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Analysis of MHD Forced Convective Flow of Variable Fluid Properties over a Saturated Porous Medium with Thermal Radiation Effect

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The present paper addresses the problem of MHD forced convective flow in a fluid saturated porous medium with Brinkman-Forchheimer model, which is an important physical phenomena in engineering applications. The paper extends the previous models to account for effects of variable fluid properties on the forced convective flow through a porous medium in the presence of radiative heat loss using bivariate spectral relaxation method (BSRM). The dynamic viscosity and thermal conductivity of the newtonian fluid are assumed to vary linearly respectively, with temperature whereas the contribution of thermal radiative heat loss is based on Rosseland diffussion approximation. The flow model is described and expressed in form of a highly coupled nonlinear system of partial differential equations. The method of solution BSRM as proposed by Motsa [25] seeks to decouple the original system of PDEs to form a sequence of equations that can be solved in a computationally efficient manner. BSRM is an approach that applies spectral collocation independently in all underlying independent variable is executed to obtain approximate solutions of the problem. The proposed algorithm is supposed to be a very accurate, convergent and very effective in generating numerical results. The results obtained show a significant effects of the flow control parameters on the fluid velocity and temperature respectively. Consequently, the wall shear stress and local heat transfer rate of the present paper are compared with the available results in literatures. Remarkable impacts and a good agreement are found.


International Frontier Science Letters (Volume 9)
K. S. Adegbie and A. I. Fagbade, "Analysis of MHD Forced Convective Flow of Variable Fluid Properties over a Saturated Porous Medium with Thermal Radiation Effect", International Frontier Science Letters, Vol. 9, pp. 47-65, 2016
Online since:
Aug 2016

[1] K. Vafai, Handbook od porous media, 2nd edition, Taylor and Francis and CRC press, Boca Raton, (2005).

[2] D.A. Nield, A. Bejan, Convection in porous media, 3rd edition, Springer-Verlag, New-York, (2006).

[3] D.B. Ingham, I. Pop, Transport phenomena in porous media III. Vol. 3, Elsevier, London, (2005).

[4] I. Pop, D.B. Ingham, Convective heat transfer: Mathematical and Computational modelling of viscous fluids and porous median, Pergamon, Oxford, (2001).

[5] M.F. El-Amin, Combined effect of viscous dissipation and joule heating on MHD forced convection over a non-isothermal horizontal cylinder embedded in a fluid saturated porous medium, Journal of Magnetism and Magnetic Materials. 263(3) (2003).

[6] D. Srinivasacharya, J. Pranitha, Ch. RamReddy, Magnetic effect on free convection in a nondaryc porous medium saturated with doubly stratifield power-law fluid, J. Braz. Soc. Mech. Sci. and Eng. 33(1) (2011) 8-14.

[7] Cheng Ching-Yang, Combined heat and mass transfer in natural convection flow from a verticla wavy surface in power-law fluid saturated porous medium with thermal and mass stratification, Int. Comm. Heat Mass Transfer. 36 (2009) 351-356.

[8] S. Mukhopadhyay, Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium, Int. J. Heat and Mass Transfer. 52(13-14) (2009) 3261-3265.

[9] A. Pantokratoras, Furhter results on variable viscosity on flow and heat transfer to a continuos moving flat plate, Int. J Engineering Sciences. 42 (2004) 1891-1896.

[10] K. S. Adegbie, F.I. Alao, Flow of temperature dependent viscous fluid between parallel heated walls: Exact analytical solutions in the presesnce of viscous dissipation, Journal of Mathematics and Statistics. 3(1) (2007) 12-14.

[11] S. Ahmad et al., Mixed convection boundary layer flow past an isothermal horizontal circular cylinder with temperature-dependent viscosity, Int. J. of Thermal Sciences. 48 (2009) 1943-(1948).

[12] P. Ganesan, G. Palani, Finite difference analysis of unsteady natural convection MHD past an inclined plate with variable surface heat and mass flux, Int. J. Heat Mass Transfer. 47 (2004) 4449-4457.

[13] M.A. Seddeek, Effect of radiation and variable viscosity on MHD free convection flow past a semi-infinte flat plate with ab aligned magnetic field in the case of unsteady flow, Int. J. Heat Mass Transfer. 45 (2002) 931-935.

