Comparison of nanofluid heat transfer properties with theory using generalized property relations for EG-water mixture

Similar documents
HEAT TRANSFER ENHANCEMENT UNDER TURBULENT FLOW FOR EG-WATER MIXTURE OF 40:60 RATIO

Numerical Analysis of Fe 3 O 4 Nanofluid Flow in a Double Pipe U-Bend Heat Exchanger

HEAT TRANSFER ENHANCEMENT WITH ELLIPTICAL TUBE UNDER TURBULENT FLOW TiO 2 -WATER NANOFLUID

Investigations of Heat Transfer Augmentation for Turbulent Nanofluids Flow in a Circular Tube: Recent Literature Review

Amir Houshmand, Ahmad Sedaghat, Kia Golmohamadi and Mohamadreza Salimpour

NANOFLUID PROPERTIES FOR FORCED CONVECTION HEAT TRANSFER: AN OVERVIEW

Thermal conductivity enhancement of TiO 2 nanofluid in water and ethylene glycol (EG) mixture

Research Article Numerical Study of Laminar Flow Forced Convection of Water-Al 2 O 3 Nanofluids under Constant Wall Temperature Condition

CONVECTIVE HEAT TRANSFER CHARACTERISTICS OF NANOFLUIDS. Convective heat transfer analysis of nanofluid flowing inside a

CFD Study of the Turbulent Forced Convective Heat Transfer of Non-Newtonian Nanofluid

Convective Heat Transfer of Al 2 O 3 and CuO Nanofluids Using Various Mixtures of Water- Ethylene Glycol as Base Fluids

Effectiveness and Overall Heat Transfer Coefficient of Fe 3 O 4 /Water Nanofluid Flow in a Double Pipe Heat Exchanger with Return Bend

Numerical Study of Forced Convective Heat Transfer of Nanofluids inside a Vertical Tube

Thermophysical characteristics of ZnO nanofluid in L-shape enclosure.

EFFECT OF TWISTED TAPE INSERTS IN DOUBLE PIPE HEAT EXCHANGER USING AL2O3/WATER NANO FLUIDS

A CFD Study of Turbulent Convective Heat Transfer Enhancement in Circular Pipeflow Perumal Kumar, Rajamohan Ganesan

Numerical Prediction of Forced Convective Heat Transfer and Friction Factor of Turbulent Nanofluid Flow through Straight Channels

Experimental Investigation of Heat Transfer Characteristics of Automobile Radiator using TiO 2. - Nanofluid Coolant

A. Zamzamian * Materials and Energy Research Center (MERC), Karaj, I. R. Iran

NUMERICAL ANALYSIS OF MIXED CONVECTION CHARACTERISTICS INSIDE A VENTILATED CAVITY INCLUDING THE EFFECTS OF NANOPARTICLE SUSPENSIONS

NANOFLUIDS. Abstract INTRODUCTION

Available online at ScienceDirect. Energy Procedia 79 (2015 )

THE EXPERIMENTAL STUDY OF THE EFFECT OF ADDING HIGH-MOLECULAR POLYMERS ON HEAT TRANSFER CHARACTERISTICS OF NANOFLUIDS

Lecture 30 Review of Fluid Flow and Heat Transfer

Buoyancy Driven Heat Transfer of Water-Based CuO Nanofluids in a Tilted Enclosure with a Heat Conducting Solid Cylinder on its Center

Numerical Investigation of Turbulent Convective Heat Transfer of Various Nanofluids in Tube

An Introduction to the. NanoFluid. By Amin Behzadmehr Hassan Azarkish

Improving Performance in Engine Cooling System using Nanofluid-Based Coolant

Flow Boiling Heat Transfer in Small Diameter Channels Using Nano Fluids: A Review

Received 31 December 2015; revised 16 October 2016; accepted 21 November 2016; available online 10 June 2017

EXPERIMENTAL STUDY ON CAVITY FLOW NATURAL CONVECTION IN A POROUS MEDIUM, SATURATED WITH AN Al 2 O 3 60%EG-40%WATER NANOFLUID

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:18 No:02 1

Heat Transfer Enhancement in Fe3O4-water Nanofluid through a Finned Tube Counter Flow Heat Exchanger

