EXPERIMENTAL STUDY OF SATURATED NUCLEATE POOL
BOILING IN AQUEOUS POLYMERIC SOLUTIONS
A Thesis Submitted to the
Graduate School University of Cincinnati
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE (M.S.)
in the Department of Mechanical Engineering of the School of Dynamic Systems
2011
By
Advait Dattatraya Athavale B.E., University of Pune, India, 2005
Committee Co-Chairs: Dr. R. M. Manglik Dr. M. A. Jog
ABSTRACT
Saturated nucleate pool boiling experiments are conducted in de-ionized, distilled water and in aqueous polymeric solutions over a horizontal, cylindrical heater. Boiling characteristic
( vs. ∆Tsat) of water, at atmospheric pressure, is first established by conducting experiments over an extended period of time and confirming repeatability of the experimental results.
Aqueous solutions of three grades of HEC (Hydroxyethyl Cellulose) polymer viz. 250-HR (1000 kg/mol), 250-MR (750 kg/mol) and QP-300 (600 kg/mol), are then used at varied concentrations in a series of nucleate pool boiling experiments, so as to study the effect of pseudoplasticity on boiling heat transfer.
Polymers, when dissolved in water, change the rheological and interfacial properties of the solution and affect the ebullient boiling behavior. This viscous non-Newtonian, shear- thinning solution also displays interfacial tension relaxation, which tends to be both concentration dependent and temporal. A corresponding increase in surface wettability (smaller contact angle) is also observed. The boiling behavior in aqueous polymer solutions is found to be significantly influenced by changes in the wetting, vapor-liquid interfacial tension, and shear- thinning viscosity of the polymeric solutions. Both the concentration of the polymer and its degree of polymerization (which is reflected in its molecular weight and rheology) have an effect on the heat transfer and associated bubble dynamics.
The ebullient dynamics is captured in photographic records to characterize changes in bubble shape, size, frequency, and coalescence in boiling in both polymer solutions and distilled de-ionized water.
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The effect of concentration (1.0 × 10-9 ≤ C ≤ 4.0 × 10-9 mol/cc) are seen in the nucleate boiling characteristics of aqueous solutions of HEC QP-300 (M ~ 600 kg/mol). The measured pool boiling heat transfer from the electrically heated horizontal cylinder in C = 1.0 × 10-9 mol/cc
(~ critical polymer concentration, C*, for HEC QP-300) aqueous solution is found to be
2 enhanced by ~ 20 % over the entire heat flux range (4.0 < < 200 kW/m ). In higher concentration solutions, however, heat transfer deteriorates at low hear fluxes (or in the incipience and partial boiling regime). At high heat fluxes or in the fully-developed nucleate boiling regime, on the other hand, heat transfer enhancement (~ 45 % maximum) is obtained.
This anomalous boiling behavior in the two regimes is characterized by respectively different ebullience signature (as depicted by photographic imaging). Also, it is shown to be scaled with changes in the liquid-solid interface wetting, vapor-liquid interfacial tension, and shear-thinning viscosity of the polymeric solutions.
The effects of liquid pseudoplasticity and dynamic interfacial tension are seen in the
Saturated nucleate pool boiling of aqueous solutions of three grades of the HEC polymer, namely, 250-HR (1000 kg/mol), 250-MR (750 kg/mol), and QP-300 (600 kg/mol). The experiments are conducted at constant molar concentration of C = 2.5 × 10-9 and 4.0 × 10-9 mol/cc, which is 2.5 – 7 times higher than critical polymer concentration, for all the three polymer grades, the latter are in the range 0.35 × 10-9 ≤ C* ≤ 1.0 × 10-9 mol/cc.
With C = 2.5 × 10-9 mol/cc solution, boiling heat transfer coefficient is found to decrease even
2 below that of water in the partial boiling regime (4.0 ≤ ≤ 20 kW/m ). The reduction increases with viscosity. However, at higher heat flux, the shear-thinning of the polymeric solutions diminishes the viscous effects giving enhancement up to 32 %. The lower molecular mass HEC
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QP-300 has a better performance than the large-chain 250-MR and 250-HR because of its lower dynamic surface tension in the high-frequency ebullience regime of fully-developed boiling.
The interplay of pseudoplasticity of the solution and dynamic surface tension is further seen in the results for C = 4.0 × 10-9 mol/cc solutions of HEC QP-300 and 250-MR. The characteristics of the consequent bubbling activity for each of these cases are identified in respective photographic records.
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ACKNOWLEDGEMENT
I would like to thank my academic advisors and mentors Dr. Raj M. Manglik and Dr.
Milind A. Jog for their excellent support and guidance throughout my M.S. program. Generous help was also offered by the mechanical department staff members, especially Mr. Larry
Schartman, departmental IT manager, Mr. Bo Westheider, departmental electronics coordinator, and Mr. Doug Hurd of the machine shop.
I specially thank my parents for their constant encouragement and support throughout my studies. I would like to thank my fellow graduate students Deepak Veettil and Gabriel
Wickizer, and all the students in the Thermal-Fluids and Thermal Processing Laboratory who showed a great support for all these years and contributed to my studies in immeasurable ways.
My friends and roommates, especially Prashant Patel, Abir Sengupta, Sagar Bhamare, Anup
Khinvasara, Abhinav Pande, and Samrish Variyath made my life outside campus enjoyable and unforgettable.
Finally, I would like to thank the University of Cincinnati, for giving me this research opportunity and to make all the resources easily available from time to time.
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TABLE OF CONTENTS Page
ABSTRACT I ACKNOWLEDGEMENTS v TABLE OF CONTENTS vi LIST OF FIGURES viii NOMENCLATURE x
1. INTRODUCTION 1
1.1 Nucleate Pool Boiling – An Overview 1
1.2 Nucleate Pool Boiling with Polymers 4
1.3 Scope of study 7
2. RHEOLOGY AND INTERFACIAL PROPERTIES OF AQUEOUS 8 POLYMERIC SOLUTIONS Introduction 8
2.1 Polymer Additives 9
2.2 Viscosity Measurement 11
2.2.1 Rheometer ‘AR-2000’ 12
2.2.2 Capillary Viscometer 13
2.2.3 Data Analysis 15
2.2.4 Results and Discussion 17
2.3 Dynamic and Equilibrium Surface Tension measurements 21
2.3.1 Maximum Bubble Pressure Method 21
2.3.2 Equilibrium Surface Tension Measurements 23
2.3.3 Dynamic Surface Tension Measurements 25
2.4 Surface Wettability 29
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2.4.1 Contact angle measurement 30
3. NUCLEATE POOL BOILING HEAT TRANSFER IN WATER 33
3.1 Nucleate Pool Boiling Experiment 33
3.1.1 Experimental Setup 33
3.1.2 Heater Design 35
3.1.3 Data Acquisition System 36
3.1.4 Photographic Record of Boiling 38
3.1.5 Experimental Procedure 40
3.2 Nucleate Pool Boiling of Water and Boiling Correlations 41
3.2.1 Literature Survey of Pool Boiling Correlations 41
3.2.1.1 Rohsenow Correlation 41
3.2.1.2 Borishanskii Correlation 42
3.2.1.3 Cooper Correlation 45
3.2.1.4 Cornwell-Houston Correlation 45
4. POOL BOILING OF AQUEOUS POLYMERIC SOLUTIONS 47
4.1 NPB of Aqueous HEC QP-300 Solutions 48
4.2 NPB of Aqueous solutions of Different HEC grades 54
5. CONCLUSION 64
BIBLIOGRAPHY 67 APPENDIX A. UNCERTAINTY ANALYSIS 70 APPENDIX B. DATA COMPILATION 73
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LIST OF FIGURES Page
1.1 Schematic of typical boiling curve with different regimes 3
2.1 Idealized molecular structure of HEC 8
2.2 Ubbeholde Viscometer 13
2.3 Usual viscous response of HEC to applied shear 16
2.4 Shear dependent viscous behavior of HEC 250-HR, 250-MR and QP-300 at 17 different concentrations 2.5 Intrinsic viscosity of HEC 250 HR, 250 MR and QP 300 18
2.6 Schematic of ‘Sendadyne – QC6000’ used for equilibrium and dynamic surface 22 tension measurements 2.7 Equilibrium surface tension variation in HECs with concentration 23
2.8 Dynamic surface tension of HEC grades at 2.5 × 10-9 mol/cc 25
2.9 Dynamic surface tension of aqueous HEC QP-300 solutions at different 27 concentrations 2.10 Interfacial Stresses 29
2.11 Contact angle variation with concentration of aquous HEC solutions 31
3.1 Schematic of Pool Boiling Apparatus 34
3.2 Schematic diagram of cylindrical heater 34
3.3 Schematic of electrical circuit used to vary heat input during boiling experiment 37
3.4 Schematic of setup for CCD camera capturing bubbling activity during boiling 39
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3.5 Pool boiling data of distilled de-ionized water in comparison with different pool 43 boiling correlations 3.6 Sweeping vapor mass along cylindrical heater surface 46
4.1 Pool boiling curves for aqueous HEC QP-300 solutions at different concentrations, 48 and distilled, deionized water 4.2 Variation of dimensionless enhancement of heat transfer coefficient with heat flux in 50 aqueous solutions of HEC QP-300 with different concentration 4.3 Visual characteristics of bubbling behavior during boiling of aqueous HEC QP-300 52 solutions of different concentrations 4.4 Pool boiling curves for aqueous HEC solutions at 2.5 × 10-9 mols/cc 54
4.5 Variation of dimensionless enhancement of heat transfer coefficient with heat flux in 56 aqueous HEC solutions at 2.5 × 10-9 mols/cc 4.6 Visual characteristics of bubbling behavior during boiling of aqueous HEC grades at 58 2.5 × 10-9 mols/cc 4.7 Pool boiling curves for aqueous HEC solutions at 4.0 × 10-9 mols/cc 60
4.8 Variation of dimensionless enhancement of heat transfer coefficient with heat flux in 61 aqueous HEC solutions at 4.0 × 10-9 mol/cc 4.9 Visual characteristics of bubbling behavior during boiling of aqueous HEC grades at 62 4.0 × 10-9 mol/cc
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NOMENCLATURE
2 Wall heat flux at heater surface [kW/m ]
Tw Temperature of heater surface [K]
Tsat Saturation temperature of test liquid pool [K]
∆T Wall temperature superheat difference (Tw - Tsat) [K] h Heat transfer coefficient [W/m2∙K]
2 hw Heat transfer coefficient of water [W/m ∙K]
2 ηa Apparent viscosity [Ns/m ]
2 ηo Zero shear viscosity [Ns/m ]
2 η∞ Infinite shear viscosity [Ns/m ] n Power law index for shear d ependent viscous behavior k Flow consistency [Nsn/m2]
Shear rate [s-1]
M Molecular weight [kDa]
C Concentration [mol/cc] or [wppm]
C* Critical polymer concentration [mol/cc] or [wppm]
σ Surface tension [N/m]
τ Surface age of bubble [s]
θ Contact angle [degrees]
x
CHAPTER 1
INTRODUCTION
1.1 Nucleate Pool Boiling - An Overview
Boiling heat transfer has become a part of our day-to-day life in many forms. Right from the home air-conditioning systems to the electricity generation by steam turbines, we use boiling as an efficient mode of heat transfer. Dating back to 17th century, the use of boiling to produce steam in steam engines became a major source of mechanical power which at present contributes around 80% of total electricity generation in the form of stream turbines. Whether the applications are in small electronic devices or large-scale thermal process and power plants, today boiling heat transfer finds a wide applicability in many micro as well as macro systems for thermal management of heat in a more efficient manner.
