heat sink and the heat flux from evaporation/ diffusion/ condensation process are presented in Figs.66 and 67. As with wool, four regions can be distinguished. The first one, for regain 0-10 %, where the amount of the water condensed and the heat flux from the evaporation/ diffusion/ condensation o o TESTS CONDUCTIVITY DURING CONDUCTION FROM SINK 5. HEAT cA INTO FABRIC, FLUX HEAT COTTON 68. FIG. oo s r ooo r (, > Eh IK> M > H COTTON Eh U Cl FOR 2 O u PROCESS", m a: w FORMULA Eh m H W 2 X CONDUCTION O X ^ u TO v- tn DUE SCHUHMEISTER FROM CONDUCTIVITY CALCULATED "THE OF 5. c4 CONDUCTIVTY COMPARISON FABRIC, AND 69. FIG. r oss oos (Oi-ui/Mui) AiiAiionaNOD avwyaHj, -112- process are equal to zero; the second one, from 10 % regain to saturation regain, where there is a very sharp increase in magnitude of measured values; the third one, from saturation regain to approximately 200 % regain, where the values are approximately constant; and the fourth one, for regains over 200 %, where there is an increase in the measured values with increasing regain. However, the amount of water condensed on the heat sink and the value of the heat flux from the process of evaporation/ diffusion/ condensation for a given regain is small, approximately equal to 2/3 that of wool or polypropylene. Because of that, the heat flux due to conduction and {K} obtained for cotton are very steep functions of regain, as illustrated in Figs. 68 and 69. As can be seen, {K} is a linear function of regain. Schuhmeister's thermal conductivity has been shown in Fig. 69 as a solid line. The same model as in the case of wool has been used, except for the fact that the amount of water which does not take part in conduction was assumed to be equal to 10 % regain. The ratio of fibres parallel and perpendicular to the direction of heat flow was again 0.33. For almost the whole range of regain tested, (the exception was very high regains), {K} values are above Schuhmeister's conductivity (shown in Fig.69). This means that, due to the very high critical surface -113- tension of water for cotton, water is evenly spread on the surface of the fibre. So water bridges are formed between separate fibres and, consequently, conduction through water is greater than in the case of wool or polypropylene . The effective thermal conductivity of cotton is much higher than for other fibres. From a comparison of the curves for the heat flux due to the evaporation/ diffusion/ condensation process and due to conduction, it can be noticed, that it is conduction that is responsible for such a high effective thermal conductivity of cotton, and this effect is due to the very high critical tension of water for cotton. The heat flux due to evaporation/ diffusion/ condensation is relatively small. The process of evaporation is probably also affected by the fibre properties. -114- 10. CONCLUSIONS The effective thermal conductivity of textile fabrics is an important parameter characterizing properties of clothing. However, due to the lack of suitable measurement methods, little is known about the effective thermal conductivity of fabrics containing water. This is despite the fact that fabrics, when in wear, almost always contain certain amounts of moisture. The literature survey conducted in the Introduction indicates the scarcity of experimental data on this subject and the lack of a reliable theory concerning effective thermal conductivity of fabrics containing moisture. Previously developed theories could not explain the characteristic shape of the curve for conductivity vs regain. It was therefore useful to study the problem of effective thermal conductivity of fabrics containing water, both experimentally and theoretically. As shown in the literature survey, transient techniques are more suitable than steady state ones for measurements on wet porous materials because they do not require long times for a steady state to get establish in a sample. Instead, they are based on measurements of energy transfer in transient conditions. -115- A technique based on the experimental arrangement of Ioffe and Ioffe <31>, for measurements of the thermal conductivity of semiconductors, has been developed to suit the particular conditions which apply to moist porous materials in the form of