Influence of rheological behavior of nanofluid on heat transfer

SSRG International Journal of Mechanical Engineering ( SSRG IJME ) Volume 2 Issue 5 May 2015

Three dimensional numerical investigations on the heat transfer enhancement in a triangular facing step channels using nanofluid

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel

Numerical Investigation of Aspect Ratio Effect on Thermal Parameters in Laminar Nanofluid Flow in Microchannel Heat Sink

Experimental Investigation of plate heat exchanger using Nanofluids

CFD analysis of CuO/water nanofluid flow in a double pipe U-Bend heat exchanger

HEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1

Effect of particle volume concentration on thermo physical properties of Silicon Carbide Water based Nanofluid

Available online at ScienceDirect. Energy Procedia 79 (2015 )

A Computational Fluid Dynamics Investigation of Solar Air Heater Duct Provided with Inclined Circular Ribs as Artificial Roughness

Forced Convection: Inside Pipe HANNA ILYANI ZULHAIMI

Heat Transfer Augmentation of Heat pipe using Nanofluids

A Numerical Investigation of Turbulent Magnetic Nanofluid Flow inside Square Straight Channel

A Theoretical Investigation on Thermal Entrance Region Heat Transfer in a Conduit Filled with Nanofluids

Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer

Studies on flow through and around a porous permeable sphere: II. Heat Transfer

Computational Analysis of CuO Nano Coolant in a Car Radiator

International Journal of Emerging Technologies in Engineering Research (IJETER)

Considerations on the Thermophysical Properties of Nanofluids

EFFECTS OF RADIATION ON CONVECTION HEAT TRANSFER OF Cu-WATER NANOFLUID PAST A MOVING WEDGE

THERMAL PERFORMANCE OF SHELL AND TUBE HEAT EXCHANGER USING NANOFLUIDS 1

Numerical Simulation for Flow and Heat Transfer Characteristics of L- Type Chaotic Channel

Mathematical Modelling for Refrigerant Flow in Diabatic Capillary Tube

COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF A V-RIB WITH GAP ROUGHENED SOLAR AIR HEATER

Application of Artificial Neural Network Model in Calculation of Pressure Drop Values of Nanofluid

Convection Heat Transfer Modeling of Nano- fluid Tio 2 Using Different Viscosity Theories

MYcsvtu Notes HEAT TRANSFER BY CONVECTION

Study on thermal conductivity of water-based nanofluids with hybrid suspensions of CNTs/Al 2 O 3 nanoparticles

ANALYSIS OF HEAT TRANSFER IN TURBULENT FLOW THROUGH THE TUBE WITH UNIFORM HEAT FLUX

Introduction to Heat and Mass Transfer. Week 12

Chapter 7 A preliminary investigation on the transport properties of nanofluids based on iron oxide

PHYSICAL MECHANISM OF CONVECTION

Principles of Convection

Performance Evaluation of Nanofluid for Heat Transfer Enhancement and Pumping Power Reduction through a Semicircular Corrugated Pipe

Effect Of Nanofluids On The Performance Of Corrugated Channel Within Out-Of-Phase Arrangement

Convection Heat Transfer. Introduction

Enhancement of Heat Transfer in Heat Exchanger using Punched and V-cut Twisted Tape Inserts

Heat Transfer And Pressure Drop of Nanofluids Containing Aluminium Oxide with Transformer Oil in Horizontal Pipe

A Study On The Heat Transfer of Nanofluids in Pipes

Heat source/sink and thermal conductivity effects on micropolar nanofluid flow over a MHD radiative stretching surface

Determination of air side heat transfer coefficient in a mini-channel heat exchanger using Wilson Plot method

STUDY OF TURBULENT HEAT TRANSFER OF THE NANOFLUIDS IN A CYLINDRICAL CHANNEL. Siberian Federal University, Krasnoyarsk 3

Measurement of temperature-dependent viscosity and thermal conductivity of alumina and titania thermal oil nanofluids

MHD Non-Newtonian Power Law Fluid Flow and Heat Transfer Past a Non-Linear Stretching Surface with Thermal Radiation and Viscous Dissipation

