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©IDOSR Publication International Digital Organization for Scientific Research ISSN: 2579-079X IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019.
Thermal Conductivity Study of South East Nigerian Woods Using Steady State Conditions on the grain directions
Nwankwo A.M.1, Festus L.Tor2 and Onah T.O.3
3Department of Mechanical Engineering, Caritas University Amorji Nike Enugu, Enugu Nigeria. 2Department of Mechanical Engineering, Kenule Beeson Sari-Wiwa Polytechnics, Bori. Rivers State, Nigeria. 1Department of Mechanical and Production Engineering, Enugu State University of Science and Technology Enugu, Enugu Nigeria. Email: [email protected]
ABSTRACT This study investigates the anisotropic property of selected wood sample from rain forest zone (south eastern part) of Nigeria. Using an experimental rig constructed for the purpose which is called modified lee-disc. The experimental investigations of five selected wood samples were done, heating each from longitudinal and at right angle (Radial) to the grain direction of each wood sample. The thermal conductivity value ‘K’ along (Longitudinal direction) grain directions of 0.12 – 0.143w/mk-1 were obtained, while in the perpendicular direction (Radial direction) to the grain values of 0.08 – 0.12w/mk-1 were obtained equally. It is observed that lower conductivity values occur at the perpendicular direction (right angle) to the heat source.
Keyword; Steady state, thermal conductivity, Nigerian woods.
INTRODUCTION Wood is hard fibrous tissue and organic poor heat conductance of wood is due material found in many plants. Natural to the paucity of free electrons which composite of cellulose fibers -with are media for energy transmission and strong tension capability rooted in a due to the porosity of wood. Wood is a matrix of lignin which repels typical a permeable raw material. Its compressive force. Wood also may be structure is complicated which makes it stated as other plant materials that has a strong anisotropic material in the area equivalent properties, and to any other of drying shrinkage and mechanical material gotten from wood, or wood applications. The complicated panels, chips and fiber. The conduction structures of wood consist of many cell of heat through wood and wood based types which have a cell wall materials has been well understood surrounding a cell lumen in the center. since the time of Fourier. The Also the arrangement of wood cells in conduction of heat across south eastern two main directions, in longitudinal Nigerian woods is less understood, direction as the tree grains direction especially since this phenomenon has and radial-transverse direction- received little attention until perpendicular to the grain direction. It investigations to alternative building is this structure that makes its physical materials starts to develop as a result of and mechanical properties directionally high cost of concrete and iron based dependent- anisotropic nature of wood. materials. Wood and wood-based [1] Thermal conductivity of wood as a materials have many applications in result of changes or differences in a areas that require good insulating grain direction, with defects and also properties. In building construction, with moisture content in the wood in wood as a building material is of special the direction of heat flow. Therefore, to concern because of its low thermal get the thermal conductivity of a conductivity and good strength. The particular wood we have to consider the
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www.idosr.org Nwankwo et al combination of the variances: the content available. Understanding the thermal conductivity values of the theory behind the wood’s thermal substance in wood, the theoretical conductivity, it makes it possible to models for examining the relationship predict its property changes with of wood structure and the experimental extended range of moisture content of rig and instrumentations to be used. the wood sample. Therefore, theoretical Thermal conductivity of wood is usually model can be step up on dry wood measured by the one-dimensional samples. In the processing of wood like steady state method, two –dimensional kiln-drying, impregnation, hot pressing and transient methods, but this research etc, knowing the thermal conductivity is focusing on the two dimensional of the wood sample is of a very big steady-state method using linear essence as long as the process involves regression method. With the moisture high temperature range. Thermal content available in the wood, insulators are those materials that are equilibrium will take longer time to be poor conductors of heat. Wood is a reached. It is not quite realistic typical example of an insulator (heat). conducting the test with the moisture
Figure 1: Three main axes of wood with respect to grain direction and growth ring.