Nucleate pool boiling experimental measurements are usually made by recording the heat flux and temperature of a heated surface submerged in a steady pool of saturated liquid, where heat transfer takes place by phase change over the heater surface. Relatively small temperature differences can sustain very high heat transfer rates due to the phase-change process. The rate is essentially governed by natural convection and ebullient conditions
(bubble inception, growth and departure) over the heater surface. This cools off the heater surface reducing the wall temperature (Tw); smaller the corresponding wall superheat
(Tw – Tsat) the better is the heat transfer, at a given wall heat flux
A typical boiling curve is generated by plotting wall heat flux versus wall superheat
(Tw – Tsat), as shown in fig 1.1. This plot represents several different regimes that are characterized by different driving mechanisms for the associated heat transfer. When heat flux is very low, there is no enough temperature potential or (Tw – Tsat) to nucleate bubbles on the heater surface and the heat is transferred only by natural convection. This region is
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indicated by line a – c in figure 1.1. At point c, known as ‘Onset of Nucleate boiling (ONB)’, temperature potential on the heater surface is just enough to initiate bubbling. ONB is characterized by appreciable drop in heater surface temperature, marked by point d, at which nucleate boiling begins. The initial phase d – e is known as ‘partially developed nucleate boiling regime’ and is marked by small number of active nucleation sites spread over the heater surface. Further increase in heat flux is marked by steep rise in number of nucleating sites, eventually causing bubbles to coalesce and form streams of vapor rising from the heater surface, and collapsing at the top surface of the pool. This section, e – f, of the boiling curve is known as ‘fully developed nucleate boiling regime’. At a certain specific high heat flux, known as ‘Critical Heat Flux (CHF, point f in fig 1.1), heater surface is so densely crowded with bubbles that no liquid is able to reach the surface to cool it down. Heater surface temperature, thus, suddenly jumps to a very high value, point g. From this point onwards, any further increase in heat flux leads to ‘film boiling’ regime g – h. This regime is characterized by noticeably low heat transfer coefficient with heater surface fully covered by vapor jacket.
On decreasing heat flux, or wall superheat, a similar boiling curve can be mapped from film boiling regime to natural convection. In this situation though, film boiling persists till point g’ on boiling curve. This is because of the vapor jacket, which was formed during film boiling, staying till lower wall superheat. At point g’, the vapor jacket breaks down and the saturated water flows down to the heater surface providing quicker heat removal causing the wall superheat to plumb down to point e’, getting the system back into partial nucleate boiling regime. Further decrease in heat flux, till boiling on the heater surface ceases (point b), traces the path e’ – d – b, skipping ONB. This hysteresis in pool boiling heat transfer, observed between increasing heat flux and decreasing heat flux boiling curves, is prominently due to the wetting of the heater surface by ambient fluid.
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Figure 1.1 Schematic of a typical boiling curve with different regimes generated in heat flux controlled system
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1.2 Nucleate pool boiling with polymers
Pool boiling of aqueous polymeric solutions is a complex interplay of various thermophysical, rheological and molecular transport properties of the solution. There has been growing interest in the literature in semi-dilute aqueous solutions to enhance or alter nucleate boiling heat transfer, as pointed out in a recent review by Manglik and Jog (2009).
The results span a wide spectrum of phase-change characteristics, which are sometimes contradictory. For instance, Kotchaphakdee and Williams (1970) found the boiling heat transfer from a plate heater to be enhanced in shear-thinning HEC-H and PA-30 solutions, of which HEC-H also reduces surface tension. Contrarily, in experiments with platinum wire heaters, Wang and Hartnett (1992) and Paul and Abdel-Khalik (1984), deterioration in heat transfer was found in very dilute aqueous polymeric solutions when compared to that in water. To complete the quorum of dissimilar results, Yang and Maa (1982) report that the boiling heat transfer performance for dilute aqueous HEC solutions is independent of heater shape (plate or platinum wire). The data of Shul’man et. al. (1993), and Levitsky et. al (1996) with a plate heater and HEC-H solutions in water indicate enhanced boiling heat transfer in dilute solutions (C = 0.015×10-9 – 0.5×10-9mols/cc), but a decreased heat transfer in highly concentrated solutions (C = 10×10-9 mols/cc).
While using polymers as additives in boiling of distilled de-ionized water, their ability to impart pseudoplasticity to the solvent and their diffusivity towards liquid-vapor and solid- liquid interface are of crucial importance. Polymers are typically large molecules, macromolecules, or agglomerates of smaller chemical units called monomers, fig.2.1. Their addition to water primarily increases the solution viscosity, which is perceived as an effect of entanglement of the polymer chains. Higher concentrations results in increased solution viscosity. Under a steady shear stress, the entangled polymer chains reorient themselves in the stress direction resulting in thinning down the solution viscosity, albeit the original
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viscosity is regained on removing the stress. This pseudoplastic nature can play a significant role in boiling nature of these solutions.
Solution viscosity was reported to have an adverse impact on boiling heat transfer.
Viscosity was conveyed to be a limiting factor in the solution’s ability to enhance boiling heat transfer by Zhang and Manglik (2005). Presence of heavy molecular chains in the solution imposes difficulty in bubble growth as well as generates more viscous drag as the bubble moves inside the pool. Hydroxyethyl cellulose (HEC), though initially effective in giving highly viscous solution, shows a continuous drop in viscosity as the solution is subjected to higher and higher shear rates. The phenomenon finds an explanation in terms of reorientation of polymer chains in the direction of shear which are randomly oriented at low or zero shear. There are other polymers also which show shear thickening nature when in solution form. In the field of boiling, this peculiar behavior of polymer solutions can find applications where a coolant or any other heat transfer fluid requires different thermal conductivity at different shear conditions. Also the study can provide a solid base for a further research on the effect of viscosity on pool boiling heat transfer.
Apart from changed rheology, aqueous HEC solutions also show a dynamic surface tension effect and increased surface wettability, pertaining to their surface active nature. The reduced surface tension is largely brought about by the molecular adsorption of surface-active additives to the vapor–liquid interface (Holmberg et al., 2003). The time scales of this process vary from order of seconds to minutes depending upon the polymer chemistry and its concentration in solution, which is possibly due to the slow diffusion transport of polymer molecules to the interface and their subsequent reorientation (Persson et al., 1996). This, along with time scales of 10–100 ms for boiling bubble dynamics in water (Prosperetti and
Plesset, 1978) thus results in a rather complex interfacial behavior.
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Surface tension as such was reported to have enhancing as well as adverse impact on boiling. Still the latest study with surfactants as additives (Wasekar and Manglik, 2000;) has shown that reduction in surface tension only eases the formation of bubbles and thus increases the amount of heat being driven away from the heater surface. In case of surface active polymers, like HECs, the said effect comes into picture along with the other changes in solvent properties due to presence of polymer molecules.
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1.3 Scope of study
The objective of the present study is to parametrically explore the effects of shear- dependent viscosity, and dynamic surface tension and altered wettability of aqueous polymeric solution’s nucleate pool boiling heat transfer. A nonionic solvable polymer,
Hydroxyethyl Cellulose (HEC) and its grades 250-HR, 250-MR and QP-300, are used as additives in deionized distilled water. The rheological and interfacial properties of these HEC solutions in different concentrations are recorded, which exhibit a viscous shear-thinning, dynamic surface tension relaxation, and increased wetting behavior. Pool boiling heat transfer is measured in controlled set of experiments with an electrically heated, horizontal cylindrical
heater (variation of wall heat flux with superheat ∆Tsat). The results that characterize ebullient phase change from ONB to fully developed nucleate boiling regimes highlight the effects of the solution’s pseudoplasticity, interfacial tension relaxation, and wettability at different polymer concentrations. Also, the associated bubble generation activity is photographically recorded to provide additional mechanistic insights.
The primary scope of work presented here can be summarized as follows:
1. A detail rheological study of the aqueous HEC solutions to characterize the effects of
degree of polymerization and polymer concentration.
2. A detail study of interfacial behavior of HEC molecules within the aqueous solutions
in terms of equilibrium and dynamic surface tension, and surface wettability.
3. Conducting saturated nucleate pool boiling experiments for deionized, distilled water.
This will establish a nucleate boiling characteristic for the heater-water combination
which will become a basis for the eventual comparison of boiling data of aqueous
polymer solutions.
4. Photographically recording the pool boiling experiments for visually comprehending
the ebullient dynamics.
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Chapter 2
RHEOLOGY AND INTERFACIAL PROPERTIES OF POLYMER SOLUTIONS
RHEOLOGY OF AQUEOUS HEC SOLUTIONS
Introduction
HEC when dissolved in water imparts a substantial increase in solution viscosity. They have an ability to make the solvent significantly viscous even at lower concentrations of around 0.01- 1.0%. The entanglement of the long polymer chains in the solution forms a complex interlocking with solvent molecules which is believed to be a basic cause of the high viscosity. Apart from imparting the viscous nature, HECs also give a shear thinning ability to their solution. Though the mechanism by which this shear thinning happens is not well established, the primary reason is assumed to the disentanglement of the molecular chains under the effect of unidirectional stress.
