A numerical study is conducted for the Joule heating effects on fluid flow and heat transfer of radiatively participating magnetohydrodynamics (MHD) under different levels of thermal radiation considering the Hall effects in a square cavity. In the cavity, the vertical walls are isothermal with constant but different temperatures, while the horizontal walls are adiabatic. The absorption, emission, and scattering of the fluid and the reflection, absorption, and emission of the walls are all taken into account. The governing equations for momentum and energy together with the boundary conditions are solved by the finite volume method (FVM), while the governing equation for radiative transfer is solved by the discrete ordinates method (DOM). Tabular and graphical results are presented in terms of streamlines, isotherms, Nusselt number, and the average temperature of the fluid. After detailed analysis, we found that the Joule heating has notable effects on fluid flow and heat transfer in the cavity and Joule heating cannot be neglected in certain range of parameters.
Issue Section:
Natural and Mixed Convection
References
1.
Osalusi
, E.
, Side
, J.
, and Harris
, R.
, 2007
, “The Effects of Ohmic Heating and Viscous Dissipation on Unsteady MHD and Slip Flow Over a Porous Rotating Disk With Variable Properties in the Presence of Hall and Ion-Slip Currents
,” Int. Commun. Heat Mass Transfer
, 34
(9–10
), pp. 1017
–1029
.10.1016/j.icheatmasstransfer.2007.05.0092.
Chang
, M. H.
, Ruo
, A. C.
, Chen
, F.
, and Chang
, S. T.
, 2011
, “The Effect of Joule-Heating-Induced Buoyancy on the Electro Hydrodynamic Instability in a Fluid Layer With Electrical Conductivity Gradient
,” Int. J. Heat Mass Transfer
, 54
(17–18
), pp. 3837
–3845
.10.1016/j.ijheatmasstransfer.2011.04.0453.
Yavari
, H.
, Sadeghi
, A.
, Saidi
, M. H.
, and Chakraborty
, S.
, 2012
, “Combined Influences of Viscous Dissipation, Non-Uniform Joule Heating and Variable Thermophysical Properties on Convective Heat Transfer in Microtubes
,” Int. J. Heat Mass Transfer
, 55
(24
), pp. 762
–772
.10.1016/j.ijheatmasstransfer.2011.10.0334.
Tang
, G. Y.
, Yang
, C.
, Chai
, J. C.
, and Gong
, H. Q.
, 2004
, “Joule Heating Effect on Electroosmotic Flow and Mass Species Transport in a Microcapillary
,” Int. J. Heat Mass Transfer
, 47
(2
), pp. 215
–227
.10.1016/j.ijheatmasstransfer.2003.07.0065.
Chen
, C. H.
, 2004
, “Combined Heat and Mass Transfer in MHD Free Convection From a Vertical Surface With Ohmic Heating and Viscous Dissipation
,” Int. J. Eng. Sci.
, 42
(7
), pp. 699
–713
.10.1016/j.ijengsci.2003.09.0026.
Alim
, M. A.
, Alam
, M. M.
, Mamun
, A. A.
, and Hossain
, B.
, 2008
, “Combined Effect of Viscous Dissipation and Joule Heating on the Coupling of Conduction and Free Convection Along a Vertical Flat Plate
,” Int. Commun. Heat Mass Transfer
, 35
(3
), pp. 338
–346
.10.1016/j.icheatmasstransfer.2007.06.0037.
Mao
, J.
, Aleksandrova
, S.
, and Molokov
, S.
, 2008
, “Joule Heating in Magnetohydrodynamic Flows in Channels With Thin Conducting Walls
,” Int. J. Heat Mass Transfer
, 51
(17–18
), pp. 4392
–4399
.10.1016/j.ijheatmasstransfer.2008.02.0058.
Rahman
, M. M.
, Alim
, M. A.
, and Sarker
, M. M. A.
, 2010
, “Numerical Study on the Conjugate Effect of Joule Heating and Magneto-Hydrodynamics Mixed Convection in an Obstructed Lid-Driven Square Cavity
,” Int. Commun. Heat Mass Transfer
, 37
(5
), pp. 524
–534
.10.1016/j.icheatmasstransfer.2009.12.0129.
Rahman
, M. M.
, Saidur
, R.
, and Rahim
, N. A.
, 2011
, “Conjugated Effect of Joule Heating and Magneto-Hydrodynamic on Double-Diffusive Mixed Convection in a Horizontal Channel With an Open Cavity
,” Int. J. Heat Mass Transfer
, 54
(15–16
), pp. 3201
–3213
.10.1016/j.ijheatmasstransfer.2011.04.01010.
Rahman
, M. M.
, 2009
, “Convective Flows of Micropolar Fluids From Radiate Isothermal Porous Surfaces With Viscous Dissipation and Joule Heating
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
(7
), pp. 3018
–3030
.10.1016/j.cnsns.2008.11.01011.
Pal
, D.
, and Talukdar
, B.
, 2010
, “Buoyancy and Chemical Reaction Effects on MHD Mixed Convection Heat and Mass Transfer in a Porous Medium With Thermal Radiation and Ohmic Heating
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
(10
), pp. 2878
–2893
.10.1016/j.cnsns.2009.10.02912.