Literature/Theoretical Underpinning longitudinal axes. [3] in their work Orthotropic and anisotropic are some of thermal properties of wood and wood wood’s attributes as an engineering panel products for use in buildings still materials [2] They conducted a study on talked about the two major properties the thermal conductivity for uniform affecting the thermal conductivity of density of wood cells Because of the wood - density and moisture content. orientation and property of the wood They also dealt with the percentage fibers and the manner in which a tree water content in a wood. [4] still talked increases in diameter as it grows, about the two major properties affecting properties vary along three mutually the thermal conductivity of wood - perpendicular axes: longitudinal, radial, density and moisture content. They also and tangential Figure1. The longitudinal dealt with the percentage water content axis and grain direction are in parallel, in a wood. In his work another method the radial axis normal to the wood’s of finding thermal conductivity was growth rings and perpendicular to the used. They used what is called cut-bar grain direction and the tangential axis thermal conductivity facility. The main of the wood is tangent to the growth aim was not to get the thermal rings and perpendicular to the grain conductivity, rather to get the contact direction. In comparative analysis, conductance of cylindrical shape inner wood’s properties differ in each of these and outer interfaces [5]. The same direction s and axis, but the main Fourier’s law was used, with known difference is between radial and temperature distribution in the inner 8 IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019.
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훿푇 and outer cylinders. Another literature At steady state = (3) had their research on thermal properties 훿푋 At steady state and if there are heat of wood, gypsum and insulation at sources into or heat-sink out of the elevated temperature. [6] objective was body: - to support the expansion of fire Then; Energy balance becomes; Energy resistance models concept for wood and in + energy generated/lost = δu + wood panels. There are so many other energy out literatures that were reviewed in the Where δu = change in internal energy. course of this work. Thus: Theory of Heat Equation 훿푇 푄 = −퐾퐴 (4) From a generalized 3-dimensional 훿푋 unsteady state equation we drive Energy generated = 푞퐴훿푥 (5) Fourier steady state equation; ∆푈 = 휌퐶푣훿푇훿푋퐴푑푥 (6) {퐾훿푇 whenever temperature gradient exists Energy out = −퐾퐴훿푇훿푋) = −퐴 + 푥+푑푥 훿푋 in a body or a system, heat will flow 훿 (퐾훿푇/훿푋) (7) from the higher temperature region to 훿푋 푑푥 } 퐾훿푇 the lower temperature region at a rate Thus, 푞 + 훿푥( ) = 휌퐶푣훿푇훿푋 (8) 훿푋 proportional to the temperature 퐾훿2푇 훿푡 From which푞 + = 휌퐶푣 gradient i.e. 훿푋 2 훿푥 푞 훿푇 = 훼 For a 3- dimensional (1) heat flow and with 퐴 훿푋 훿푇 no internally generated heat: 푞 = −퐾퐴 퐾훿2푇 훿푇 (2) 훿푋 = 휌퐶푣 (9) 훿푋 2 훿푋
Figure 2: 3D analysis of heat flow
∆푄 푥 Thus, for 퐾 = (11) 훿2푇 훿2푡 훿2푡 훿푡 퐴∆푡 ∆푇 3D:퐾 + ]′ + = 휌퐶푣 (10) 훿푋 2 훿푦 2 훿푧 2 푑푥 Where ΔQ is the quantity of heat, Δt is 훿2푇 훿2푡 훿2푡 푞 1 the time rate of change through a Or 훿2푇 = + + + = this is 훿푋 2 훿푦 2 훿푧 2 푘 훼훿푡 /훿푥 thickness x, in a direction normal to a the vertical divergence of temperature, surface of area A, per unit area of A. Due with internal heat generation q. Where to a temperature difference ΔT, 푘 훼 = = thermal diffusivity. Having assumptions are: under steady state 휌푐 conditions and heat transfer is reliant generated this equation Fourier’s steady on only on the temperature slope. state equation is chosen since our δt/δx Alternatively, it can be thought of as a =0, therefore the equation (9) after flux of heat (energy per unit area per transformation is given by; 9 IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019.
