Hydromagnetic soret convection in a shallow porous enclosure with a shear stress applied on the free upper surface

Abstract

Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.The fluid flow induced by combined effects of thermal gradient, thermal diffusion, magnetic field and an external shear stress in a horizontal porous layer, subject to uniform heat flux along its long horizontal walls is studied analytically and numerically. The shear stress is applied on the top horizontal free surface while the bottom one is assumed to be rigid. The problem formulation is based on the Brinkman model with the Boussinesq approximation. The governing parameters are the thermal Rayleigh number, RT , the Lewis number, Le, the separation parameter, ϕ, the Darcy number, Da, the Hartmann number Ha, the dimensionless shear stress, τ and the aspect ratio of the enclosure, Ar. The analytical solution is derived on the basis of the parallel flow approximation and validated numerically using a finite difference method. The critical Rayleigh numbers for the onset of stationary, subcritical and oscillatory convection are determined explicitly as functions of the governing parameters for infinite layers in the absence of the external shear stress. The effect of the main governing parameters on the fluid flow and heat and mass transfer characteristics is discussed.