Heat transfer enhancement in natural convection in micropolar nanofluids

Analysis of Two-Layered Journal Bearing Lubricated with Ferrofluid

EXPERIMENTAL AND NUMERICAL STUDY THE HEAT TRANSFER OF FLAT PLATE SOLAR COLLECTOR BY USING NANOFLUID UNDER SOLAR SIMULATION

HEAT TRANSFER STUDY IN A COAXIAL HEAT EXCHANGER USING NANOFLUIDS

Analysis of Heat Transfer in Pipe with Twisted Tape Inserts

Application of Nano-Fluids as Coolant in Heat Exchangers: A Review

Computational Analysis to Enhance Laminar Flow Convective Heat Transfer Rate in an Enclosure Using Aerosol Nanofluids

Boundary Layer Flow and Heat Transfer due to an Exponentially Shrinking Sheet with Variable Magnetic Field

A new numerical approach for Soret effect on mixed convective boundary layer flow of a nanofluid over vertical frustum of a cone

Investigation of Nanofluid MHD Flow and Heat Transfer in a Channel

Department of Mechanical Engineering, VTU, Basveshwar Engineering college, Bagalkot, Karnataka, India

FORCED CONVECTION IN NANOFLUIDS OVER A FLAT PLATE

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

CFD Simulation on Supercritical Fluid Extraction of Black Pepper's Bioactive Compounds: Single Particle Study

Thermal Nanofluids flow in Corrugated Facing Step - A Review

Untersuchungen zum Wärmeübergang in einem quadratischen Mikrokanal mit Al 2 O 3 -H 2 O Nanofluid

NUMERICAL STUDY OF MIXED CONVECTION HEAT TRANSFER IN LID-DRIVEN CAVITY UTILIZING NANOFLUID Effect of Type and Model of Nanofluid

Study of Forced Convection Heat Transfer with Single phase and mixture phase Nanofluid Model at different Reynolds Numbers

Australian Journal of Basic and Applied Sciences. Numerical Study of a Concentric Tube Heat Exchanger Using Dimpled Tubes with Al 2 o 3 NanoFluid

Analysis of a Double Pipe Heat Exchanger Performance by Use of Porous Baffles and Nanofluids

Research Article Numerical Investigation of Heat Transfer Enhancement in a Rectangular Heated Pipe for Turbulent Nanofluid

Numerical Analysis of Magneto-Hydrodynamic Flow of Non-Newtonian Fluid Past Over a Sharp Wedge in Presence of Thermal Boundary Layer

Transcription:

Comparison of nanofluid heat transfer properties with theory using generalized property relations for EG-water mixture Seshu Kumar Vandrangi 1,a), Suhaimi bin Hassan 1,b) Sharma K.V. 2,c), and Prasad Reddy 3,d) 1 Department of Mechanical Engineering, Universiti Teknologi PETRONAS 32610 Tronoh, Malaysia 2 Department of Mechanical Engineering, JNTU Hyderabad, India 3 Department of Chemical Engineering, Universiti Teknologi BRUNEI Abstract. A numerical analysis for the determination for turbulent characteristics of fluid flow and heat transfer have been developed by employing the eddy diffusivity equation of Van Driest. The properties of Silicon dioxide (SiO2) nanofluid with spherical particles in base liquid ethylene glycol (EG) -water (W) mixture of 60:40 ratio is employed for a wide range of concentrations and bulk temperature. A good agreement of the numerical results with the experimental data for properties and heat transfer is observed. A comparison of Copper oxide (CuO), Aluminum dioxide (Al2O3) and Silicon dioxide (SiO2) nanofluids revealed that SiO2 attain higher temperature gradients in comparison to CuO nanofluid at the same concentration and temperature. 1 Introduction Studies using conventional heat transfer fluids such as water, ethylene glycol (EG) and engine oil are subjected to system alterations to meet the desired performance requirements. The methods of augmentation include the use of additives with micron size metal particles dispersed in the liquid [1, 2] are quite outdated. Moreover, the size of these particles for heat transfer enhancement proved to be undesirable, due to problems associated with clogging, sedimentation, erosion of pipe lines and large pressure drop. In order to meet the requirements of greater heat transfer rates, the application of nanotechnology has been employed successfully. Nanofluids are formed by the dispersion of small quantities of nanometer size metal and metal oxide particles in base liquids such as water or ethylene glycol proved to possess higher values of thermal conductivity compared to base liquid. Recent trends suggest that using nanofluids dispersed in EG and water mixture as base liquid has proved to be beneficial for low temperature applications. Experiments undertaken with nanoparticles dispersed in EGwater mixture as base fluid in different ratios seems to be encouraging. * Corresponding author: suhaimiha@utp.edu.my The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).