www.idosr.org Nwankwo et al unit time) divided by a temperature unit length) gradient (temperature difference per METHODOLOGY In order to evaluate the thermal bears the working drawing of the conductivity of Nigerian woods, through modified lee disc. a triangular interface and pyramid Heat was supplied to the assembly by Q- volume, a known thermal conductivity link manufacturing company with a apparatus was modified - lee disc was triangular shaped 210 x110mm electric re-designed to obtain data over a iron of 1100w capacity, Too avoid heat temperature range of Nigerian wood loss; the wood samples were cut in the samples and under some certain same shape with the electric iron of thermal conditions. The primary triangular shape and coated with fiber influence of the modified lee disc (as it glass heat insulator, with a little was called after re-design) is that the dimensional difference. The heat materials are locally sourced. These source is from mains of supposedly materials are readily available at the 240v. common Nigerian markets and could P= 퐼푉 (12) withstand the experimental temperature Where Q = P representing applied heat. range without giving way for the Instrumentation: The calculation of samples first. These materials are also thermal conductivity of woods and in relatively wide use, somewhat easy to other materials involves the use of some machine and weld. The dimensions of instruments to acquire some vital data all the materials -- U-channel iron part A needed for the calculation. Some of the and B (460mmx 40mmx25mm) stand instruments used are; and u-channel iron part C-- Thermocouple: Type K thermocouple (355mmx40mmx25mm) used as the was used. The range is -323k to 1573k base, flat iron bar part F – with tolerance of ±0.75%. K- Type is (204x38x5mm) used as the handle, M12 described as 3.24x150mm metal sheath x 120mm long bolt and nut were used 100cmcompensating wire. for fastening the handles. All these Thermometer: TES- 1303 digital dimensions were determined after thermometer for the thermocouple considering the constraints of available (probe) above was used. This digital space for the selected wood samples, temperature sensor used followed NBS also the u-channel for the base was also and IEC 584 temperature /voltage dimensioned based on the total standard table for K-type thermocouple. dimension of the electric iron and the Dimension of the temperature sensor sample material and the space to screw includes; 135(L) x 72(W) x 31(H) mm and them together. There is an iron pipe of 235g weight with battery and has a 127mmx 65mm diameter used to hold display rate of approximately 2.5 times the electric iron and the wood sample as per second. you tighten the handle of the apparatus Ameter: Analog AC ammeter of 0- [7]. A work bench of 25amps measurement ranges was used 3120x6180x614mmwas provided to to measure the current that is supplied create ergonomic and for the other to the heater. instruments like thermocouple, Volmeter: Also an analog AC voltmeter ammeter and voltmeter to rest on it. Lee range of 0- 500volts was used to disc was chosen from the list ofso many measure the voltage coming to the other methods, because other methods heater. are either for good conductors, out of Meter Rule: This was used to measure temperature range or even complex, the distance of the two probes unreliable and unavailability of the (thermocouples) and also helped in material for design. Also the fact that measuring the width and the height. this modified lee disc can be used for Thermal Conductivity other heat source shapes like circle for The thermal conductivity of the experiments is an added advantage. For materials used in this investigation was rigidity welding was used to join the u- determined by means of the modified channels to each other while nut and lee disc method. This method, as bolt were used to fasten the apparatus employed in this investigation, imposes to the laboratory table. In appendix 1, a flow of heat through a triangular 10 IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019.
www.idosr.org Nwankwo et al shaped wood samples. The samples and thermal conductivity at any distance on the heat source are placed together, and the sample. Fourier’s Law was used to heat is introduced at one end of the determine the thermal conductivity of surface of the samples and removed at the samples for the anisotropic behavior the other end of the sample [8]. The of wood. Each sample has two pieces heat applied, the temperature difference each of different grain direction and the thermal conductivity were The schematic diagram and the picture calculated using linear regression of the experimental test rig are shown in equation for two samples prediction of figure 3 and plate 1.