textile fabrics. It was found that the effective thermal conductivity of fabrics containing moisture is higher than for dry or conditioned fabrics. This is because of two mechanisms: (i) Before the fabric is wet it is a mixture of fibre and air. The conductivity of water is very high, 23 times that of air, and when it replaces some of the air the conductivity of the fabric increases; (ii) The second mechanism is that, as soon as water is introduced into the fabric, a new mode of heat transfer takes place. This is by evaporation of water from the hot face, diffusion of water vapour and condensation of water vapour at the cold face of the fabric. The heat conducted in this way increases with regain. By testing four kinds of fabrics made of different fibre types, wool, cotton, porous acrylic and polypropylene, the influence of fibre sorption properties on the effective thermal conductivity has been determined. -116- When the effective conductivity is presented as a function of regain, generally four regions can be distinguished. The first region is characteristic only of absorbent fibres. It occurs in the range of regain from zero to 15 or 10 % for wool and cotton accordingly. The value of the conductivity is low, almost independent of regain. In the second region, between 15 or 10 % (0 % regain for non-absorbent fibres, polypropylene and porous acrylic) and saturation regain, the conductivity rises sharply to a value approximately double that of dry fabric. From saturation regain to about 200 % regain the conductivity changes slowly with water content, and for regain above 200 % there is a further steep increase in the conductivity. In the range of regains 0-200 % wool had the lowest thermal conductivity of the four fibre types . It is useful to compare the conductivity as a function of regain for two fabrics, of contrasting sorption properties, namely man-made non-absorbent polypropylene and natural fibre absorbent wool. It can be seen that the conductivity of polypropylene rapidly increases as soon as any water is introduced into the fabric. -117- However, wool retains its conductivity unchanged for regains as high as 18 %, because water becomes absorbed into the fibre, while for this range of regain it exists in polypropylene as free liquid. For higher regains we see that wool does not become saturated until 33 % regain while polypropylene reaches saturation and therefore low thermal resistance at a very low regain. So wool, being an absorbent fibre, has better insulating properties than non-rabsorbent, man-made fibres like polypropylene. By comparing the effective thermal conductivity of fabrics of different packing factors but the same fibre types, as a function of regain, it was established that packing factor has very little influence on the thermal conductivity. Samples of higher packing factors were of higher conductivity because of higher content of fibre . However, structural properties were found to affect the effective thermal conductivity. Tests with brushed fabrics show that the conductivity is lower when the brushed side is in contact with the heat source than when the smooth side is in contact with the heat source. The reason for this behaviour is that, when a temperature gradient is applied to a wet fabric, the -118- process of evaporation of water, diffusion of water vapour, and condensation of water vapour is an important mechanism in total energy transfer. The hot face of the fabric is important in insulation. If it has a brushed, hairy structure it impedes the generation of water vapour, diminishing in this way the transfer of heat by decreasing the evaporation of water. The hot face of the apparatus can, in practice, be compared with the skin, the cold face with the ambient air. It is therefore important, for good insulating properties, that the fabric has a hairy structure against the skin. Wool with its hairy structure is therefore an ideal insulator and because, in contrast to other fibres, it retains this structure when wet, it maintains its insulating properties in this condition. A theoretical analysis of the effective conductivity tests established that the effective thermal conductivity consists of three terms, as the heat transfer during the tests takes place by three modes: by