Hayat
, T.
, and Qasim
, M.
, 2010
, “Influence of Thermal Radiation and Joule Heating on MHD Flow of a Maxwell Fluid in the Presence of Thermophoresis
,” Int. J. Heat Mass Transfer
, 53
(21–22
), pp. 4780
–4788
.10.1016/j.ijheatmasstransfer.2010.06.01413.
Su
, X. H.
, Zheng
, L. C.
, Zhang
, X. X.
, and Zhang
, J. H.
, 2012
, “MHD Mixed Convective Heat Transfer Over a Permeable Stretching Wedge With Thermal Radiation and Ohmic Heating
,” Chem. Eng. Sci.
, 78
, pp. 1
–8
.10.1016/j.ces.2012.04.02614.
Zhang
, J. K.
, Li
, B. W.
, and Hu
, Z. M.
, 2013
, “Effects of Optical Parameters on Fluid Flow and Heat Transfer of Participating Magnetic Fluid
,” Int. J. Heat Mass Transfer
, 59
, pp. 126
–136
.10.1016/j.ijheatmasstransfer.2012.12.00415.
Tanno
, I.
, Morinishi
, K.
, Satofuka
, N.
, and Watanabe
, Y.
, 2011
, “Calculation by Artificial Compressibility Method and Virtual Flux Method on GPU
,” Comput. Fluids
, 45
(1
), pp. 162
–167
.10.1016/j.compfluid.2011.02.00516.
He
, X. Y.
, Doolen
, G. D.
, and Clark
, T.
, 2002
, “Comparison of the Lattice Boltzmann Method and the Artificial Compressibility Method for Navier–Stokes Equations
,” J. Comput. Phys.
, 179
(2
), pp. 439
–451
.10.1006/jcph.2002.706417.
Gatiganti
, R. M.
, Badcock
, K. J.
, Cantariti
, F.
, Dubuc
, L.
, Woodgate
, M.
, and Richards
, B. E.
, 1998
, “Evaluation of an Unfactored Method for the Solution of the Incompressible Flow Equations Using Artificial Compressibility
,” Appl. Ocean Res.
, 20
(3
), pp. 179
–187
.10.1016/S0141-1187(98)00014-518.
Esfahanian
, V.
, and Akbarzadeh
, P.
, 2008
, “The Jameson's Numerical Method for Solving the Incompressible Viscous and Inviscid Flows by Means of Artificial Compressibility and Preconditioning Method
,” Appl. Math. Comput.
, 206
(2
), pp. 651
–661
.10.1016/j.amc.2008.05.08719.
Thynell
, S. T.
, 1998
, “Discrete-Ordinates Method in Radiative Heat Transfer
,” Int. J. Eng. Sci.
, 36
(12–14
), pp. 1651
–1675
.10.1016/S0020-7225(98)00052-420.
Vaillon
, R.
, Lallemand
, M.
, and Lemonnier
, D.
, 1996
, “Radiative Heat Transfer in Orthogonal Curvilinear Coordinates Using the Discrete Ordinates Method
,” J. Quant. Spectrosc. Radiat. Transfer
, 55
(1
), pp. 7
–17
.10.1016/0022-4073(95)00145-X21.
Ganapol
, B. D.
, 2011
, “Radiative Transfer With Internal Reflection Via the Converged Discrete Ordinates Method
,” J. Quant. Spectrosc. Radiat. Transfer
, 112
(4
), pp. 693
–713
.10.1016/j.jqsrt.2010.03.01422.
Mohamad
, A. A.
, 1996
, “Local Analytical Discrete Ordinate Method for the Solution of the Radiative Transfer Equation
,” Int. J. Heat Mass Transfer
, 39
(9
), pp. 1859
–1864
.10.1016/0017-9310(95)00282-023.
Li
, B. W.
, Yao
, Q.
, Cao
, X. Y.
, and Cen
, K. F.
, 1998
, “A New Discrete Ordinates Quadrature Scheme for Three-Dimensional Radiative Heat Transfer
,” ASME J. Heat Transfer
, 120
(2
), pp. 514
–518
.10.1115/1.282427924.
Ratzel
, A. C.
, and Howell
, J. R.
, 1983
, “Two-Dimensional Radiation in Absorbing-Emitting Media Using the P–N Approximation
,” ASME J. Heat Transfer
, 105
(2
), pp. 333
–340
.10.1115/1.324558325.
Rudraiah
, N.
, Barron
, R. M.
, Venkatachalappa
, M.
, and Subbaraya
, C. K.
, 1995
, “Effect of a Magnetic Field on Free Convection in a Rectangular Enclosure
,” Int. J. Eng. Sci.
, 33
(8
), pp. 1075
–1084
.10.1016/0020-7225(94)00120-926.
Markatos
, N. C.
, and Pericleous
, K. A.
, 1984
, “Laminar and Turbulent Natural Convection in an Enclose Cavity
,” Int. J. Heat Mass Transfer
, 27
(5
), pp. 755
–772
.10.1016/0017-9310(84)90145-5Copyright © 2015 by ASME
You do not currently have access to this content.