Figure 3. Schematic Diagram of modified lee disc apparatus
Keys to the Schematic diagram above A – Laboratory Table B – Modified Lee Disc Apparatus C – Ammeter D – Voltmeter E – TES-1303 Digital Thermometer with Type-K Thermocouple F – 1.5kw Power Source G – Wood Sample
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Plate 1. Photo of the experimental set up of modified lee disc apparatus Sample Characterization fiber glass was used to coat the As mentioned earlier the five selected samples. All conductivity measurements samples used for the steady state were taken while the specimens were at method of determining the anisotropic steady state. Steady state was property of wood were chosen due to ascertained by timing with a clock to their availability in the market and their know when the variation of the control rampant usage in Nigeria. All the parameters and the measured value samples are of the same shape- does not exceed our specified drift triangular. Their dimensions vary with tolerance range for fifteen minutes for average value of ± 3mm. Melina this experiment. (Gmelina Arborea), Mahogany (Swietenia The selection of the heater settings is Macrophylla),wall-nut (Genus influenced by the maximum Juglans),Inyi (Family of Bignoniaceac) temperatures. The epoxy used to pot the and Agba (Prioria Balsamifera) are the thermocouples softens at elevated names of the wood samples used [9]. temperature (at least, until it is Each of these samples has their completely out-gassed), but since no different grain direction from the strain was applied to the wire this was applied heat. Longitudinal direction is not taken into account to determine the measured 1800 to the grain direction over-temperature condition. The while radial direction is measured 900 to temperature used to determine if an the grain direction. over-temperature condition existed was Steady State Testing 823k, ensuring that none of the Before the heater element and the components or instrumentation was mains, an ammeter (in series) and a damaged. Preliminary testing of the test voltmeter (in parallel) were placed. For facility revealed that maximum heater good contact with the probes and the settings could be used without violating wood samples a little oil was added in the over-temperature criteria. Therefore, the holes. Voltage and the current were all testing includes the maximum heater held steady. They were heated until the setting. But the rheostat in the electric temperature of probe 1 and probe 2 heater was supposed to help us to became steady, while differences in the regulate the heat applied, to avoid temperature were measured every burning the wood. Fourier steady state 15minutes time interval. This means equation was applied since our dt/dx = that the heat in to the surface every 0 the use of steady state equation of 10 minute is the same to the heat out of was possible [10]. Here below is our the end surface of the wood sample table and values were obtained from every minute. We assumed that there is test measurements and calculations. no heat loss since our dx is small and
Table 1: Experimental data from the modified lee disc using steady state. Samples Grain direction (dx) Area δT Density Thermal Probe (A) M2 T1-T2 (ρ) g/m3 conduc. distance (K) K (W/MK-1) (m)
Agba Longitudinal180 0.072 0.013 330.4 1643 0.13 Radial900C 0.043 0.012 350.4 1427 0.08 Inyi Longitudinal1800C 0.064 0.013 298 2911 0.14 Radial900C 0.062 0.012 340.8 3057 0.12 Melina Longitudinal1800C 0.076 0.013 352.4 1251 0.13 Radial900C 0.066 0.012 365.3 1574 0.12 Mahogany Longitudinal1800c 0.065 0.012 331.4 1917 0.13 Radial900C 0.058 0.013 347 1950 0.10 Tick Longitudinal1800c 0.063 0.013 330.9 2270 0.12 (Wallnut) Radial900C 0.072 0.013 358.7 2280 0.12 Mean 0.063 0.013 342.8 2028 0.13 values 12 IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019.
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훿푋 Comparing the values of ‘K’ in the 퐾 = 푞퐴 (15) literature it shows that they are between 훿푇 Where;K is the thermal conductivity the established values of thermal unknown (w/mk-1), q is the heat applied conductivity of wood, which is from in watt (w) 0.001 → 0.4. However, some literature dT is the temperature difference we are has the value less. During the test the measuring Kevin (K), dx is the distance mean values of ‘I’ and ‘V’ are 0.035amps between the probes T1 → T2 (m), A is and 230 respectively. Area; from the the cross section area of the wood triangular shaped sample the area was samples (m2).Calibration of the calculated using area of a triangle 1 thermocouple was made using mercury 푥푏푥ℎ (13) 2 in glass thermometer, after boiling Density; The weight of the wood water at 373k and getting an ice block samples was weighed with scale and the Calibration volume of a pyramid was used in Before the use of the thermocouple calculating the volume. calibration was done to confirm the 1 푥푏푥ℎ푥푙 (14) measurement range of the 3 And the density is the mass per unit thermocouple. Sachet water at zero volume of the samples Kg/m3 temperature (blocked) and water boiled The applied heat source from the mains at 373k were used. Measurement was is gotten from the electrical relations of done with mercury in glass equation 12 thermometer and again measured with Therefore, the thermal conductivity is the TES thermometer with type K given by the same Fourier’s law of thermocouple being used in this work equation (2). The equation was for confirmation [11]. The range is - transposed to get the K which is what 323k to 1573k, making the basic we are looking for, and we have thus; accuracy at 23± 278k calibration. RESULTS From the graph compares the longitudinal and radial grain directions of the selected wood samples.