conduction, radiation, and by a process of evaporation, diffusion and condensation of water. It was further -119- revealed that it is the evaporation process which is responsible for the characteristic shape of the conductivity curves . In the simplified model developed here, the total heat flux through the sample is a superposition of the fluxes from evaporation/diffusion/condensation, radiation and conduction processes . The curve of heat flux from the evaporation/diffusion/condensation process as a function of regain consists of the previously described four characteristic regions (or three for non-absorbent fibres), which depend on the sorption the properties of the fibre. The heat flux from conduction was found to be a linear function of regain. From that observation, the value {K}, characterizing the conductive properties of a fabric, was calculated. This is also a linear function of regain. There is a discrepancy between Schuhmeister's conductivity and {K}. There is a need to develop a better model than the Schuhmeister model for estimation of the conductivity of fabrics . The heat flux from radiation decreases with increasing regain, as the free space between fibres covered with water decreases with increasing regain. It was established that radiation is an important means of heat transfer in fabrics, especially for low regains. -120- This is despite the fact that radiation is negligible in fibre beds of the packing factors characterisic for fabrics. It is yarn diameter that influences the radiant heat transfer and not fibre diameter as in fibre beds. However, more work is needed on this subject, and the development of new techniques for the measurement of radiant heat transfer in fabrics is necessary. The model for the thermal fluxes in the fabric is a simple one and assumes that all the above described modes of heat transfer take place independently of each other. In practice they are coupled processes and a more detailed model is needed to obtain a more realistic description of thermal processes in wet fabrics. The work presented in this thesis gives an explanation to well known claims that wool fabrics are preferred to other fabric types for wearing outdoors in cold wet weather when there is a possibility of the clothes becoming wet. The sorption and the mechanical properties of wool lead to its extra warmth. The information about the unique properties of wool fibre, which cause the low value for the effective thermal conductivity of wool fabrics, can be used in the development of products for specific end-uses. -121- In this thesis, the positive thermal attributes of wool have been demonstrated in a comparatively new area, namely for fabrics containing water. The same experimental method can also be applied for critical evaluation of the claims of synthetic fibre producers. -122- LITERATURE CITED 1. Thermal environmental conditions for human occupancy. ASHRAE Standard/ ANSl/ASHRAE 55/ 1981. 2. Marsh, M. C., Proc. Phys. Soc. (London)/ 1930/ p.42/ 570. 3. Rees/ W. H., J. Text. Inst., 1946, 37,p.132. 4. Pierce, F. T. and Rees, W. H., J. Text. Inst., 1946, 37, T181. 5. Morris, M. A., Text. Res. J., 1955, 25, 766. 6. Monego, et al., Amer. Dyest. Rep., 1963, 52, 21. 7. Holcombe, B. V. and Hoschke, B. N., Dry heat transfer characteristics of underwear fabrics, Text. Res. J., 1983, pp.368-374. 8. Steadman, R. G., The effect of moisture flow on the thermal resistance of hygroscopic materials, with particular reference to clothing fabrics., Ph.D. thesis, The University of New South Wales. ( Decr ' CS) -123- 9. Voinov, Yu. F. and Knyazeva, K. V., Conditions of moisture accumulation in clothing assemblies, Tekhnologiya Legkoi Promyshlennosti, 1981, 24, No.6 (144), pp.63-65. 10. Pratt, R. L.,Fonseca, G. F., and Woodcock, A.,H., Some effects of absorbency of clothing materials, Headquarters Quartermaster Research and Development Command, Quartermaster Research and Development Center, U.S. Army, Natick, Massachusetts, Environmental Protection Research Division, Research Study Report, BP-3, Project No.7-64-12-004A, 19 June 1956. 11. Farnworth, B., Calculations of heat and vapour transport in clothing: transient effects in hygroscopic materials. Research and Development Branch, Department of National Defence, Canada, Defence Research Establishment, Ottawa, Technical Note No.88-25, Project NO.14B00. 