Convection in Superposed Fluid and Porous Layers in the Presence of a Vertical Magnetic Field

A linear stability analysis is applied to a system consisting of a horizontal fluid layer overlying a layer of porous medium saturated with the same fluid, with uniform heating from below in the presence of a vertical magnetic field. The flow in porous medium is assumed to be governed by Darcy’s law. The Beavers-Joseph condition is applied at the interface between the two layers. Numerical solutions are obtained using expansion of Chebyshev polynomials. This spectral method has a strong ability to solve multilayered problems and allows us to obtain a highly accurate eigenvalues in a very efficient manner. Numerical results are obtained for different values of the parameter d̂ (= depth of fluid layer/depth of porous layer) and different values of the magnetic parameter Q. The effect of magnetic field is investigated and it is found that the linear stability curves for the onset of convection motion are bimodal even for higher values of d̂ . Key-Words: -Superposed porous and fluid layersThermal convectionDarcy's lawMagnetic fieldStationary convection, Chebyshev tau method.