In nucleate pool boiling, the formation, growth and movement of bubbles through the fluid causes high amount of turbulent flows in the pool. This induced shear in the boiling process and the shear dependent viscous nature of aqueous polymer solution generates an interesting boiling nature. The pattern in which the shear thinning takes place in boiling and its effect on the heat transfer capacity of the system demands a detail study of the basic rheology of these solutions.
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2.1 Polymer Additives
Hydroxyethyl cellulose (HEC) is a nonionic cellulose polymer. Figure 1.2 shows an idealized molecular structure of HEC. They are produced by treating alkali cellulose with ethylene oxide. The raw materials for the production of HEC are high purity chemical cotton
(or wood-pulp) and ethylene oxide. The reaction product is purified and ground to a fine granular powder. HEC polymers are available commercially with different grades based on various factors like amount of viscosity they impart, molecular weight, and application specific grades like thickener, binder, stabilizer etc. In the present study, we are using three grades of HEC polymers viz. 250-HR, 250-MR and QP-300; with decreasing molecular weights. Table 1.1 compiles various chemical and physical properties of these grades.
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Table 2.1. Chemical and physical properties of Hydroxyethyl Cellulose (HEC)
HEC type Mol. wt. Viscosity, cP Ionic Appearance Manufacturer/
(kDa) nature Brand name
HR 1000 1500 – 2500 Non-ionic white powder Ashland /
Natrosol 250
MR 750 4500 – 6500 Non-ionic white powder Ashland /
(2% aq. solution) Natrosol 250
QP- 300 600 300 – 400 Non-ionic white powder Dow /
(2% aq. solution) Cellosize
Figure 2.1 Idealized molecular structure of HEC
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2.2.1 Viscosity Measurement
Viscosity measurements were made over a range of shear-rates using a high-tech
Rheometer and simple capillary viscometers. Rheometer, ‘AR2000’- manufactured by TA
Instruments Inc., was used in mapping the low shear viscous behavior of the polymer solutions. A set of five Cannon-Fenske capillary-tube viscometers of different capillary diameters, was used to generate the data of viscosities at higher shear rates which were difficult to achieve otherwise using the Rheometer.
The test solution for viscosity measurement was prepared by carefully adding a precisely weighed ( ± 0.1 mg accuracy on an electronic scale) quantity of polymer powder to water.
The mixture was then stirred at a constant speed on a magnetic stirrer till the powder is completely dissolved and the solution looked transparent. It was then aged over a minimum period of 10-12 hours before using for viscosity measurement.
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2.2.1 Rheometer ‘AR-2000’
The basic function of this rheometer is to get shear dependent viscosity values at very low shear rates, near zero. The rheometer was used for mapping near zero shear viscosities of aqueous HEC solutions. A conventional rheometer has a spindle rotating in the test solution held in a walled chamber or on a flat plate depending upon its fluidity. A measured torque is applied to rotate the spindle inside the solution. As the solution starts moving along with the spindle, the outer periphery of the solution-volume imposes a torque on the container chamber wall. This torque is measured using a high precision normal force transducer and then is used to get the amount of torque transmitted through the solution. This calculated torque, in relation with the gap between the spindle and the chamber walls, is used to calculate the apparent viscosity of the solution at the applied shear. At each step, the rheometer waits until the test fluid attains equilibrium, before recording the final reading.
The AR-2000 rheometer was used with two different spindle-chamber geometries viz. a. concentric cylinder geometry and b. flat plate geometry. Both were found to generate similar profiles for HEC solutions till a certain shear rate range (10-1 to 400-1) above which centrifugal force dominates over viscous force giving erratic readings. Temperature control was maintained by the built in Peltier heating system. The maximum single-sample error propagation method based uncertainty in viscosity and temperature were ±1.4% and
±0.5%, respectively.
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2.2.2 Capillary Viscometers
a c b
Metered B Volume
C A
2.2(a) 2.2(b)
Figure 2.2 (a) Actual Ubbeholde Viscometer, (b) Schematic of Ubbeholde
Ubbelohde viscometer was used to get the apparent viscosity values in higher shear rate range. Before and after every reading, the viscometer was thoroughly cleaned using distilled water. As HECs are dissolvable in water, the viscometer can be soaked in water over a period to dissolve the polymer stuck on the inner walls. Afterwards acetone was used to rinse and remove water from the capillary. Acetone is a strong dehydrating agent and it also evaporates quickly without any residuals. Clean- dry air can also be used to blow the viscometer tubes for removing any final traces of acetone / water/ dirt.
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After the thorough cleaning, HEC solution was poured in bulb-A till a level somewhere between the two horizontal dotted lines. The solution was then pulled by suction into bulb-B. This was accomplished by closing the opening c and attaching a vacuum ball at opening b. A metered volume of solution was allowed to flow down to bulb-C through the capillary. The flow time was recorded carefully using a stopwatch. This procedure was repeated 5 times for every solution and average of the readings was reported. A set of capillary viscometers was used to get a range of capillary diameters. For every capillary diameter, the velocity of the solution flowing is different and thus gives different shear rates.
The same capillary-tube viscometers were also used for the measurements with weak concentration aqueous solutions so as to obtain the intrinsic viscosity, or the limiting viscosity number of the polymer.
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2.2.3 Data Analysis
For extrapolating the shear thinning trend beyond the measurement limits, equation 2.1 was used . The equation is based on modified cross model (Cross, 1965). This equation considers the pseudoplastic behavior of the aqueous polymer solutions to be comprised of two asymptotes. One being close to zero shear viscosity (region I in fig 2.3) while other is shear thinning gradient (region II in fig 2.3). Confluence of these two asymptotes is given by the exponent ‘p’.
………. (2.1)
The (ηa Vs. ) curves of HEC grades have three prominent regions as shown in fig
2.3. ‘Region I’ is the low shear rate regime, where the solution’s response almost appears to be Newtonian (in reality it’s not) and there is negligible change in viscosity. ‘Region II’ is marked by steep drop in apparent viscosity as response to increasing shear rate. Shear rate at the start of this region is called as ‘critical shear rate- ( c)’. The ‘Region III’, usually hard to achieve by experiments, is the region where the apparent viscosity looks unchanged over any further increase in shear rate and asymptotically reaches its lowest value (η∞).
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Figure 2.3 Usual Viscous Response of HEC to Applied Shear
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2.2.4 Results and discussion
Figure 2.4 Shear Dependent Viscous Behavior of HEC 250-HR, 250-MR and QP-300 at Different Concentrations
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Figure 2.5 Intrinsic viscosity of HEC 250 HR, 250 MR and QP 300. Hollow markers are ‘Huggins plot’ and filled markers are ‘Kraemer plot’
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Along with imparting considerable viscosity to the basic solvent, HECs also show a shear thinning behavior under the applied shear. Looking at shear rate dependent apparent viscosity variation graphs ( ) of the HEC grades, in fig.2.4, it was easily perceived that the solutions of a same grade with higher molar concentrations, are thicker at zero shear rate and possess a higher degree of pseudoplasticity. Considering the three concentrations of
HEC QP-300, plotted in fig 2.4, gives a better understanding of shear-dependent viscosity variation within a same grade of HEC solution. At low shear rates the rheology tends to be
Newtonian, albeit significantly more viscous than the solvent, with shear-thinning behavior manifest at high shear rates. Over a shear rate range of 100 – 1000 s-1, QP-300 shows an apparent viscosity drop of 2.2%, 4.7% and 12.5% for 1.0, 2.5 and 4.0 × 10-3 mols/cc concentrations respectively.
On the other hand, if we keep the molar concentration constant and go to the higher molecular weight HEC solutions, a similar but substantial rise could be seen in the zero shear viscosity as well as the pseudoplasticity of the solutions, table 2.1. For instance, at a same
-9 molar concentration of 2.5×10 mols/cc, zero shear viscosity of QP-300 is 2.10 cP as compared to 11.40 cP of 250-HR (5.7 times that of QP-300) and 4.95 cP of 250-MR (2.5 times that of QP-300). In-spite of having higher in 250-HR and 250-MR, an early and faster thinning was observed in their solutions as compared to QP-300 solutions.
Set-1 in fig 2.4 comprises of three HEC grades 250-HR, 250-MR and QP-300, at
2.5×10-9 mols/cc concentration. All three grades, though at same molar concentration, start to thin down at different shear rates. HR, the heaviest molecule in the set, shows a steeper response to increasing shear. Over a shear rate range of 15 – 100 s-1, 250-HR shows nearly
11.5% drop in apparent viscosity while 250-MR and QP-300 show 4% and 0% drop respectively. Thus, while possessing highest zero shear viscosity (11.40 cP), 250-HR loses its
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viscosity rapidly with increasing shear rate to cross over the ( ) curve of 250-MR (at around 2500 s-1) and eventually QP-300 as well (at around 4500 s-1). Interestingly, this effect reflects quite promisingly in their boiling characteristics plotted in fig. 4.1 and fig. 4.4. At the beginning of nucleate boiling, viscous forces seem to dominate the convective currents and also suppress the bubble growth in the solution lowering the heat transfer capacity of the system.
A more fundamental measure of the ability of a polymer to alter the solvent viscosity in solution is the intrinsic viscosity [η] of the polymer (Mocosko, 1994; Hiemenz, 1997).
Also referred to as the limiting viscosity number, and as Staudinger’s index in older literature
(Ibrahim, 1965), the intrinsic viscosity [η] for HEC grades was determined by measuring the viscosity η with several different weak-concentration aqueous solutions using a capillary viscometer. From these measurements and knowing the solvent viscosity ηs (water in this case), the specific viscosity ηsp and relative viscosity ηrel, respectively, for each dilute concentration solution can be determined as follows:
Thus, by extrapolating the graph of (ηsp/C) vs. C to zero concentration, the intercept of the consequent Huggins plot gives the value for [η]; this can also be obtained from the intercept of the Kraemer plot through the graph of ln[ηrel/C] vs. C. The two plots are given in fig. 2.5.
This limiting value at infinite dilution is a direct measure of the molecular properties of the polymer, and it essentially quantifies the volume occupied by a unit mass of the macromolecule. Higher [η] suggests increased capability of a polymer to enhance the solution viscosity, and in general it is related to the molecular weight or degree of polymerization
(Hiemenz, 1984; De Gennes, 1979; Foroutan 2008).