Figure 4. Comparison of longitudinal direction and radial direction
DISCUSSION From the finding that was evident to us graph. It comes to show that the that the radial directions seem to be directions of the grain have a role to transferring heat slower than the play in the heat conduction of woods. longitudinal direction. The entire This further confirms that the applied sample showed the same phenomenon. heat is 90 degrees to the radial direction The area of the samples is plus or minus which has more paucity than the 0.001 [12]. From the results the radial longitudinal direction of 180 degrees to line is below the longitudinal line in the the applied heat
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Implication to Research and Practice information on the choice of wood we Radial directions of grain growth of would be selecting for various projects woods are better insulators than the depending on the amount of heat longitudinal directions of wood’s grain insulation we wish to have [13]. growth. This research gives first-hand CONCLUSION This study did not include the concluded that wood for insulation temperature and moisture content purposes are better used in the radial effects on thermal conductivity. (perpendicular) direction of the grain Anisotropic property of wood was growth to the heat source. Analysis studied and values obtained confirm its shows that wood is anisotropic, also importance while dealing with woods as that grain directions of wood affects it an insulator. From our values it may be conductivity. FURTHER RESEARCH Investigation for more grain directions done on the sample with moisture in wood apart from radial and content, to know the behavior of the longitudinal gran directions need to be wood when soaked in water worked on. This research needs to be REFERENCES 1. Ayers, G. H, Fletcher, L. S and Warsaw University of life science Madhusudana, C. V. (1999) –SGGW Forestry and wood Thermal conductance of technology, 101-105. cylindrical joints, International 9. MacLean, J. D. (1941) Thermal Journal of heat and mass Conductivity of wood, heating, transfer. 42, 1273-1287. piping & air conditioning. 2. Benchiou, J, Sultan, M. A, Madison, USA. MacCallum, C and Hum, J. (2000) 10. Suleiman, M, Larfeldt, J, Leckner, Thermal conductivity of wood B and Gustavsson, M. (1999) and composite cylinders, Journal Thermal conductivity and of thermo-physics and heat diffusivity of wood, Wood transfers, 11. Science and Technology, 33 465- 3. Dana, K, Monika, C, Eva, V, 473. Martin, K and Robert, C. (2014) 11. Tenwolde, J. D, McNatt, L and Thermal properties of selected Krahn. (1998) Thermal property timbers, advanced research 982, of wood and wood panel for use 100-103. in buildings, USDA Forest 4. Hankalin, V, Tuukka, A and Risto, product laboratory for US R. (2009) Thermal properties of a department of Energy. pyrolysing wood particle, 12. Wilkes, K. E. (1981) Thermo- Finnish-Swedish flame days’ Physical Properties Data Base conference, Naantali, Finland. Activities at Owens-Corning 5. Holman, J. P. (1990) Heat transfer Fiberglas, Thermal Performance in mechanical engineering, Tenth of the Exterior Envelopes of Edition, McGraw-Hill Series. Buildings, ASHRAE, American 6. Hsiao-an, H. (1983) Thermal Society of Heating, Refrigerating conductivity measurement with a and Air-Conditioning Engineers, thermal probe, in the presence of Inc., Atlanta, GA. 28, pp 662-770. IRC – 710, (http://irc.nrc- 13. Williamson, G. B. (1992) Thermal cnrc.gc.ca/ircpub). conductivity study of wood and 7. Hunt, J. F, Gu, H, and Lebow, P. wood cell, by springer series K. (2008) Theoretical thermal wood and fiber science journal. conductivity equation for 40 (2). uniform wood cells, Wood and Fiber Science. 40 (2) pp 167-180. 8. Jankowska, P. and Kozokiewicz. (2004) Comparison of thermal properties of selected wood species intended to woodwork windows production, Annals of 14 IDOSR JOURNAL OF SCIENCE AND TECHNOLOGY 4(2): 7-14, 2019.