Magnetohydrodynamic Effect on Rayleigh-Benard convection In a Rectangular Porous Enclosure with Sinusoidal Wall Temperature

Abstract

A numerical study of the magnetohydrodynamic (MHD) effect on the Rayleigh-Benard convection in a rectangular porous enclosure has been investigated. For the fluid flow and heat transfer the Darcy’s law and the energy equation are considered as the governing equations. For the boundary conditions of enclosure, the bottom wall is heated with sinusoidal variation and the top wall is cold while the vertical walls are adiabatic. The governing equations are initially transformed into non-dimensional form using appropriate transformations. The non-dimensional governing equations along with boundary conditions are solved numerically, employing the finite difference method, using the Successive Over-Relaxation (SOR) scheme for the Darcy’s law and the energy equation is solved by Alternative Direction Implicit (ADI) scheme. The in-house FORTAN code is used in this study. The Rayleigh number (Ra), Hartmann number (Ha) and the angle of inclination ( ) are the pertinent parameters of this study. The numerical results are presented in terms of the streamlines, isotherms, velocity and temperature distribution as well as the variation of the local rate of heat transfer in terms of the local Nusselt number at the heated wall. Finally, the average Nusselt number has been shown against Rayleigh number (Ra), Hartmann number (Ha) and the angle of inclination ( ).