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INTERFACIAL PROPERTIES OF HEC SOLUTIONS
2.3 DYNAMIC AND EQUILIBRIUM SURFACE TENSION OF HEC
Change in surface tension plays a vital role in boiling characteristics pertaining to its impact on ebullience, and bubble dynamics in general. HECs are surface active in nature.
Aqueous Hydroxyethyl Cellulose (HEC) solutions show 7 to 8 % drop in surface tension than the surface tension of water. This surface active nature is an interfacial phenomenon with molecular chains in the solution showing a natural tendency of getting adsorbed at solid- liquid and liquid-gas interface. Molecular physisorption at gas-liquid interface in HEC solutions results in lowering the surface energy of the interface. The migration is also time dependent and thus gives rise to dynamic surface tension effect.
2.3.1 Maximum Bubble Pressure Method
Maximum bubble pressure method (MBPM) was used to get equilibrium as well as dynamic surface tension values of the polymer solutions. MBPM resembles the actually bubble formation on the heater surface. ‘SensaDyne-QC6000’ instrument, manufactured by Chem-
Dyne Research Corp., was used for the measurements. It gave a wide range of bubble frequencies, commonly encountered in nucleate boiling, useful for mapping the dynamic surface tension inherent to the polymer solutions. A combination of probes with 1mm and
4mm capillary diameters was used for all the measurements. During the measurements, the test fluid is maintained at a constant temperature, which is measured using a well-calibrated thermistor (±0.1˚C precision) attached to the orifice probes. When dry air is bubbled through the orifices, a differential pressure signal is produced, which is proportional to the gas-liquid interfacial tension. Smaller probe (0.5 mm capillary diameter) can be used for σ measurement in surfactant solutions. In case of polymers though, small capillary diameter probes get blocked due to polymer deposition on the inner walls at the orifice.
21
Figure 2.6 Schematic of ‘Sendadyne – QC6000’ used for Equilibrium and Dynamic Surface Tension Measurements
22
2.3.2 Equilibrium Surface Tension Measurement
74
T= 230C 73 σwater = 72.47 mN/m
72
71
70 [mN/m]
σ HEC 250-HR, MW= 1000 kDa 69 HEC 250-MR, MW= 750 kDa 68 HEC QP-300, MW= 600 kDa
67 σequilibrium = 66.8 mN/m
66 10-11 10-10 10-9 C [mols/cc]
Figure 2.7 Equilibrium Surface Tension variations in HECs with Concentration
23
-3 In aqueous HEC solutions, water’s surface tension (σw = 72.4 × 10 N/m) drops down with increasing concentration. Exceeding a certain minimum concentration, known as critical polymer concentration (CPC or C*) surface tension reaches an asymptotic value and will remain stable at that value for any further increase in concentration. This is similar to the critical micelle concentration observed in surfactants. At CPC or C*, polymer agglomeration or coil entanglements begin to form in solution, which would then be in the semi-dilute regime. This interfacial tension relaxation is a diffusion-rate dependent behavior, which is generally governed by the bulk concentration and diffusion-adsorption kinetics of the polymer-solvent systems.
Three grades of HEC when tested for equilibrium surface tension using Maximum
Bubble Pressure Method (MBPM) reached an asymptotic value of 66.8 × 10-3 N/m (7.73 % relaxation) as shown in fig. 2.7. The C* values were determined using the σ vs. C graphs in fig. 2.7, and were found to be 0.35 – 0.45 × 10-9 mol/cc for 250-HR, 0.65 – 0.75 × 10-9 mol/cc for 250-MR and 1.0 – 1.5 × 10-9 mol/cc for QP-300.
The critical overlap concentration can also be determined from the intrinsic viscosity, because [η]-1 approximately represents the concentration within the polymer, or its overlap concentration in a solvent, exceeding which molecules will touch and interpenetrate to form a semi-dilute solution. According to the Einstein model, which considers dilute dispersions of unsolvated spherical particles, when the volume fraction f of the spherical particles is small the relative viscosity is given by the following function.
From the limiting condition of above equation, it can be shown that as υ→0 the overlap concentration can be approximated as C* ≈ 0.25[η]-1.
24
2.3.3 Dynamic Surface Tension Measurement
74
HEC @ 2.5 x 10-9 mol/cc, T = 230 C
σwater = 72.4 mN/m 72
70 250-HR, 2500 wppm
σ [mN/m] σ 250-MR, 1875 wppm
68 QP-300, 1500 wppm
σequilibrium = 66.8 mN/m
66 10-3 10-2 10-1 100 τ [s]
Figure 2.8 Dynamic surface tension of HEC grades at 2.5 × 10-9 mol/cc
25
Surface tension relaxation is a time dependent process. Given a sufficient time, the molecular migration towards the interfaces reaches an equilibrium state. This migration thus becomes a function of the time for which an interface stays in the solution, which is known as ‘surface age (τ)’ of the interface. Under the conditions of insufficient time (low surface age) available for complete migration to take place, surface tension relaxation does not reach the equilibrium value and the interface experiences higher surface tension, closer to the surface tension of solvent water. If we keep on reducing surface age of the interface, eventually it will reach a state at which it will experience the surface tension of water and no surface tension relaxation will take place. This dynamic effect of surface tension in HEC solutions is recorded in fig. 2.8. Generally a surface age of τ > 1.0 s is needed for complete interfacial relaxation, and for τ < 50 ms, the interfacial tension essentially corresponds to that of the solvent (water); the interim period of 50 ms < τ < 1.0 s is characterized by sharp gradients in
σ. It may be noted here that the values for σ at very small surface age are extrapolated from the time-dependent adsorption isotherm fit through the data by the method outlined by Hua and Rosen (1988).
250-HR, with heaviest molecules among the three grades, shows a steep rise in dynamic surface tension relaxation on a reducing surface age scale; followed by 250-MR and
QP-300. At the concentration of 2.5×10-9 mol/cc, 250-HR jumps to the solvent water’s surface tension within the surface age range of 1 – 0.03s, for which 250-MR takes 1 – 0.005s and QP-300 takes around 1 – 0.001s range. This dynamic nature of surface tension shows its effect during boiling as the bubbling frequency increases with increasing surface heat flux of the heater.
26
Figure 2.9 Dynamic surface tension of aqueous HEC QP-300 solutions at different
concentrations.
27
The change in surface tension with surface age, or the time period of a newly formed bubble from inception to departure, is graphed in fig.2.9 for aqueous solutions of HEC QP-
300 with bulk concentrations of 1.0×10-9 ≤ C ≤ 4.0×10-9 mol/cc. It is seen that a finite time is required for complete interface relaxation, as to attain an equilibrium between the surface and bulk concentrations. This dynamic surface tension behavior, facilitated and governed by the molecular mobility of the polymer in solution and its interfacial adsorption (Miller and
Neogi, 1985; Miller and Fainerman 1994; Manglik et al., 2001), lends to the modification of ebullience and the attendant boiling heat transfer.
28
2.4 SURFACE WETTABILITY
Surface wettability is an ability of a fluid to wet a surface it comes in contact with. In
the boiling process, wettability has its importance at the nucleation phase. A cavity on the
heater surface will start generating bubbles only after the wall superheat dominates over
the surface wetting forces. For a specific cavity, highly wetting surface-fluid combination
will flush its volume completely while a low wetting solution will remain at the outer
edge of the cavity due to the surface active forces.
Figure 2.10 Interfacial Stresses
29
2.4.1 Contact Angle Measurement
Akin to the molecular adsorption at gas-liquid interface, polymer solutions also show molecular migration towards solid-liquid interface. This peculiar property of polymer solutions results in change in surface wettability of the parent solvent, which can be measured in terms of contact angle θ. In the present study the contact angle is measured with sessile drop method by placing a droplet of the solution on a stainless steel substrate, and is plotted in fig.2.11. Contact angle measurements were accomplished by using a simple Goniometer. A small drop of the test solution (2-3 μL volume) was carefully placed on a steel specimen held under the goniometer lens. One minute settling time was allowed after the droplet is placed on the substrate. Goniometer radius line was aligned tangentially to edge of the droplet, touching the steel specimen. Contact angle was then measured from the angular scale engraved on the eyepiece. The minimum precision in this measurement was ±0.5˚
30
78
T - 23 oC 0 θwater= 77 77
76
75
[degrees] θ 74 HEC 250-HR, MW = 1000 kDa
HEC 250-MR, MW = 750 kDa 73
HEC QP-300, MW = 600 kDa Substrate: Stainless Steel
72 10-10 10-9 C [mols/cc]
Figure 2.11 Contact angle variations with concentration of aqueous HEC solutions
31
The contact angle relaxation for the aqueous polymer solutions considered here was observed to be 4 to 5 % from that of water (θwater = 77˚). With increasing concentration, the solutions reach an asymptotic value near C*. This minimum contact angle plateau is attained when C > C* (the overlap concentration), where molecular agglomeration of the polymer begins to form in solution. This is representative of typical physisorption behavior of surface- active solutes at liquid-solid interfaces, and where wetting is influenced by the kinetics of interfacial molecular adsorption (Kwok, 1999; Lee 2008).
32
CHAPTER 3
NUCLEATE POOL BOILING HEAT TRANSFER IN WATER
Nucleate pool boiling experiment was initially conducted with distilled deionized
water. A reference boiling curve ( vs. ∆T) was generated for water and was verified every time when the apparatus was disassembled- assembled for cleaning. The experiments were conducted at atmospheric pressure over a horizontal cylindrical heater centrally located in a pool of distilled de-ionized water.
3.1 Nucleate Pool Boiling Experiment
3.1.1 Experimental Setup
Figure 3.1 shows the experimental setup for nucleate pool boiling. It was made using two large glass vessels. The small vessel (230 x 170 x 310 mm) was positioned inside the large one (300 x 300 x 290 mm). The gap between the two vessels was filled with silicon oil
(50 cSt). The oil was maintained at an elevated temperature (~1350 C) above the saturation temperature of the test fluid, which worked as a thermal jacket around the pool. NESLAB’s
RTE-221 oil bath circulator was used for heating and circulating the silicon oil so as to maintain a uniform and constant temperature throughout the oil bath.
