Abstract
Thermal convection in a two-layer system consisting of a horizontal fluid layer overlying a layer of porous medium saturated with the same fluid, with uniform heating from below and in the presence of a vertical magnetic field, is investigated. The flow in the porous medium is assumed to be governed by the Brinkman model. The onset of convection is seen to have a bimodal nature in which convection may be dominated by the porous medium or by the fluid, depending on the depth of the relative layers and the strength of the magnetic field. Numerical results are obtained for different values of the parameter (sic) (= depth of fluid layer/depth of porous layer) and for different values of the magnetic parameter Q. A comparison between the critical Rayleigh numbers in Brinkman and Darcy models reveals that in the absence of a magnetic field, the critical Ra-m for the Brinkman model is always greater than the corresponding one in the Darcy model; however, in the presence of a magnetic field when (d) over cap >= 0.33, the critical Ram for the Darcy model is larger.