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Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium. (English) Zbl 1157.80332
Summary: A numerical investigation of the steady magnetohydrodynamics free convection in a rectangular cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field, inclined at an angle $\gamma$ with respect to the horizontal plane, is externally imposed. The values of the governing parameters are the inclined angle $\gamma =0,\pi /6,\pi /4$ and $\pi /2$, Hartmann number $Ha=0,1,5$, 10 and 50, Rayleigh number $Ra=10,100,{10}^{3}$ and ${10}^{5}$, and the aspect ratio $a=0·01$, 0.2, 0.5 and 1 (square cavity). It is shown that the intensity of the core convection is considerably affected by the considered parameters. It is also found that the local Nusselt number $N{u}_{Y}$ decreases on the bottom wall as $\gamma$ increases (magnetic field changes its direction from the horizontal to the vertical direction) and vice versa for the top wall of the cavity. The reported results are in good agreement with the available published work in the literature.
##### MSC:
 80A20 Heat and mass transfer, heat flow 76W05 Magnetohydrodynamics and electrohydrodynamics 76S05 Flows in porous media; filtration; seepage 76R10 Free convection (fluid mechanics) 76M20 Finite difference methods (fluid mechanics) 80M20 Finite difference methods (thermodynamics)
##### Keywords:
porous media; natural convection; heat generation; MHD
##### References:
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