An auxiliary heater, immersed in the pool, was used to heat up the pool quickly to its saturation temperature (oil bath alone takes much longer time). A simple plastic tube manometer was designed and installed on the apparatus to monitors the pool pressure up to
.001 atm (5mm of water column) visual accuracy. Two water cooled condensers were used to condense back the vapor, generated during boiling, and return the condensate to the pool.
One of the condensers is outside the pool enclosure while the other is inside the pool enclosure hanging by the lid approximately 10cm above the pool level.
33
Figure 3.1 Schematic of Pool Boiling Apparatus
FIGURE 3.2 Schematic diagram of cylindrical heater
34
3.1.2 Heater design
The cylindrical heater used in the pool boiling experiment has a peculiar design as shown in the diagram above. A cylindrical cartridge heater, available in the market, was tightly fitted inside a copper sleeve. The outer surface of the sleeve was coated with 0.127 mm thick gold plating to prevent corrosion. The cartridge heater with 88.9 mm length and
22.2 mm diameter had a capacity of 1500 W at 240 V. Three holes were drilled along the length of the sleeve for fitting in the thermocouples. After inserting the thermocouples, the holes were filled with thermal grease (OMEGATHERM-201) with extremely high thermal conductivity (16 BTU-in/ hr-ft2-0F) and with very high electrical insulation (1014 ohm-cm).
The heater was mounted on a Teflon block, as shown in the schematic diagram, hanging by the two stainless-steel rods attached to the lid.
35
3.1.3 Data Acquisition System
Temperature measurement was done using T- type thermocouples with an accuracy of 0.5˚C, manufactured by OMEGA Inc. Three thermocouples were immersed in the pool while other three were fitted on the heater just below the surface. National Instruments’ (NI) 4051-X hardware was used to process the voltages generated by the thermocouples which was then recorded by using a virtual instrument programmed in NI’s LABVIEW software.
Heater current measurement was done using NI’s 4051-X hardware and a virtual digital multi-meter (DMM) programmed in LABVIEW. As the current flowing through the heater is quite large to be measured directly using an ammeter, a junction box with a current shunt was introduced in the circuitry. The NI hardware actually measured a voltage drop across the current shunt (0.15 Ω, with 1% accuracy). This voltage drop was then scaled to the relative value of electric current through the circuit by simply dividing it with the shunt resistance, which was 0.15Ω in this case.
The Voltage supplied to the heater was directly measured using a simple DMM fitted across the voltage variac (Transformer).
36
Figure 3.3 Schematic of electrical circuit used to vary heat input during boiling experiment
37
3.1.4 Photographic Record of Boiling
PULNiX TMC-7 series CCD camera was used to capture bubble dynamics during boiling. It provided a resolution of 768(H) x 494(V) pixels. The camera had 8 (0-7) different shutter speeds with the fastest being 1/10,000 sec. It was fitted with FUJI 12.5mm x 75mm zooming lens for clearer and closer images. The camera was interfaced with a PC using a
USB based digital surveillance system ‘DQP-A4 Premier’.
Images were taken for all the stages during the boiling runs. It helped exploring the nature of boiling in terms of recording the changes in bubble size, shape, coalescence and roughly estimating the bubble frequency.
38
Figure 3.4. Schematic of setup for CCD camera capturing bubbling activity during boiling\
39
3.1.5 Experimental procedure
Inner pool was always maintained at 6 liters level. This kept a constant hydrostatic head over the heater for all the experimental runs. The pool was slowly heated using the oil bath and the auxiliary heater, which takes around two and half hours to reach the saturation temperature. Afterwards the pool was thoroughly degassed using the auxiliary heater for 2 to
3 hours till there are no visual traces of trapped air or dissolved gases. At the end of degasification the main heater was also switched on to half of its maximum heat flux capacity for half an hour. Both the heaters were then switched off and the system was left still to attain equilibrium.
After this initial preparation, the pool boiling experiment was started by switching on the main heater. The voltage input to the main heater was increased in predetermined steps to clearly observe various stages in nucleate boiling. 30 – 40 minutes interval was given after each voltage increment to allow the system to attain equilibrium. It was observed that at higher heat fluxes system requires lesser time to reach equilibrium.
Initially nucleate pool boiling runs were conducted with distilled deionized water.
Multiple water runs were conducted over a period of six months to check the repeatability and to establish the effects of aging of the heater surface. 10 % of degradation in heat transfer was observed over the period with an excellent repeatability as the heater surface got older.
When compared, the water boiling data showed a good agreement with the boiling curves generated using different nucleate pool boiling correlations proposed by Rohsenow (1952),
Borishanskii (1969), Cooper (1984) and Cornwell- Houston (1994).
A calibration water boiling run was conducted every time the system was opened and cleaned. Excellent repeatability was observed for all the water runs. This ensured the calibration of entire boiling apparatus during the pool boiling of polymer solutions.
40
3.2 Nucleate Pool Boiling of Water and Boiling Correlations
First recorded study of nucleate pool boiling of water was reported by Nukiyama
(1934). He successfully traversed the entire nucleate pool boiling curve with all the phases of boiling revealing the critical heat flux phenomenon. Nukiyama conducted his experiments with a wire heater and a plate heater and carefully recorded all the observations. He reported that the nucleate pool boiling regime has the highest heat transfer coefficient and it was limited by a maximum value above which an abrupt rise in ∆T was observed. In later years, nucleate pool boiling received much attention owing to its high heat transfer efficiency and its intriguing unpredictable nature. Efforts were made to understand the nucleation process, bubble growth and the heat and mass transport mechanisms. Various studies reported the roles of different factors in pool boiling like heater surface condition, heater material, sub- atmospheric or super-atmospheric pool pressures, pool sub-cooling and the thermo-physical properties of water / vapor generated in the process. This led to a vast array of nucleate pool boiling correlations based on above mentioned factors, among others.
3.2.1 Literature survey of Nucleate Pool Boiling Correlations
3.2.1.1 Rohsenow’s Correlation:
Rohsenow in 1952 proposed a correlation for nucleate pool boiling which has been widely accepted and publicized. Rohsenow based his correlation on different fluid properties like density, surface tension, viscosity and thermal conductivity and incorporated an equation coefficient (Csf) which was a function of particular heater surface- fluid combination. An extended study has been done till now on Rohsenow’s correlation questioning its applicability to vast variety of systems. In later studies, many other researchers proposed their own correlations for nucleate boiling heat transfer specific to the systems used for study. In this chapter, water boiling data generated during the experimentation has been compared with
41
some of the correlations applicable to the system used. Rohsenow’s correlation was plotted using the Csf values given by Vachon (1968), for different ‘heater surface-fluid’ combinations. Correlations formulated by Borishanskii (1969), Cooper (1984) and Cornwell-
Houston (1994) were also included in the comparison. Pertaining to the dependence of boiling phenomenon on the system, the current experimental data did falls within the band generated by the correlations.
3.2.1.2 Borishanskii’ Correlation:
Borishanskii (1969) used ‘Reduced Pressure (Pr)’, the ratio of system pressure and critical pressure (P / Pcr), as a driving factor in predicting nucleate pool boiling. Pcr is the pressure at which latent heat of vaporization is zero and fluid directly flashes into gaseous phase. It also represents the minimum pressure required to liquefy vapor at critical temperature. The only difficulty in using this correlation is determining Pcr for fluid mixtures and solutions. Critical pressures of pure fluids are easily available in the literature. In the present comparison, Borishanskii’s correlation predicted an enhanced heat transfer coefficient over the experimental data of water (Pcr = 217.4 bars).
42
200
Rohsenow (1952) Borishanskii (1969) Cooper (1984) 100 Cornwell & Houston (1994) Run 1 Run 1 d
Run 2 ] 2 Run 3
Run 4
[kW/m
w
" q
Distilled water
o Tsat = 100 C 10 p = 1 atm Rp = 0.244 μm 8 1 ∆Tw [K] 10 20
Figure 3.5. Pool boiling data of distilled de-ionized water in comparison with different pool boiling correlations
43
Table 3.1 List of Nucleate Pool Boiling Correlations compared with the data from present study
Rohsenow (1952)
Can also be written as,
Borishanskii (1969) Where,
(Pressure in bars)
Cooper (1984) Also,
Where,
Cornwell and Houston (1984)
44
3.2.1.3 Cooper’s Correlation:
Cooper (1984) formulated a correlation with inherent simplicity based on only three factors viz. reduced pressure, molecular weight and surface roughness of the heater. The correlation does not involve any thermo-physical property of the test fluid. According to
Cooper, the fluid properties which are normally used in boiling correlations like density, latent heat, viscosity, surface tension and thermal conductivity can be expressed as products of powers of Tr, Pr and (1-Tr). Out of these, effects of Tr and (1-Tr) can be omitted being insignificant in comparison with the effect of Pr. Inculcation of molecular weight in the correlation was based on his observations about a definite trend of heat transfer degradation with increasing molecular weight of the test fluids. Heater surface roughness (Rp) used in the correlation accounts for the effect of heater surface on boiling heat transfer, which was incorporated by Rohsenow in the form of coefficient (Csf).
The Cooper’s correlation satisfactorily matched with the existing water pool boiling data, on using the surface roughness value indicated on the graph. It was an average of roughness values measured at five different points on the heater surface, scattered axially as well as radially. In many cases, difficulty in measuring surface roughness accounts for an error in predicting heat transfer coefficient by using Cooper’s correlation. Nevertheless, simplicity provided by this correlation is highly appreciated in the boiling research field.
3.2.1.4 Cornwell-Houston Correlation:
The Cornwell-Houston correlation (1994), included in the comparison, shows a good agreement with the experimental data. The correlation is based on pool boiling on horizontal tubes which is similar to the horizontal cylindrical heater used in this study. It takes into consideration the heater diameter, test fluid viscosity, latent heat along with critical and reduced pressures used in previous correlations. In case of horizontal heater, the sweeping
45
vapors have considerable influence on heat transfer. The bubble layer model considered by
Cornwell and Houston in developing the correlation takes into consideration the boiling
Reynolds number (Reb) of this flow of vapor mass sweeping along the heater surface.
Figure 3.6. Sweeping vapor mass along cylindrical heater surface (courtesy- Cornwell-Houston (1994))
A detail list of correlations available in the literatures till date is given in appendix III.