Vajjha et al. [3-5] have conducted various experiments to determine the properties of Al 2O 3, CuO, SiO 2 and ZnO nanofluids. Praveen et al. [6] determined the rheological properties of CuO nanofluids. Sundar et al. [7] reported enhanced thermal properties of nanodiamond nanofluids. Sahoo et al. [8, 9] carried out experiments with SiO 2 and Al 2O 3 nanofluids to determine the thermal conductivity and viscosity. Kulkarni et al. [10] performed experiments for the estimation of viscosity with SiO 2 nanofluid. Experiments for the determination of nanofluid forced convection heat transfer coefficients in the turbulent range are undertaken with Al 2O 3 (45nm), CuO (29nm), and SiO 2 (20, 50, 100nm) for a maximum concentration of 10.0% for temperature varying from 20-90 o C by Vajjha and Das [11] in base liquid EG-water mixture in 60:40 ratio. They have reported an enhancement of 81.74% in heat transfer for Al 2O 3 nanofluid at a concentration of 10%. The pressure loss is reported to increase with volume concentration of the nanofluid. The increase of pressure loss for a 10% Al 2O 3 nanofluid at a Reynolds number of 6700 is about 4.7 times that of the base fluid. The authors developed equations for the nanofluid properties and the Nusselt number. Kulkarni et al. [10] undertook experiments to estimate the convective heat transfer and pressure loss of SiO 2 (20, 50, 100nm) nanofluids dispersed in EG-water mixture for volume concentration in the range of 0-10% with temperatures varying between 20-90 o C. They have reported an enhancement of 16% in heat transfer coefficient at a concentration of 10.0% with 20nm particle size at Re = 10000. Theoretical analysis for turbulent flow has been modeled by Sarma et al. [12] who introduced a correction factor for the mixing length. Expressions for eddy diffusivity of momentum (ε nf ϑ nf ) and heat (ε H α nf ) have been proposed, where ε nf is momentum eddy diffusivity (m 2 /s) of nanofluid, ε H is thermal eddy diffusivity (m 2 /s), α nf is thermal diffusivity (m 2 /s) of nanofluid and ϑ nf is kinematic viscosity (m 2 /s) of nanofluids. They compared the theoretical values of Nusselt number with experimental data of water based Al 2O 3 nanofluid for a maximum volume concentration of 0.5%. The analysis has been extended to 4% vol. concentration by Sharma et al. [13],. A good agreement of the numerical results with the experimental data have been reported. The numerical values of temperature gradients at the wall determined are reported to be inversely proportional to nanoparticle density for water based nanofluids. The determination of nanofluid heat transfer coefficient in base liquid EG-water mixture of 60:40 ratio is mostly undertaken through experiments. The heat transfer enhancement reported by Vajjha et al. [11] is 82% with Al 2O 3 nanofluid while Kulkarni et al. [10] reported only 16% with SiO 2 nanofluid at the same volume concentration of 10%. The reason for the deviation in heat transfer enhancement with Al 2O 3 and SiO 2 nanofluids has not been explained by the authors in the turbulent range and hence numerical analysis is undertaken in the turbulent range of Reynolds number for EG-water mixtures of 60:40 ratio. The characteristics of SiO 2 nanofluid flow and heat transfer employing the van Driest eddy diffusivity equation is undertaken to determine the influence of properties on heat transfer coefficient. Only Salient result from the numerical analysis is presented. 2 Base fluid and nanofluid properties The properties such as density, specific heat, viscosity and thermal conductivity of EG-W mixture were developed through regression equations employing experimental data available in the literature [14]. The properties of the base liquid are estimated with the regression equations in the numerical analysis and are given in Eqs. (4)- (7) by Sharma et al. [15]. Nanofluid properties are required for the estimation of heat transfer coefficients and friction factor. The nanofluid properties such as density and specific heat are well known conventional mixture relation and are given by Pak and Cho [16]. The thermal conductivity and viscosity of EG-water based CuO, Al 2O 3 and SiO 2 nanofluids are developed for different 2

