Effect of the magnetic field and heat generation on the free convection flow in a tall cavity filled with a porous medium

Abstract

An analytical study of the steady magnetohydrodynamics (MHD) free convection in an tall cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. It is considered that the Darcy law model is used. It is assumed that a uniform magnetic field normal to the walls of the cavity is externally imposed. The values of the governing parameters are as follows: Hartmann number \(\operatorname{Ha}=0, 10\) and \(50\), Rayleigh number \(\operatorname{Ra} = 10^{3}\), and the aspect ratio \(a=0.01\). The velocity and temperature profile are determined. These profiles are presented graphically at the center line of the cavity. It is found that the analytical solution is in very good agreement with the numerical solution which is obtained by solving partial differential equations using a finite-difference method.

Keywords

• analytical solution
• porous media
• natural convection
• heat generation