Most of the correlations are system specific and are not universally applicable considering the wide range of boiling applications. This makes an experimental study unavoidable in the cases where a new fluid-heater surface combination is used or a different heater shape, size, orientation, system pressure and pool dimensions are implemented. The four correlations, selected for the above discussion, are specifically derived for the systems close to the boiling apparatus used in the present study and agree with the data within an acceptable error band.
46
CHAPTER 4
POOL BOILING OF AQUEOUS POLYMERIC SOLUTIONS
Three grades of Hydroxyethyl cellulose (HEC) are used in the present study viz. 250-
HR, 250-MR and QP-300. All the three grades have an identical monomer with idealized molecular structure as shown in fig 1.2. Degree of polymerization though, varies from grade to grade giving different molecular weights; which is 1000 g/mol, 750 g/mol and 600 g/mol for the three HEC grades mentioned above.
Aqueous polymeric solution for the boiling experiment was prepared using two large glass beakers each filled with three liters of distilled de-ionized water. A precisely measured quantity of HEC powder was slowly added to the beaker by measuring on a high precision electronic weighing scale with ± 0.01 gm accuracy. On hydration, HECs have a tendency of forming lumps which are difficult to dissolve. Hence water was stirred vigorously while adding HEC powder to avoid any lump formation. Once the polymer powder disperses evenly, a sufficient speed was maintained to keep all the polymer mass moving continuously.
Approximately 4 hours of stirring is required for complete hydration of HEC. The solution was then allowed to age overnight, keeping the stirrer ON at slow speeds.
47
4.1 Nucleate Pool Boiling of Aqueous HEC QP-300 solutions
200
HEC QP-300
1.0 × 10-9 mols/cc 100 2.5 × 10-9 mols/cc
4.0 × 10-9 mols/cc
Zhang and Manglik [5] -9
] 5.0 × 10 mols/cc 2
Water
[kW/m
w
" q
10
Tsat = 100˚C
P = 1 atm
3 1 10 20 ∆Tw [K] Figure 4.1 Pool boiling curves for aqueous HEC QP-300 solutions at different concentrations, and distilled, deionized water
48
In general, the changes in surface tension and rheology of the liquid, and heater surface wettability alter the boiling behavior of a liquid. While wetting of the heater surface controls nucleation and the site density thereof, gas-liquid interfacial tension and shear- dependent viscosity of a polymeric solution alters the post-nucleated bubble dynamics
(Zhang and Manglik, 2005). This is implicit in the post boiling curves presented in fig.4.1 for different concentrations of aqueous HEC QP-300 solutions, along with that for distilled
-9 and deionized water. The substantial leftward shift in the curve for C = 1.0×10 mol/cc (~C* or CPC) relative to that for water is indicative of the heat transfer enhancement over the entire range of heat flux considered in the experiments. This represents the largest overall enhancement, which is consistent with previous finding that the highest boiling performance is attained with critical or overlap concentration of the polymer (Zhang and
Manglik, 2005). However, an anomalous boiling behavior is seen in solutions with higher concentration (C = 2.5×10-9 and 4.0×10-9 mol/cc). There is a significant rightward shift with heat transfer even less than water in the low-heat-flux, partial boiling regime, but much larger enhancement, relative to that with C*, at higher hear fluxes ( > 100 kW/m2) or the fully developed boiling regime.
49
0.5
o HEC QP-300 @ Tsat = 100 C
0.4 1.0 × 10-9 mols/cc
2.5 × 10-9 mols/cc
4.0 × 10-9 mols/cc 0.3 Zhang and Manglik [5]
1.0 × 10-9 mols/cc
w ) / h / )
w 0.2
h
- (h
0.1
0
-0.1 100 101 102 q" [kW/m2] w Figure 4.2 Variation of dimensionless enhancement of heat transfer coefficient with heat flux in aqueous solutions of HEC QP-300 with different concentration
50
A much clearer and quantitatively amplified delineation of the boiling performance in the three different concentrations of HEC QP-300, relative to that in water, is given in fig.4.2.
The variation of the enhanced heat transfer coefficient, given by the dimensionless [(h-hw) /
hw], with heater wall heat flux is graphed. The consistent and virtually constant enhancement of about 20% in the 1.0×10-9 mol/cc (~ C*) aqueous solution is evident in fig.4.2, along with the agreement with previous data by Zhang and Manglik (2005). A more curiously unexpected set of results are those for C = 2.5×10-9 and 4.0×10-9 mol/cc, where
2 there is a deterioration in heat transfer when < 30 kW/m but much larger enhancement
* 2 than that with C when > 100 kW/m . The higher of the two concentrations lends to about
2 6% decrease in heat transfer when compared with water for 7 < < 30 100 kW/m . This is a direct consequence of the higher polymeric solution viscosity (2 – 3 × water, as seen in fig.2.4) at low shear rates at the liquid-vapor interface of ebullient transport in the partial boiling regime. With increasing heat flux and hence larger vapor generation, the shear rate increases and thereby the viscosity of the shear-thinning solutions decrease; at very high shear rates the higher concentration solution even becomes less viscous than the lower C ones
(fig.2.4). As a result, the retarding viscous forces become less significant and the low surface-
2 tension-driven enhancement is re-established with peak performance when > 100 kW/m .
51
q” Water HEC QP-300 2 (kW/m ) 1.0 × 10-9 2.5 × 10-9 4.0 × 10-9 mols/cc mols/cc mols/cc
20
40
115
Figure 4.3 Visual characteristics of bubbling behavior during boiling of aqueous HEC QP- 300 solutions of different concentrations
52
The nucleate boiling performance can further be characterized by the respective ebullient signatures in the three solutions at different heat fluxes. Photographic records of the
2 boiling history for increasing heat flux ( = 20, 40 and 115 kW/m ) are presented in fig.4.3.
The bubble generation features (shape, size, coalescence, and surface density and distribution) in the polymer solutions are seen to be very distinct from that in water. The boiling is more vigorous in C ~ C* (= 1.0×10-9 mol/cc) solutions, which is distinguished by smaller bubble production, spread over a wider portion of the heater surface. There is reduced coalescence of bubbles that have higher departure frequency, both outcomes of reduced liquid-vapor interfacial tension. Also, molecular physisorption of the polymer on the heater surface may contribute to the formation of new sites (Shul’man et al., 1993; Levitskiy et al.,
1996) which would perhaps account for the increase in number of nucleation sites despite a slight increase in the surface wettability (as measured by the contact angle; fig.2.11).
However, in the larger concentration solutions (C = 2.5×10-9 and 4.0×10-9 mol/cc) and at a low heat flux of 20 kW/m2, the extent of bubbling activity decreases substantially. This is possibly due to the increased viscosity of the higher concentration polymer solution which tends to suppress the nucleation and growth of vapor bubbles; this then leads to increasing deterioration of boiling performance with C at the low heat flux. The higher shear rate
2 associated with greater vapor generation when ≥ 40 kW/m , however, lowers the viscosity of the pseudoplastic solutions and the bubbling activity again increases. The shear thinning is more pronounced in the C = 4.0×10-9 mol/cc solution, thereby further intensifying the ebullience and the boiling heat transfer.
53
4.2 Nucleate Pool Boiling of Aqueous Solutions of different HEC grades
200
HEC 250-HR, M = 1000 kDa
HEC 250-MR, M = 750 kDa 100 HEC QP-300, M = 600 kDa
water
C = 2.5 x 10-9 mols/cc
]
2
[kW/m
" q
10
0 Tsat = 100 C
P = 1 atm
3 1 ∆T [K] 10 20 w
Figure 4.4 Pool boiling curves for aqueous HEC solutions at 2.5 × 10-9 mols/cc
54
While plotting the boiling characteristics of 250-HR, 250-MR and QP-300 at same molar concentration of 2.5 × 10-9 mol/cc and comparing them with the boiling characteristic of water, as shown in fig.4.4, a signature behavior was observed for all the solutions. As it was observed during experimentation, boiling subjects the solutions to a range of bubbling frequencies and hence a range of shear rates to which the solutions respond in a peculiar manner. Figure 4.5 compares dimensionless hear transfer coefficients of the three solutions and of deionized distilled water. All the solutions showed decreased heat transfer from ebullience to partial boiling regime. Higher viscosity solutions like 250-HR and 250-MR tend to show higher degradation in heat transfer. 250-HR shows maximum heat transfer degradation of 12.5 % at 20 kW/m2 wall heat flux while 250-MR and QP-300 show 8.8% and
0.4% degradation at the same wall heat flux respectively. This is possibly a result of suppression of bubble growth and the overall bubble movement due to the higher solution viscosity; restricting the heat removal process from the heater surface.
55
0.4
HEC QP-300, MW= 600 kDa
0.3 HEC 250-MR, MW= 750 kDa
HEC 250-HR, MW= 1000 kDa
0.2 C = 2.5 x 10-9 mols/cc
w ) / h )h /
w 0.1
h h
- (h
0
-0.1
0 Tsat = 100 C
-0.2 100 101 102 q" [kW/m2] w
Figure 4.5 Variation of dimensionless enhancement of heat transfer coefficient with heat flux
in aqueous HEC solutions at 2.5 × 10-9 mols/cc
56
An exactly opposite trend was observed over the wall heat flux of 25 kW/m2 and above. All the three solutions begin to show improvement in heat transfer coefficients, exceeding that
2 2 2 water at > 30 kW/m for QP-300, > 40 kW/m for 250-MR and > 50 kW/m for
250-HR. The recovery of heat transfer coefficient was faster in 250-HR, pertaining to the quick loss of viscosity as response to increasing shear rates at high heat fluxes, generated by higher bubbling activity. A similar behavior was also observed in 250-MR, and in QP-300, but on a smaller scale. At a heat flux of 70 kW/m2 enhancement in 250-HR solution even exceeds the enhancement in 250-MR. This can be a attributed to the highly pseudoplastic nature of 250-HR causing its viscosity to drop below that of 250-MR. The polymer solutions continued the trend of giving heat transfer enhancement with higher heat fluxes, with QP-300 giving the highest heat transfer enhancement of 31.5 % at the wall heat flux of 170 kW/m2.