12. Farnworth, B., Calculations of combined heat and vapour transport through clothing systems: application to water-vapour-permeable rainwear, -124- Research and Development Branch, Department of National Defence, Canada, DREO Technical Note No.79-16, Project NO.14B00, October 1979. 13. 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Ioffe, Soviet Physics, Technical Physics, Vol.3, No.11, Nov.1958, pp.2169-2172. 33. Niven, C. D., A simplified hot plate appararus, Text. Res. J. , Nov.1962, pp.890-897. 34. Hollies, 'R. S. and Bogaty, H., Some thermal properties of fabrics, Part 2: The influence of water content, Text. Res. J., February 1965, pp.187-190. -128- 35. Kawabata, S. ,Development of a device for measuring heat and moisture transfer properties of apparel fabrics, J. Text. Mach. Soc. Jap., 37, No.8, pp.38-49, (1984). 36. Yoneda, M. and Kawabata, S., Analysis of transient heat conduction and its application, Part 1: The fundamental analysis and application to thermal conductivity and thermal diffusivity measurement, J. Text. Mach. Soc. Jap., 34, T183, (1981). 37. Yoneda, M., Senoo, J., Niwa, M. and Kawabata, S. On thermal conductivity and warm/cool feeling of fabrics containing water, Objective evaluation of apparel fabrics, ed. Postle, R., Kawabata., S. and Masako Niwa, Text. Mach. Soc. Jap., 1983, p.477. 38. Naka, S. and Kamata, Y., Thermal conductivity of wet fabrics, J. Text. Mach. Soc. Jap., 23, No.4, pp.114-119, (1977) . 39. Naka, S. and Kamata, Y., Determining the thermal conductivity of fabrics by non-steady state -129- method, J. Text. Mach. Soc. Jap., 24, No. 2, pp.33-40, (1978). 40. Suzuki, A., Sato, A., and Ohira, M., Measurement of thermal conductivity of wet fabrics, Bulletin of Research Institute for Polymers and Textiles, No.3, pp.160-170, 1974. 41. Suzuki, A. and Ohira, M., Study of the model of the thermal conductivity of wet fabrics, J. Text. Mach. Soc. Jap., 30, No.9, pp.158-166, (1977). 42. Salivon, N. I., Kazanskii, M.F., Lucik, P.P., Lucyk, R. V. and Litevchuk, D.P., Influence of moisture and porous structure on heat and mass transfer factor of some wool fabrics, Izvestiya Vysshikh Uchebnykh Zavedenii, Tekhnologiya Legkol Promyshlennosti, No.5, pp.24-29, (1978). 43. Volkenshtein, V. S., Method of measurements of thermal properties of materials, Part 2, ZhurnaL Tekhnicheskoi Fiziki, 24, pp.200-204, (1954). 44. Eckert, E. R. and Pfender, E., Heat and mass transfer in porous media with phase change, Proc. -130- 6th Int. Heat Transfer Conference, Toronto, Canada, pp.1-12, Hemisphere, Washington, D.C., (1978). 45. Dinulescu, H. A. and Eckert, E. R., Analysis of the one dimensional moisture migration caused by temperature gradients in a porous medium, Int. J. Heat Mass Transfer, 23, pp.1069-1078, (1980). 46. Crow, R. M., Heat and moisture transfer in clothing systems, Part 2: Theoretical consideration of the effect of some variables on thermal conductivity, Research and Development Branch, Department of National Defence, Canada, Defence Reserch Establishment, Ottawa, Tech. Note No.75-19, Oct.1975. 47. Krischer, 0., Die Wissenschaftlichen Grundlagen der Trocknungstechnik, pp.268-277, Springer-Verlag, 1963. 48. Carslaw, H. S. and Jaeger, J. C., Conduction of heat in solids, 2nd ed., Oxford University Press, 3.13 V, p . 12 9 . -131- 49. Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series , 55, 1964. 50. Warme-Isolation mit Thinsulate, Chemiefasern/ Textilindustrie, October 1982, p.718. 51. International Electrotechnical Commission Standard, Publication 584-1, 1977, Thermocouples, Part 1: Reference Tables. 52. Farnworth, B. and Osczevski, R. J., Heat transport in cold weather clothing, Defence Research Establishment Ottawa, Ottawa, Canada, prepared for the Fourteenth Commonweal^ Defence Conference on Operational Clothing and Combat Equipment, Australia 1985. 53. Holcombe, B. V. , The evaluation of protective clothing, Fire Safety Journal, 4, pp.91-101, (1981). 54. Watt, I. C., personal communication. 