Analytical and Numerical Study of Combined Effects of a Magnetic Field and an External Shear Stress on Soret Convection in a Horizontal Porous Enclosure

Abstract

The fluid flow induced by combined actions of Soret effect and shear stress applied on the top horizontal free surface (the lower one being rigid) in a horizontal porous layer, under an external magnetic field, is studied analytically and numerically. The horizontal walls of the porous layer are subject to uniform heat fluxes. The porous layer is sparsely packed then the flow is governed by the Brinkman model assuming the Boussinesq approximation. The governing parameters are the thermal Rayleigh number, R_T, the Lewis number, Le, the separation parameter, ϕ, the effective Darcy number, Da, the Hartmann number Ha, the dimensionless shear stress, τ, and the aspect ratio of the enclosure, A_r. An analytical solution is derived on the basis of the parallel flow approximation, assuming enlarge aspect ratio layer, 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 with a zero shear stress, τ = 0. The codimension-2 point is identified and different flow behaviors are observed and discussed. The effects of the governing parameters on the fluid flow intensity and heat and mass transfer characteristics are also discussed.