particle sizes, temperatures and concentration that are available in the literature [4]. The data available from experimental results of literature are used in the development of Eqs. for viscosity and thermal conductivity through regression analysis using numerical program and are given by Sharma et al. [15] in eqs (14) and (15). The experimental heat transfer coefficients of nanoparticles dispersed in base liquid EG-water mixture in 60:40 ratio by Vajjha and Das [11] is used to develop a regression equation resulting in Eq. (1) Nu = 0.0257Re 0.8 Pr bf 0.4 (1 + Pr nf ) 0.04297 (1 + 100 )5.205 (1) Where Nu, Re are Nusselt number and Reynolds number respectively and Pr bf and Pr nf are prandtl number of base fluid and nanofluid respectively. The Eq. (1) is developed with an average deviation of 7.8% and a standard deviation of 9.3% with the exception of a few data points deviating from the correlation equation by 18%. The equation is valid in the temperature range of 20-90 o C for a maximum concentration of 4% for particle diameters lower than 53nm. It can be observed that the substitution of = 0 and Pr nf = 0 in Eq. (1) simplifies to Nu = 0.0257Re 0.8 Pr bf 0.4 which is the conventional Dittus-Boelter equation applicable for pure fluids with a deviation of 11%. 3 Results and discussions The base liquid and nanofluid properties, heat transfer coefficients are validated with the experimental data. The experimental data of base liquid and SiO 2/EG-W nanofluid thermal conductivity are compared with Eqs. (6) and (15) of Sharma et al. [15] respectively. The thermal conductivity data is plotted in Fig.1 for two concentrations. The results show a satisfactory agreement with a maximum deviation of 7% among all the concentrations. (2) Fig.1 Comparison of thermal conductivity data with theory Fig.2 Comparison of viscosity data with theory The values of viscosity estimated with Eqs. (7) and (14) given by Sharma [15] for base liquid and nanofluid respectively are in good agreement with the experimental data with a maximum deviation of 14% among all concentrations, shown plotted in Fig.2. The experimental determination of heat transfer coefficients with base liquid EG-water 60:40 mixture were performed by Kulkarni et al.[10] and Vajjha et al. [11] in the turbulent range 3

of Reynolds Number at unspecified temperatures. The temperatures are predicted using the theoretical results which is observed to be in agreement with the base liquid experimental ata at 30 o C and 70 o C for Kulkarni et al.[10] and Vajjha et al. [11] with a maximum deviation of 20% and 15% respectively as shown plotted in Fig.3. Thus, the base liquid temperatures determined, the nanofluid heat transfer coefficient at different Reynolds number for 2 and 4% concentration are shown plotted in Fig.4. The numerical results employing the property relations indicate that the experiments could have been undertaken at 30 o C and 70 o C by Kulkarni et al. [10] and Vajjha et al. [11] respectively. Fig.3 Comparison of base fluid heat transfer coefficient with theoretical results Fig.4 The variation of heat transfer coefficients with Reynolds number It can be observed that the theoretical results are in close agreement with the experimental data with Eqs. (4)- (7) and (12)-(15) given by sharma et al. [15] are employed in the theoretical model. The concentration at which maximum heat transfer enhancement is possible can be determined with Enhancement Ratio (ER). The ER is defined as the ratio of enhancement in viscosity to that of thermal conductivity given in Eq. (21) of Sharma et a. [15]. The variation of nanofluid concentration with temperature for maximum heat transfer enhancement at various operating temperatures are shown plotted in Fig.5 for laminar and turbulent flow conditions. From Fig.5, it is evident that at 30 o C, heat transfer enhancement for SiO 2 nanofluid is not attainable for concentrations greater than 1%. For experiments undertaken at 70 o C, Fig.5 indicates heat transfer enhancements can be obtained up to 5% volume concentration under turbulent flow conditions. The influence of particle properties on heat transfer coefficients is undertaken by a comparison of the temperature gradients rawn for SiO 2, Al 2O 3 and CuO nanofluids shown plotted in Fig.6 with Reynolds number. It can be observed that the temperature gradients decrease with increase in operating temperature which is reflected in lower values of heat transfer coefficients obtained at higher temperatures. Further, the thermal conductivity of CuO is greater than SiO 2 nanoparticle. It is generally expected that CuO nanofluid to predict higher heat transfer coefficients compared to SiO 2 nanofluids. However, the temperature gradient decrease with increase in nanoparticle density of SiO 2 (2220kg/m 3 ) to CuO (6900kg/m 3 ). Similar observation was reported for water based nanofluids [17]. Further studies are undertaken in this regard to determine the flow and heat transfe characteristics. 4