55. Roff, W. J. and Scott, J. R. , Fibres, films, plastics and rubbers, Butterworth, London, 1971. -132- 56. de Jong, S., Snaith, J. W. and Michie, N. A., A mechanical model for lateral compression of woven fabrics, to- be published-. ^ MSi, tfoli, Oex. '<**» 7*1-767 57. Algie, J. E. and Watt, I. C., The effect of changes in the relative humidity on the electrical conductivity of wool fibres, Text. Res. J., 35, No.10, pp. 922-929, (1965). 58. Cook, J. G., Handbook of textile fibres, Merrow Publishing Co. Ltd., 1968, p.626. 59. Stuart, I. M. and Holcombe, B. V., Heat transfer through fiber beds by radiation with shading and conduction, Text. Res. Jour., Vol. 54., No. 3, March 1984,p. 55. 60. Farnworth, B., The mechanism of heat flow through clothing insulation , Text. Res. J., 53, p . 717-724 ( 1983) . 61. Holcombe ,B. V. and Stuart, I. M., Method of numerical solution of equations describing heat transfer in fibrous beds., Jour. of Thermal Insulations, Vol.7, Jan. 1984, p.214-227. -133- 62. Holcombe, B. V., The influence of infra-red radiation on heat transfer through fibrous assemblies, in preparation. 63. Schuhmeister, Der Kaiser Akad . Wien Math. Nature, 76 (1877), 283. 64. Hayward, D. 0. and Trapnell B. M. W., Chemisorption (London, Butterworths, 1964). 65. Brooks, J. H., personal communication. 66. Melliand Textilberichte 6/1980, p.539. 67. Textile Terms and Definitions., The Textile Institute, Manchester, 1970. Paper presented at The Nineteenth International Thermal Conductivity Conference Tennessee Technological University Cookeville, Tennessee 38505 U.S.A. October 20-23, 1985 MEASUREMENTS OF THERMAL CONDUCTIVITY OF TEXTILE FABRICS Anna M. Schneider,* B.N. Hoschke* and H.J. Goldsmid+ * CSIRO Division of Textile Physics, North Ryde, New South Wales, Australia. + School of Physics, University of New South Wales, P.0. Box 1, Kensington. NSW 2033, Australia. ABSTRACT The effect of moisture on the thermal conductivity of textile materials is being determined. To prevent changes in water content, the measurement must be rapid. Thus, we describe a transient technique based on that of Ioffe and Ioffe. One face of the specimen is kept in contact with a heat source of constant temperature. The other face is then contacted by a thin copper plate heat sink of known heat capacity. The rate of change of temperature of the thin plate is directly related to the thermal conductivity. The heat sink is guarded by a quick-response plate heater to minimise errors. INTRODUCTION The thermal conductivity of a textile fabric is an important parameter in determining its comfort in use. However, its effective value is not a constant quantity but depends, for example, on the amount of moisture present and the form in which it is retained (i.e. whether it is absorbed or adsorbed). This is particularly important when the textile material is to be employed in clothing for strenuous work or sporting activity. Unfortunately, most methods for measuring the thermal conductivity of fabrics require a long period to reach steady state conditions and, during this time, the moisture content may change. Recently, however, it has been demonstrated that this problem can be overcome by the use of a transient technique.! Here we describe a new transient heat flow apparatus, for use with textile fabrics, that is designed to eliminate stray heat losses and, thus, to attain greater accuracy. EXPERIMENTAL METHOD Our method is based on the dynamic technique that was described by Ioffe and Ioffe2 for application to semiconductors. The same principle was also adopted by Yoneda and Kawabata^ in their measurements on textiles. Fig. 1. Schematic diagram of apparatus 1,2,3 thermometers 4 heat source 5 heat sink 6 test sample 7 guard ring 8 guard plate 9 polyurethane foam 10 micrometers The heat source is maintained at a constant temperature, which is above that of the surroundings, and is covered by the test sample and a heat sink, both being initially at the ambient temperature. Then, if no heat losses occur, the amount of heat flowing through the sample is equal to that which is gained by the sink. Thus, the effective thermal conductivity can be obtained from the time dependence of the temperature difference between the source and the sink. In the earlier use of this method, the principal source of error was the loss of heat from the sink. The new apparatus, which is shown in Figure 1, eliminates this shortcoming through the provision