Analysis of convective heat transfer in a square cavity filled with a porous medium under a magnetic field

Steady and laminar natural convection flow of electrical conducting fluid in a square cavity filled with a porous medium such as fibrous material, and beds of spheres under a strong magnetic field is investigated numerically. The vertical walls of the cavity are differentially heated, and the horizontal walls are adiabatic while a uniform magnetic field is applied in the normal direction of vertical walls. The Brinkman-Forchheimer extended Darcy model is used to simulate the flow in the porous medium. The penalty finite element method with biquadratic rectangular elements is used to solve the nondimensional governing equations. The companied effects of Hartmann number (Ha = 0 - 100) and modified Darcy number (Da = 10^-5 - 10^-3) on the flow, temperature distributions, and heat transfer rate are investigated in terms of the stream functions, isotherm contours, and average Nusselt number for Ra = 10⁶ and Pr = 0:054 (liquid metals). It has been observed that the heat transfer rate is decreases smoothly as Ha is increases for Da = 10^-3 and 10^-4, while it is almost constant for Da = 10^-5. It also found that effects of the magnetic filed decreases on the heat transfer rate as Darcy number decreases due to domination of Darcy drag in porous medium.