57
q” C = 2.5 10-9 mols/cc (kW/m2) Water HEC- QP 300 HEC- 250 MR HEC- 250 HR
10
40
80
160
Figure 4.6 Visual characteristics of bubbling behavior during boiling of aqueous HEC grades
at 2.5 × 10-9 mols/cc
58
Figure 4.6 compiles the photographic records of the boiling experiments at = 10,
40, 80 and 160 kW/m2. The bubble generation features (shape, size, coalescence, and surface density and distribution) in the polymer solutions are seen to be very distinct from that in water. There is reduced coalescence of bubbles that have higher departure frequency, both outcomes of reduced liquid-vapor interfacial tension. Also, molecular physisorption of the polymer on the heater surface contributes to the formation of new sites (Kotchaphakdee and
Williams, 1970; Zhang and Manglik, 2005) which would perhaps account for the increase in number of nucleation sites despite a slight increase in the surface wettability (as measured by the contact angle; fig.2.11). In spite of being at a same molar concentration, QP-300 solution shows noticeably higher bubble density over the entire range of heat flux. Solution of 250-
HR shows less bubbling activity at low heat fluxes, which can be perceived as an effect of higher viscous forces. For heat flux of 80 kW/m2 and above, the bubbling activity in 250-HR solution jumps up, pertaining to the shear thinning nature of the solution.
59
200
HEC 250-MR, M = 750 kDa
100 HEC QP-300, M = 600 kDa
water
C = 2.5 x 10-9 mols/cc
]
2
[kW/m
" q
10
0 Tsat = 100 C
P = 1 atm
3
1 ∆Tw [K] 10 20
Figure 4.7 Pool boiling curves for aqueous HEC solutions at 4.0 × 10-9 mols/cc
60
0.5
HEC QP-300, MW = 600 kDa 0.4 HEC 250-MR, MW = 750 kDa
-9
0.3 C = 4.0 x 10 mols/cc w
0.2
) / h )h /
w h h
- 0.1 (h
0
-0.1 0 Tsat = 100 C
-0.2 100 101 102 " 2 q w [kW/m ]
Figure 4.8 Variation of dimensionless enhancement of heat transfer coefficient with heat flux
in aqueous HEC solutions at 4.0 × 10-9 mol/cc
61
C = 4.0 10-9 mols/cc q” Water HEC- 250 MR HEC- QP 300 (kW/m2)
10
40
80
160
Figure 4.9 Visual characteristics of bubbling behavior during boiling of aqueous HEC grades
at 4.0 × 10-9 mol/cc
62
A similar experimental study was conducted with two HEC grades, 250-MR and QP-
300, at a higher molar concentration of 4.0 × 10-9 mol/cc. The results are plotted in fig.4.7.
2 Akin to the prior set, both the solutions show the heat transfer degradation at < 20 kW/m .
The change of trend of the heat transfer coefficient is also similar with both the solutions
2 giving enhancement in heat transfer for > 40 kW/m . Apparent viscosity of 250-MR drops by 6.15 % over shear rate range of 15 – 100 s-1 while QP-300 show a drop of 1.6 % over the same shear rate range, fig.2.4. This rapid shear thinning of 250-MR explains its faster heat transfer recovery over increasing hear flux, resulting in heat transfer enhancement
2 2 almost as equivalent as QP-300 over the range of 30 kW/m < < 100 kW/m . An
2 exceedingly higher enhancement was shown by QP-300 for > 100 kW/m . This can be attributed to the small size, regularly shaped bubbling with lesser coalescence, evidently seen in the pictorial comparison shown in fig.4.9. It records less coalescence and higher nucleation density in HEC QP-300 solutions. Higher grades polymer solutions seem to generate smaller bubbles but with increased coalescence. This can result in forming a partial vapor jacket over the heater surface causing decreased heat transfer.
63
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
Conclusions
Boiling behavior of water was found to alter significantly on addition of high as well as low concentrations of HEC grades. Different case studies presented here gave a spectrum of results which can be summarized as follows:
1. That different bulk concentrations of the HEC QP-300 in water anomalistically alter
the nucleate boiling performance is evident from the results (fig.4.1 – 4.3). The
rheological behavior of the solution provides the primary influence, where the shear-
thinning behavior affects different boiling regimes differentially. The pseudoplasticity
in turn increases with polymer concentration. Furthermore, the reduction in dynamic
surface tension (which decreases the required superheat for the onset of boiling), and
possibly the macromolecular physisorption of the polymer onto the heating surface (
perhaps aid to the formation of new nucleation sites and increased bubble frequency)
are also the controlling factors for the boiling heat transfer enhancement in lower
concentrations (c ~ c*) solutions. Improvements in the boiling performance ranging
from 19% - 22% were obtained with C = 1.0 × 10-9 mols/cc over the heat flux range
of the experiments. On the other hand, the decreases in the nucleate boiling heat
transfer coefficients with higher concentrations (c > c*) at low heat flux levels are due
to the viscous suppression of micro-convection in the bubble boundary layer and the
growth of vapor bubbles. This decreased ebullience gets enhanced at higher heat
2 2 fluxes (> 40 kW/m ) with peak performance when > 100 kW/m ; up to 45%
increase in the boiling heat transfer coefficient is obtained with C = 4.0 × 10-9mols/cc.
64
2. From the observations of the experimental study with polymeric solutions at
concentrations 3 – 6 times higher than C*, it can be concluded that the viscous forces
are the main dictating factors in deciding boiling characteristics; specially at low heat
fluxes (< 100 kW/m2). Pseudoplastic behavior of polymer solutions generates a
peculiar nature of boiling characteristics with initial deterioration in heat transfer and,
subsequent recovery and enhancement. At the concentration of 2.5 × 10-9 mols/cc
maximum heat transfer deterioration of 12.5% was observed in HEC 250-HR solution
while maximum heat transfer enhancement of 31.5% was observed in HEC QP-300
solution, at the same concentration. Within the second set of polymers at
concentration 4.0 × 10-9 mols/cc, HEC 250-MR showed maximum degradation of
13.1% while HEC QP-300 showed maximum enhancement of 45.0%.
Overall, it can be concluded that the heat transfer coefficient is greatly influenced by
degree of polymerization of the dissolved polymer chains.
3. A significant enhancement was obtained at higher heat fluxes which could be
attributed to the shear-thinning effect as well as the surface tension forces coming
back in action. Peak performance was given by HEC QP-300 in both the sets with
42.9% higher enhancement at 4.0 × 10-9 mols/cc than the enhancement at 2.5 × 10-9
mols/cc concentration.
65
Recommendations for Future Work
Pool boiling is a complex and hence difficult to predict phenomenon. Involvement of large number of factors like thermophysical properties of the boiling fluid and surface properties of the heater surface, along with system specific properties, make boiling process complicated to control and less repetitious. Present investigative study was conducted by fixing some of these factors as system invariants. Future work can target to change and reach beyond the limits of present study and explore the boiling phenomenon to greater depths.
On the basis of the conclusions from the present study, the future work in this field can be directed on the following lines:
1. A focused study can be made to understand the molecular migration at solid-liquid
interface using different metallic substrates. Also, temperature based migration can be
tracked that can tell us about the effect of temperature on the molecular mobility.
2. Viscous behavior of the polymer solutions can be mapped experimentally, and in an
elaborate manner, that will unleash the pseudoplastic response close to the infinite
shear rate asymptote of apparent viscosity.
3. Heat flux range can be extended to reach near the critical heat flux (CHF) to gauge the
effect of polymer molecules near CHF.
4. A generalized correlation can be reached for pool boiling with aqueous polymeric
solutions, which would enable us to perform computational simulations for any
required polymer type and at any given concentrations.
66
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69
APPENDIX A
UNCERTAINTY ANALYSIS
Uncertainty analysis is a powerful tool in experimental work. It can be implemented right from the planning stage of an experiment for checking the final data recorded. It is useful in knowing the accuracy of experiments beforehand and thus can give a fair idea about usefulness of data generated. As rightly conceived by Kline (1985), uncertainty analysis is an essential ingredient in planning, controlling and reporting experiments. Uncertainty in a given measurement ensures that the measured value is certain to lie within the ± interval stated by uncertainty. It is said correctly that uncertainty analysis empowers experimenter to make completely certain statements.
Uncertainty in single measurement like length, angle, etc. is half the least count of measurement. In the present experimental data where we calculate quantities like heat flux by multiplying readings taken for V, I and area (A), we analyzed the results by the single-sample error propagation method. The method was outlined by R. J. Moffat (1988) and used by V.
M. Wasekar (2001) in his doctorate thesis. The method involves an estimation of overall uncertainty δR in a calculated result R using the following equation:
………. (A.1)
70
Where,
……… (A.2)
As pointed out by above equations, the uncertainty in the final data is a product of uncertainties involved in measuring the primary physical constants and the direct or assumed values used in the calculations. These uncertainties propagate through the data reduction equations into the end results.
Table A.1. Measurement uncertainties in experimental parameters
Parameter (R) Range/Nominal value Uncertainty (δR)
V (volts) 40-240 ± 1.5%
T (˚C) 100-114 ± 0.1
D (mm) 22.17 ± 0.0254
L (mm) 95 ± 0.0254
Rp (Ω) 0.15 ± 0.1%
A (m2) 6.6256 × 10-3 ± 0.12 %
I (A) 0.5 - 5.5 ± 2.6 % - ± 2.38 %
2 (kW/m ) 4 - 230 ± 1.44 % - ± 0.01 %
71
Uncertainty in Measuring Heat Flux
………. (A.3)
Above equation was used to calculate the heat flux on the surface of the heater. There are uncertainties involved in the measurement of the basic parameters voltage (V), current (I) and
area of the heater (A). These uncertainties will flow down in the calculations of to
generate an uncertainty in the final recorded values of . Equations (A.1) and (A.2) are used in this case to calculate this final uncertainty. The maximum experimental uncertainties calculated by this method are listed in table A.1.