Fig.5 Evaluation of concentration for optimum heat transfer coefficient of SiO2 nanofluid at different temperatures Fig. 6 Variation of temperature gradient with Reynolds number for different nanofluids 4 Conclusions The salient observations from the numerical results on the nanofluid properties and heat transfer coefficients can be listed as: (i) The proposed correlations of nanofluid viscosity and thermal conductivity can predict heat transfer coefficients satisfactorily with a maximum deviation of 7 and 14% respectively. (ii) The Enhancement Ratio predicts an increase in heat transfer coefficient for nanofluid concentration up to 5% under turbulent flow and 4% for laminar region at an operating temperature of 70 o C. (iii) The increase in Nusselt number of SiO 2 nanofluid with concentration is not significant. (iv) Higher heat transfer coefficients can be expected with SiO 2 in comparison with CuO nanofluid, based on the temperature gradients obtained. (v) SiO 2 nanofluids predicts a higher temperature gradient when compared to Al 2O 3 and CuO based nanolfuids. The authors acknowledge the financial assistance from Department of Mechanical Engineering, Universiti Teknologi PETRONAS, Malaysia. 5 References 1. A. S Ahuja, J of App Phy, 46(8): p. 3408-3416 (1975). 2. A. E. Bergles, A. E., Techniques to augment heat transfer, in Handbook of heat transfer applications, p. 31-380 (1985). 3. R. Vajjha, D. Das, and B. Mahagaonkar, PETROL SCI TECHNOL, 27(6): p. 612 624 (2009). 4. R. S Vajjha, and D. K. Das, Int J Heat Mass Transf,. 52(21): p. 4675 4682 (2009). 5. R. S. Vajjha, and D. K. Das, J. Heat Transfer, 131(7): p. 071601 071601 (2009). 6. P. K. Namburu, D. P. Kulkarni, D. Misra, and D. K. Das, Exp. Therm Fluid Sci. 32(2): p. 397 402 (2007). 7. L. S. Sundar, L. S., M. K. Singh, E. V. Ramana, B. Singh, J. Grácio, and A. C. M. Sousa,. Sci. Rep. 4 (2014). 5

8. B. C. Sahoo, D. K. Das, R. S. Vajjha, and J. R. Satti, J Nanotechnol Eng Med. 3(4): p. 041006 (2012). 9. B. C Sahoo, R. S. Vajjha, R. Ganguli, G. A. Chukwu, and D. K. Das, PETROL SCI TECHNOL,. 27(15): p. 1757 1770 (2009). 10. D. P. Kulkarni, P. K. Namburu, H. Ed Bargar, and D. K. Das, HTrEn,. 29(12): p. 1027-1035 (2008). 11. R. S. Vajjha, D. K. Das, and D. P. Kulkarni,. Int J Heat Mass Transf,. 53(21 22): p. 4607 4618 (2010). 12. P. K. Sarma, Chada, K. V. Sharma, L. S. Sundar, P. S. Kishore, and V. Srinivas, IJHT,. 28. (2010). 13. K. V. Sharma, W. H. Azmi, S. Kamal, and S. Hassan. Appl Mech Mater.. Trans Tech Publ (2016). 14. ASHRAE, Handbook of fundamentals. American Society of Heating Refrigerating and Air Conditioning Engineers, Atlanta, GA, (2005). 15. K. V. Sharma, S. K. Vandrangi, K. Habib, and S. Kamal, IJSER..7(6) (2016) 16. B. C. Pak and Y. I. Cho, EXP HEAT TRANSFER,. 11(2): p. 151 170(1998). 17. K. V. Sharma, W. Azmi, S. Kamal, P. Sarma, and B. Vijayalakshmi, Can. J. Chem. Eng., (2015). 6