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Abstract
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 between the vertical walls is imposed. The problem is governed by three dimensionless parameters; the Darcy-Rayleigh number Ra, the cavity aspect ratio A, and the Hartmann number Ha. On the basis of Darcy's equation, an approximate analytical solution, valid in the limit of a shallow cavity ( A→0), is developed using matched asymptotic expansions. The solution is given up to 0( A3). A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is also conducted. The study covers the range of Ra from 0 to 500, Ha from Oto5, and A from O.O5 to 1. Results are presented for the velocity and temperature profiles and heat transfer in terms of the governing parameters. Upon comparing the analytical and the numerical results, the range of validity of the approximate analytical solution is discussed.
Notes
Address correspondence to Dr. P. Vasseur, Department of Mechanical Engineering, Ecole Polytechnique de Montreal, C.P. 6079, succ. Centre-ville, Montreal, Quebec H3C 3A7, Canada.
