NATURAL-CONVECTION IN AN INCLINED FLUID LAYER WITH A TRANSVERSE MAGNETIC-FIELD - ANALOGY WITH A POROUS-MEDIUM

In this paper the effect of a transverse magnetic field on buoyancy-dr iven convection in an inclined two-dimensional cavity is studied analy tically and numerically. A constant heat flux is applied for heating a nd cooling the two opposing walls while the other two walls are insula ted. The governing equations are solved analytically, in the limit of a thin layer, using a parallel flow approximation and an integral form of the energy equation. Solutions for the flow fields, temperature di stributions, and Nusselt numbers are obtained explicitly in terms of t he Rayleigh and Hartmann numbers and the angle of inclination of the c avity. In the high Hartmann number limit it is demonstrated that the r esulting solution is equivalent to that obtained for a porous layer on the basis of Darcy's model. In the low Hartmann number limit the solu tion for a fluid layer in the absence of a magnetic force is recovered . In the case of a horizontal layer heated from below the critical Ray leigh number for the onset of convection is derived in term of the Har tmann number. A good agreement is found between the analytical predict ions and the numerical simulation of the full governing equations.