[14] P. Dulal, M. Hiranmoy, Influence of thermophoresis and soret-dufour magnetohydrodynamic heat and mass trnasfer over a non-isothermal wedge with thermal radiation and ohmic dissipation, J. of Magnetism and Magnetic Materials. 331 (2007) 250-255.

[15] M.A.A. Mahmoud, Thermal radiation effects on MHD flow of micro-polar fluid over a stretching surface with variable thermal conductivity, Physica A: Statistical Mechanics and its Applications. 375(2) (2007) 401-410.

[16] Promise Mebine, Rhoda H. Gumus, On steady MHD thermally raidating and thermosolutal visocus flow through a channel with porous medium, Int. J. Mathematics and Mathematical Sciences. (2010) article ID 287435. doi: 10. 1155/2010/287435.

[17] E. M Aboeldahab, M.S. El Gendy, Radiation effect on MHD free convective flow of a gas past a semi-infinite vertical plate with variable thermophysical properties for high-temperature differences, Can. J. Phys. 80 (2002) 1609-1619.

[18] A. Md Miraj, Md Abdul A., S. A. Laek, Conjugate effects of radiation and joule heating on Magnetohydrodynaics free convection flow along a sphere with heat generation, American Journal of Computational Mathematics. 1 (2011) 18-25.

[19] A.M. Salema, R. Fathy, Effectsof variable properties on MHD heat and mass trnasfer flow near a stagnation point toward a stretching sheet in a porous medium with thermal radiation, Chin. Phys. B. 21. 5 (2012) 0547011.

[20] W.J. Minkowyez, A. Haji-Sheikh, Heat transfer in parallel plate and circular porous passages with axial conduction, Int. J. Heat and Mass transfer. 49 (2006) c2381-2390.

[21] Md. A. Hossain, Md. S. Munir, Mixed convection flow from a verticla flat plate with temperaturedependent viscosity, Int. J. Thermal Sci. 39 (2000) 635-644.

[22] I. A Hassanien, T.H. Al-arabi, Non-darcy unsteady mixed convection flow near the stagnation point on a heated vertical surface embedded in porous medium with thermal radiation and variable viscosity, Comm, Nonlinear Sci. Numer Simulat. 14 (2009).

[23] B.R. Sharma, Hemanta Konwar, MHD flow, heat and mass transfer about a horizontal cylinder in porous medium. Internation Journal of Innovative Research in Sciences, Engineering and Technology. 3(10) (2014).

[24] S.S. Motsa, Z.G. Makukula, On spectral relaxation method approach for steady von karman flow of a reiner-rivlin fluid with joule heating, viscous dissipation and suction/injection. Cent. Eur. J. Phys. 11 (2013) 363-374.

[25] S. S Motsa, A new spectral relaxation method fora similarity variable nonlinear boundary layer flow systems, Chemicla Engineering Communications. 201 (2014) 241-256.

[26] S.S. Motsa, P.G. Dlamini, M. Khumalo, Solving hyperchaotic systems using the spectral relaxation method, Abstract and Applied Mathematics. 12 (2012) Article ID 203461.

[27] S.S. Motsa, P.G. Dlamini, M. Khumalo, A new multistage spectral relaxation method for solving chaotic initial value systems, Nonlinear Dyn. 72 (2013) 265-283.

[28] K.K.P. Sivagnana, R. Kandasamy, R. Savaranan, Lie group analysis for the effect of viscosity and thermophoresis particle deposition on free convective heat and mass transfer in the presence of suction/injection, Theoritical and Applied Mechanics. 36 (2009).

[29] S.S. Motsa, P.G. Dlamini, M. Khumalo, Spectral relaxation method and spectral quasilinearization method for solving unsteady boundary layer flow problems, Advances in Mathematicla Physics. (2014) Article ID 341964.

[30] S.S. Motsa, V.M. Magagula, P. Sibanda, A bivariate chebyshev spectral collocation quasilinaerization method for nonlinear evolution parabolic equations, The Scientific World Journal. (2014) Article ID 581987.

[31] C. Canuto et al., Spectral methods in fluid dynamics, Springer-Verlag, Berlin, (1988).

[32] L.N. Trefethen, Spectral Methods in MATLAB, SIAM (2000).

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