72
APPENDIX B
DATA COMPILATION
APPARENT VISCOSITY (ηapp Vs. ) DATA
C = 2.5 × 10-9 mol/cc HEC QP-300 HEC 250-MR HEC 250-HR -1 -1 -1 [s ] ηapp [cP] [s ] ηapp [cP] [s ] ηapp [cP] 15.85 2.10 15.85 5.00 4.64 11.75 25.12 2.10 25.12 4.95 6.81 11.62 39.81 2.10 39.81 4.90 10.00 11.54 63.10 2.10 63.10 4.85 14.68 11.40 100.00 2.10 100.00 4.80 21.54 11.22 158.50 2.05 138.62 4.76 31.62 11.05 251.20 2.02 318.41 4.48 46.42 10.84 327.60 2.01 503.44 4.30 68.13 10.53 737.90 1.94 665.90 3.98 100.00 10.20 1135.50 1.91 1008.25 3.63 138.47 10.01 1443.70 1.83 232.92 9.02
2072.50 1.76 302.47 8.50
466.31 7.62
73
C = 4.0× 10-9 mols/cc HEC QP-300 HEC 250-MR -1 -1 [s ] ηapp [cP] [s ] ηapp [cP] 15.00 3.20 5.97 9.84 20.00 3.20 9.46 9.78 50.00 3.20 15.00 9.65 100.00 3.15 23.77 9.52 150.00 3.12 37.68 9.39 215.50 3.09 59.72 9.25 461.00 2.98 72.70 9.20 748.80 2.88 164.20 8.67 976.00 2.75 272.70 7.93 1434.00 2.55 361.00 7.34 548.60 6.67
HEC QP-300 1.0 × 10-9 mols/cc -1 s ηapp (cP) 15.00 1.35 20.00 1.35 50.00 1.35 100.00 1.35 150.00 1.35 488.54 1.35 1081.34 1.32 1658.16 1.30 2076.90 1.28 2891.87 1.27
74
INTRINSIC VISCOSITY DATA
75
EQUILIBRIUM SURFACE TENSION στ → ∞ (mN/m) DATA
HEC 250-HR C [wppm] C × 109 [mol/cc] σ [mN/m] 3000 3.00 66.80 2500 2.50 66.80 2000 2.00 67.11 1700 1.70 67.10 1350 1.35 67.17 1000 1.00 67.43 850 0.85 67.36 700 0.70 67.46 600 0.60 67.68 500 0.50 67.68 400 0.40 67.94 350 0.35 68.30 300 0.30 68.67 270 0.27 69.17 230 0.23 69.86 200 0.20 70.74 170 0.17 71.67 130 0.13 72.10 100 0.10 72.21
76
HEC 250-MR C [wppm] C × 109 [mol/cc] σ [mN/m] 3000 4.00 66.80 2750 3.67 66.77 2500 3.33 66.78 2250 3.00 66.90 2000 2.67 66.78 1750 2.33 66.95 1350 1.80 67.01 1000 1.33 67.20 800 1.07 67.40 700 0.93 67.53 600 0.80 67.74 500 0.67 67.94 400 0.53 68.64 350 0.47 69.16 300 0.40 69.80 250 0.33 71.00 200 0.27 72.06 150 0.20 72.33 50 0.07 72.40
77
HEC QP-300 C [wppm] C × 109 [mol/cc] σ [mN/m] 2400 4.00 66.80 2000 3.33 66.90 1500 2.50 67.00 1200 2.00 67.10 1000 1.67 67.20 700 1.17 67.60 600 1.00 67.80 500 0.83 68.40 400 0.67 69.60 250 0.42 71.50 150 0.25 72.30 100 0.17 72.42
78
DYNAMIC SURFACE TENSION (σ Vs. τ) DATA
C = 2.5 × 10-9 mol/cc HEC QP-300 HEC 250-MR HEC 250-HR τ [s] σ [mN/m] τ [s] σ [mN/m] τ [s] σ [mN/m] 1.76 67.10 1.86 66.80 2.00 66.80 1.00 67.15 0.99 67.10 0.90 67.30 0.57 67.25 0.57 67.40 0.60 68.10 0.29 67.80 0.30 68.50 0.30 69.90 0.19 68.00 0.20 68.98 0.20 70.90 0.10 68.65 0.10 70.10 0.10 71.90
C = 4.0× 10-9 mol/cc C = 1.0× 10-9 mol/cc HEC QP-300 HEC 250-MR HEC QP-300 τ [s] σ [mN/m] τ [s] σ [mN/m] τ [s] σ [mN/m] 1.86 66.80 1.87 66.90 1.94 67.60 0.99 67.05 1.01 67.40 1.00 67.80 0.57 67.10 0.58 67.90 0.56 67.90 0.29 67.70 0.30 69.35 0.30 68.30 0.19 67.90 0.20 70.10 0.20 68.80 0.10 68.95 0.11 71.18 0.10 69.45
79
CONTACT ANGLE (θ Vs. C) DATA
HEC QP-300 HEC 250-MR HEC 250-HR C × 109 [mol/cc] θ [degrees] C × 109 [mol/cc] θ [degrees] C × 109 [mol/cc] θ [degrees] 4.17 74.0 4.00 74.0 3.00 73.0 2.50 74.0 2.50 74.0 2.00 73.0 2.00 74.0 1.25 74.0 1.00 74.0 1.67 74.0 0.83 75.0 0.80 74.5 1.43 74.5 0.62 76.0 0.60 75.5 1.25 75.5 0.50 77.0 0.50 76.0 1.00 76.0 0.42 77.0 0.38 77.0 0.83 76.5 0.21 77.0 0.10 77.0 0.56 77.0 0.42 77.0 0.21 77.0
80
NUCLEATE POOL BOILING HEAT TRANSFER DATA
NPB CORRELATIONS ( Vs. ∆T)
Rohsenow (1952) Borishanskii (1969)
∆T ∆T 2.128 2.490 2.128 3.273 8.263 3.896 8.263 4.917 14.431 4.683 14.431 5.813 19.748 5.194 19.748 6.386 25.766 5.671 25.766 6.917 33.491 6.183 33.491 7.483 40.206 6.567 40.206 7.905 48.745 6.998 48.745 8.375 62.352 7.591 62.352 9.017 78.502 8.190 78.502 9.662 96.822 8.777 96.822 10.289 117.129 9.346 117.129 10.894 145.062 10.030 145.062 11.616 163.984 10.444 163.984 12.051
Cooper (1984) Cornwell-Houston (1994)
∆T ∆T 2.128 3.296 2.128 3.054 8.263 5.157 8.263 4.779 14.431 6.199 14.431 5.744 19.748 6.875 19.748 6.370 25.766 7.506 25.766 6.955 33.491 8.184 33.491 7.583 40.206 8.693 40.206 8.055 48.745 9.263 48.745 8.583 62.352 10.047 62.352 9.310 78.502 10.841 78.502 10.045 96.822 11.618 96.822 10.765 117.129 12.371 117.129 11.463 145.062 13.276 145.062 12.301 163.984 13.824 163.984 12.809
81
DISTILLED DE-IONIZED WATER ( Vs. ∆T)
Run 1 Run 1 Run 2
∆T ∆T ∆T 8.289 3.450 143.290 12.830 8.263 4.030 14.399 4.810 102.490 11.060 14.431 5.420 19.458 5.870 58.141 8.890 19.748 6.380 25.640 6.550 40.436 7.530 25.766 7.050 32.717 7.320 25.584 6.650 33.491 7.640 40.159 7.720 14.533 4.800 40.206 8.120 57.344 8.950 8.162 3.430 48.745 8.890 78.864 9.865 4.695 2.180 62.352 9.380 103.252 10.720 1.960 1.280 78.502 10.120 146.614 12.950 96.822 11.000 117.129 11.850 145.062 12.950 163.984 13.520
Run 3 Run 4
∆T ∆T 10.220 5.350 9.951 4.480 14.461 6.110 14.525 5.360 19.815 6.590 19.513 6.140 25.641 7.040 25.712 7.090 33.015 7.680 32.223 7.670 40.216 8.220 39.483 8.280 48.545 8.940 48.125 8.900 58.128 9.520 57.730 9.540 67.947 10.070 67.698 10.200 78.151 10.600 78.725 10.820 90.482 11.160 89.638 11.350 103.037 11.700 103.958 12.020 116.546 12.240 113.327 12.410 130.433 12.760 131.413 13.100 146.826 13.310 146.883 13.760 161.980 13.840 163.255 14.250 178.344 14.360 173.316 14.600
82
AQUEOUS HEC SOLUTIONS ( Vs. ∆T)
C = 2.5 × 10-9 mol/cc HEC QP-300 HEC 250-MR HEC 250-HR
∆T ∆T ∆T 3.601 2.480 3.599 2.620 3.648 2.690 6.195 3.530 6.507 3.900 6.668 4.000 10.177 4.600 9.950 5.000 9.707 4.863 14.326 5.550 14.495 6.120 14.567 6.256 19.757 6.260 19.828 6.850 19.561 7.100 25.256 6.880 25.576 7.418 25.769 7.810 32.414 7.490 32.384 7.817 32.307 8.252 39.964 7.950 39.364 8.200 40.356 8.356 48.776 8.380 48.158 8.420 48.510 8.780 58.055 8.750 57.802 8.824 57.585 9.050 67.672 9.100 67.945 9.240 67.423 9.150 79.361 9.490 78.570 9.600 78.866 9.550 90.905 9.800 90.149 9.960 90.044 9.850 103.037 10.097 102.651 10.350 102.635 10.140 117.214 10.350 116.752 10.700 117.146 10.450 130.125 10.570 131.831 11.000 131.159 10.740 146.115 10.830 146.826 11.222 146.691 11.010 162.384 11.000 163.153 11.473 161.677 11.260 170.094 11.100 179.085 11.700 172.148 11.465
83
C = 4.0 × 10-9 mol/cc C = 1.0 × 10-9 mol/cc
HEC QP-300 HEC 250-MR HEC QP-300
∆T ∆T ∆T 3.612 2.700 3.617 2.730 8.229 3.370 6.527 3.870 6.499 4.000 14.682 4.490 9.981 4.750 10.041 5.100 19.648 5.030 14.556 5.710 14.714 6.250 25.247 5.720 19.554 6.450 19.603 7.050 32.476 6.475 25.601 7.190 25.971 7.750 39.982 6.880 32.226 7.700 32.615 8.050 47.701 7.350 39.880 8.020 39.864 8.350 61.707 8.070 48.189 8.360 48.468 8.650 78.401 8.780 56.806 8.760 58.298 9.040 96.524 9.530 67.868 9.150 68.012 9.360 116.477 10.360 78.614 9.350 78.586 9.540 145.560 11.400 91.479 9.610 91.132 9.850 172.483 12.280 103.456 9.740 103.505 10.050 116.734 9.900 117.009 10.470 129.528 10.000 131.231 10.500 146.787 10.050 144.185 10.700 161.657 10.100 162.020 11.000 171.838 10.110 179.085 11.419
84