Technical Brief

Semi Analytical Solution of Heat Transfer of Magnetohydrodynamic Third-Grade Fluids Flowing Through Parallel Plates With Viscous Dissipation

[+] Author and Article Information
Sumanta Chaudhuri

School of Mechanical Engineering,
KIIT, Deemed to be University,
Bhubaneswar 751024, Odisha, India
e-mail: sc4692@gmail.com

Sushil Kumar Rathore

Assistant Professor
Department of Mechanical Engineering,
National Institute of Technology Patna,
Patna 800005, Bihar, India
e-mail: isushilrathore@gmail.com

1Present address: Department of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela 769008, Odisha, India.

2Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received February 16, 2018; final manuscript received October 7, 2018; published online December 6, 2018. Assoc. Editor: Yit Fatt Yap.

J. Thermal Sci. Eng. Appl 11(2), 024504 (Dec 06, 2018) (7 pages) Paper No: TSEA-18-1086; doi: 10.1115/1.4041682 History: Received February 16, 2018; Revised October 07, 2018

This study deals with the heat transfer characteristics of magnetohydrodynamic (MHD) flow of a third-grade fluid through parallel plates, subjected to a uniform wall heat flux, but of different magnitudes. The effect of viscous dissipation has been included for both heating and cooling of the fluid. The least square method (LSM) has been adopted for solving the nonlinear equations. The expressions for the velocity and temperature fields have been derived which, in turn, is utilized to evaluate the Nusselt number. The results indicate an increase in Nusselt number for higher values of the third-grade fluid parameter during heating and indicate a reverse trend for cooling. Nusselt number increases with an increase in Hartmann number during heating, whereas it decreases with increasing values of the Hartmann number while cooling the fluid.

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Chakraborty, R. , Dey, R. , and Chakraborty, S. , 2013, “ Thermal Characteristics of Electrohydrodynamic Flows in Narrow Channels With Viscous Dissipation and Joule Heating Under Constant Wall Heat Flux,” Int. J. Heat Mass Transfer, 67, pp. 1151–1162. [CrossRef]
Kakarantzaz, S. C. , Benos, L. T. , Sarris, I. E. , Knaepen, B. , Grecos, A. P. , and Vlachos, N. S. , 2017, “ MHD Liquid Metal Flow and Heat Transfer Between Vertical Coaxial Cylinders Under Horizontal Magnetic Filed,” Int. J. Heat Fluid Flow, 65, pp. 342–351. [CrossRef]
Narain, A. , 1986, “ On K-BKZ and Other Visco-Elastic Models as Continuum Generalizations of the Classical Spring-Dashpot Models,” Rheol. Acta, 25(1), pp. 1–14. [CrossRef]
Joseph, D. D. , Narain, A. , and Riccius, O. , 1986, “ Shear Wave Speeds and Elastic Modulli for Different Liquids–Part 1: Theory,” J. Fluid Mech., 171(1), pp. 289–308. [CrossRef]
Siginer, D. A. , and Letelier, M. F. , 2010, “ Heat Transfer Asymptotes in Laminar Flow of Non-Linear Visco-Elastic Fluids in Straight Non-Circular Tubes,” Int. J. Therm. Sci., 48(11), pp. 1544–1562.
Letelier, M. F. , Hinojosa, C. B. , and Siginer, D. A. , 2017, “ Analytical Solution of the Graetz Problem for Non-Linear Visco-Elastic Fluids in Tubes of Arbitrary Cross-Section,” Int. J. Therm. Sci., 111, pp. 369–378. [CrossRef]
Sisko, A. W. , 1958, “ The Flow of Lubricating Greases,” Ind. Eng. Chem. Res., 50(12), pp. 1789–1792. [CrossRef]
Akbarzadeh, P. , 2016, “ Pulsatile Magneto-Hydrodynamic Blood Flows Through Porous Blood Vessels Using a Third Grade Non-Newtonian Fluid Models,” Comput. Methods Programs Bio Med., 126, pp. 3–19. [CrossRef]
Wang, L. , Jian, Y. , Liu, Q. , Li, F. , and Chang, L. , 2016, “ Electromagnetohydrodynamic Flow and Heat Transfer of Third Grade Fluids Between Two Micro-Parallel Plates,” Colloids Surf. A: Physicochem. Eng. Aspects, 494, pp. 87–94. [CrossRef]
Ozisik, M. N. , 1985, Heat Transfer: A Basic Approach, McGraw-Hill, New York.
Fakour, M. , Vahabzadeha, A. , Ganji, D. D. , and Hatami, M. , 2015, “ Analytical Study of Micro Polar Fluid Flow and Heat Transfer in a Channel With Permeable Walls,” J. Mol. Liq., 204, pp. 198–204. [CrossRef]
Chaudhuri, S. , and Das, P. K. , 2018, “ Semi-Analytical Solution of the Heat Transfer Including Viscous Dissipation in the Steady Flow of a Sisko Fluid in Cylindrical Tubes,” ASME J. Heat Transfer, 140(7), p. 071701.
Tso, C. P. , Sheela-Francisca, J. , and Hung, Y. M. , 2010, “ Viscous Dissipation Effects of Power-Law Fluid Flow Within Parallel Plates With Constant Heat Fluxes,” J. Non-Newtonian Fluid Mech., 165(11–12), pp. 625–630. [CrossRef]


Grahic Jump Location
Fig. 1

Hydrodynamically and thermally fully developed flow through parallel plates

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Fig. 2

Nondimensional temperature for different A when N = −5, Br = 0.5, q = 1, and Ha = 1: (a) for heating and (b) for cooling

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Fig. 3

Nondimensional temperature for different values of Hartmann number when N = −5, A = 0.3, q = 1, and Br = 2: (a) for heating and (b) for cooling

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Fig. 4

Nondimensional temperature for different Brinkman numbers when N = −4, A = 0.4, q = 1, and Ha = 2: (a) for heating and (b) for cooling

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Fig. 5

Nondimensional temperature for different values of heat flux ratio when N = −4, A = 0.4, Ha = 2, and Br = 5

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Fig. 6

Variation of Nu with Br with Ha = 1, N = −4, and q = 1

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Fig. 7

Variation of Nu with A for different Ha when N = −5, and Br = 4: (a) for heating and (b) for cooling

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Fig. 8

Nondimensional velocity distribution for different values of Ha when N = −3 and A = 0.4



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