of a top thermal guard to the heat sink with the additional use of a side guard ring to prevent edge losses. The source consists of a heavy copper plate, 8 mm thick and 310 mm x 310 ram in cross-section, that is heated to the desired temperature by a hot plate. The sink is a thin copper plate, 1 mm thick and 150 mm x 150 mm in cross-section, surrounded by a guard ring of the same material. It is surmounted by a thin, rapidly-responding plate, which is provided with an electronically-controlled heater, so that it follows the temperature of the heat sink. This guard plate is separated from the sink by a 2 mm air gap and is insulated on its upper face with rigid polyurethane foam. The heat sink assembly rests on three micrometer screws that can be adjusted so as to correspond to the fabric thickness. The temperatures of the source, the sink, and the guard plate are measured by thermistors and fed directly into a computer. The fabric thickness was determined at a pressure of 10 Pa on 3. specimens that had been conditioned at 20 ± 2°C and 65 ± 2% relative humidity. The desired water content was obtained by the drying of wetted samples. At the start of each test, the fabric specimen was weighed to determine its water content and then quickly placed on the heat source plate and covered by the heat sink. From this time onwards, the temperatures were measured and recorded at 8 second intervals. The temperature of the source was approximately 50°C, while that of the sink was initially about 20°C. THEORY Suppose that a sample of infinite cross-section is maintained with one face, at x = 0, in contact with a heat sink, which is initially at the ambient temperature, while the other face, at x = d, is held at the constant temperature TQ with respect to ambient. Then, according to Carslaw and 4 Jaeger, the temperature with respect to ambient at time t, for a particular value of x, is T = TQ{1 - ZA^sinff^Cl - x/d)] exp(- m^t)}, (1) the summation being over all values of n from 1 to <», where An = 2/fn[l + 2 sin2fn/3 - sin(2f )/2f ], and m^ = af^ /d , a being the thermal diffusivity. The values of f are the roots of the equation cot f «=■ f /3, n n (2) where 3 “ C2/Ci, C2 being the thermal capacity of the sample and Ci that of the sink. From equation (1) we find that the temperature difference across the sample is T0 ZA sin f exp(- m t). n n n (3) where Tx is the value of T at x c 0. Thence, on differentiation, dTx/dt Zm A. sin f exp(- m t) n n n___ n (A) ZA sin f exp(- m t) n n n At sufficiently long times (dTx/dt)/(T0 - Tx) - m l • (3) 4 d ■ 4.3mm C2« 26 J K K - 37mW m Fig. 2. Temperature distribution in a typical thick specimen as a function of time. Also, for 3 < 1, equation (2) may be solved by a series expansion of cot f giving f,2 = 3/(1 + 3/3) (6) From equations (5) and (6) the thermal conductivity is found to be given by d(C1 + C2/3) dT1 K = A(Tq - Tx) dt * where A is the cross-section area of the heat sink. Because is so much greater, the term C2 can be omitted for dry materials, without introducing a significant error, but it must be included for water- saturated fabrics. We now consider the conditions under which equation (7) is valid. In physical terms, the time must be great enough for the temperature gradient in the sample to be essential uniform. We illustrate this for a particular case in Figures 2 and 3. Figure 2 shows plots of the ratio of the temperature T, at a position x, to the sink temperature Tx against x/d, for a rather thick sample having d = 4.3 mm and C2 = 26 J/K with K = 37 mW/ra.K. The temperature distribution is strongly non-linear at 10 s but has become close to linear at a time of 100 s. The corresponding plot in Figure 3 shows that the relative error in using equation (7) has become negligible at a time of 100 s. 40 5. (mWm K ) TIME Fig. 3. Relative error in conductivity calculated from equation (7) as a function of time, for samples with different characteristics. Figure 3 also shows the relative error as a function of time for other sample parameters. It has been found that satisfactory results can be obtained for wet specimens of 5 mm thickness within 100 s. Thin woven fabrics, of up to 2 mm thickness and conditioned to standard regain, can be measured within 10 s. It should be