EFFECTS OF A MAGNETIC-FIELD ON THE ONSET OF CONVECTION IN A POROUS-MEDIUM

The stability of a conducting fluid saturating a porous medium, in the presence of a uniform magnetic field, is investigated using the Brink man model. In the first part of the paper constant-flux thermal bounda ry conditions are considered for which the onset of convection is know n to correspond to a vanishingly small wave number. The external magne tic field is assumed to be aligned with gravity. Closed form solutions are obtained, based on a parallel flow assumption, for a porous layer with either rigid-rigid, rigid-free or free-free boundaries. In the s econd part of the paper, the linear stability of a porous layer, heate d isothermally from below, is investigated using the normal mode techn ique. The external mag- netic field is applied either vertically or ho rizontally. Solutions are obtained for the case of a porous layer with free boundar- ies. Results for a pure viscous fluid and a Darcy (dens ely packed) porous medium emerge from the present analysis as limiting cases.