EFFECT OF AN EXTERNAL MAGNETIC-FIELD ON BUOYANCY-DRIVEN FLOW IN A SHALLOW POROUS CAVITY

A study is made of steady, natural convection in a shallow horizontal porous layer, saturated by an electrically conducting fluid, to which a transverse magnetic field Is applied. The enclosure is insulated on the top and bottom walls, while an end-to-end temperature difference b etween the vertical walls is imposed. The problem is governed by three dimensionless parameters: the Darcy-Rayleigh number Ra, the cavity as pect ratio A, and the Hartmann number Ha. On the basis of Darcy's equa tion, an approximate analytical solution, valid in the limit of a shal low cavity (A --> 0), is developed using matched asymptotic expansions . The solution is given up to O(A(3)). A numerical study of the same p henomenon, obtained by solving the complete system of governing equati ons, is also conducted. The study covers the range of Ra from 0 to 500 , Ha from 0 to 5, and A from 0.05 to 1. Results are presented for the velocity and temperature profiles and heat transfer in terms of the go verning parameters. Upon comparing the analytical and the numerical re sults, the range of validity of the approximate analytical solution is discussed.