noted that there is also an upper limit to the time at which worthwhile measurements can be made. After too long a period the difference between T1 and T0 becomes so small that the technique becomes limited by the precision with which the temperature can be determined. EXPERIMENTAL RESULTS To date, experiments have been performed on knitted fabrics made of four fibre types. These and their specifications are listed in Table 1. Table 1. Fabric Specifications Fibre Type Thickness at 10 Pa Mass Packing Factor mm g/m2 (Fibre vol.fraction' Cotton 2.33 260 0.73 (Wicking absorbent) Porous acrylic 2.28 282 0.106 (Wicking, non-absorbent) Wool 2.56 290 0.086 (Non-wicking, absorbent) Polypropylene 2.35 289 0.135 (Non-wicking, non-absorbent) In Figure 4, the thermal conductivity of each of the four fabrics is 6. plotted against the percentage regain. Regain is defined as the ratio of the weight of water to the weight of the oven-dried fabric. The effect of moisture is somewhat different in each case. The change of conductivity depends on the way in which the water is contained within the fabrics. For example, it may be absorbed into the fibre polymer, retained in micropores within the fibre structure, or held as free water between fibres and yarns. Polypropylene, which does not absorb water, shows a rapid increase in conductivity as soon as moisture is present. The porous acrylic material absorbs less than 6% of water into the polymer but about 30% can be retained in micropores in the fibre. Thus, although the polymer is classed as non-absorbent, the fibre is absorbent. For this reason, it is expected that the conductivity of dry material that has been moistened will differ from that of wet material that has been partially dried, and experiments are in hand to establish this point. From the present data, the relatively steep rise of conductivity of porous acrylic with water content from oven dry to "saturation regain" is followed by a much slower rise with further water addition. ---- POROUS ACRYLIC -- COTTON POLYPROPYLENE REGAIN % Fig. 4. Effective thermal conductivity plotted against percentage regain for cotton, porous acrylic, polypropylene and wool samples. For both cotton and wool, the increase of conductivity with regain is quite slow, this being consistent with the fact that both are absorbent. Over most of the range of regain, the wool fabric had the lowest thermal conductivity of all the types that were tested. CONCLUSIONS It has been shown that the experiments can be carried out sufficiently rapidly for changes in the moisture content of the fabrics to be minimised Perhaps the major source of error is due to imperfect flatness of the heat sink plate, which has to be thin to allow rapid measurements to be made. The shape of the plate is presumably not quite constant since, when five measurements were carried out on cotton fabric of only 0.9A mm thickness, readings differed from the mean by as much as 7%. However, for a sample of 2.63 mm thickness, the greatest departure of any one of the five readings from the mean was only 2.5%. We think that the uncertainty does not exceed this order for the results shown in Figure A. We conclude that the technique yields data both rapidly and accurately. ACKNOWLEDGEMENTS Valuable discussions with Dr. B.V. Holcombe and Mr. I.M. Stuart are gratefully acknowledged. The Australian Wool Corporation supported this work through the provision of a Junior Research Fellowship to one of the authors (A.M.S.). The presentation of this paper has been assisted by Marlow Industries Inc. REFERENCES 1. Yoneda, M., Senoo, J., Niwa, M. and Kawabata, S. 198A, Objective evaluation of apparel fabrics, ed. R. Postle, S. Kawabata and M. Niwa, Textile Mach. Soc. Japan, Osaka, A77. 2. Ioffe, A.V. and Ioffe, A.F., 1958, Measurement of the thermal conductivity of semiconductors in the vicinity of room temperature, Soviet Physics-Technical Physics, 3:2163. 3. Yoneda, M. and Kawabata, S., 1959, Analysis of transient heat conduction and its application, Part 1: the fundamental analysis and application to thermal conductivity and thermal diffusivity measurements, J. Text. Mach. Soc. Japan, 3A:T183. A. Carslaw, H.S. and Jaeger, J.C., 1959, "Conduction of Heat in Solids", 2nd. ed., Oxford Univ. Press, 129.