Abstract
This article contains a computational study of free convective flow through a square enclosure filled with liquid gallium saturated porous medium in the presence of a uniform inclined magnetic field. Lower boundary of enclosure is considered to be heated uniformly, upper horizontal boundary is taken insulated, left wall of the cavity is heated linearly, and right wall is heated linearly or taken cold. Navier–Stokes equations governing the flow problem are first exposed to penalty method to eliminate the pressure terms and then Galerkin FEM is employed to solve reduced equations. Grid independent results are achieved and shown in tabular form for numerous ranges of physical flow parameters. To ensure the accuracy of developed code, computed results are compared with those available in earlier studies through figures. It is found that the strength of streamlines circulation is increased due to increase in Darcy number while imposition of vertical magnetic field instead of horizontal magnetic field causes slow rate of increase in strength of streamlines circulation. Whereas, in the case of linearly heated right wall, the average Nusselt number is an increasing function of the Darcy number, and vertical magnetic field causes higher values for average Nusselt number as compared to horizontal magnetic field along bottom and side walls of cavity. Contrarily, in the case of cold right wall, the horizontal magnetic field results in higher values of average Nusselt number as compared to the vertical magnetic field case, and the average Nusselt number reduces as we move along lower and right boundary while increases along left wall with increase in distance.
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References
I. Pop and D.B. Ingham, Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluid and Porous Media, Pergamon, Oxford, 2001.
D.A. Nield and A. Bejan, Convection in Porous Media. 3rd ed., Springer–Verlag, N.Y., 2006.
O. Martynenko and P. Khramtsov, Free–convective Heat Transfer, Springer, Berlin, 2005.
M.G. Braunsfurth, A.C. Skeldon, A. Juel, T. Mullin, and D.S. Riley, Free convection in liquid gallium, J. Fluid Mech., 1997, vol. 342, p. 295–314.
O. Ben–David, A. Levy, B. Mikhailovich, and A. Azulay, Gallium melting in a rectangular box, in: Proc. 15th Int. Heat Transfer Conf., Koyoto, Japan, 2014. P. 8539–8552.
Y. Yamanakaa, K. Kakimotoa, H. Ozoea, and S.W. Churchill, Rayleigh–Benard oscillatory natural convection of liquid gallium heated from below, Chemical Engng J., 1998, Vol. 71. P. 201–205.
M. Sathiyamoorthy and A. Chamkha, Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s), Int. J. Thermal Sci., 2010, vol. 49, p. 1856–1865.
A.A. Mohamad and R. Viskanta, Flow structures and heat transfer in a lid–driven cavity filled with liquid galli–um and heated from below, Experimental Thermal and Fluid Sci., 1994, vol. 9, p. 309–319.
T. Javed, M.A. Siddiqui, Z. Mehmood, and I. Pop, MHD natural convective flow in an isosceles triangular cavi–ty filled with porous medium due to uniform/non–uniform heated side walls, Zeitschrift für Naturforschung A, 2015, vol. 70, p. 919–928.
C. Revnic, T. Grosan, I. Pop, and D.B. Ingham, Magnetic field effect on the unsteady free convection flow in a square cavity filled with a porous medium with a constant heat generation, Int. J. Heat Mass Transfer, 2011, vol. 54, p. 1734–1742.
C. Jiang, E. Shi, Z. Hu, X. Zhu, and N. Xie, Numerical simulation of thermomagnetic convection of air in a po–rous square enclosure under a magnetic quadrupole field using LTNE models, Int. J. Heat Mass Transfer, 2015, vol. 91, p. 98–110.
D.D. Gray and A. Giorgini, The validity of Boussinesq approximation for liquid and gases, Int. J. Heat Mass Transfer, 1976, vol. 19, p. 545–551.
P.A. Davidson, An Introduction to Magnetohydrodynamics, Cambridge University Press, Cambridge, 2001.
N. Hannoun, V. Alexiades, and T.Z. Mai, Resolving the controversy over tin and gallium melting in a rectangu–lar cavity heated from the side, Numer. Heat Transfer, 2003, vol. 44, p. 253–276.
J.N. Reddy and D.K. Gartling, The Finite Element Method in Heat Transfer and Fluid Dynamics, CRC–Press, Florida, 1994.
B. Loret and J.M. Huyghe, Chemo–mechanical Coupling in Porous Media Geomechanics and Biomechanics, Springer–Verlag, Wien–N.Y., 2004.
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Javed, T., Siddiqui, M.A. & Mehmood, Z. MHD natural convective flow through a porous medium in a square cavity filled with liquid gallium. Thermophys. Aeromech. 25, 405–420 (2018). https://doi.org/10.1134/S0869864318030083
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DOI: https://doi.org/10.1134/S0869864318030083