Magnetohydrodynamic stability of natural convection in a vertical porous slab

• MHD stability of natural convection in a vertical layer of Brinkmanporous medium is investigated.
• Successfully used Squire′s transformation to show that 2D are more unstable than 3D.
• The magnetic field, porous parameter and the ratio of viscosities have a stabilizing effect on the system.
• A sudden change in streamlines and isotherms is observed at the transition mode.

The stability of the conduction regime of natural convection in an electrically conducting fluid saturated porous vertical slab is investigated in the presence of a uniform external transverse magnetic field. The flow in the porous medium is described by modified Brinkman-extended Darcy equation with fluid viscosity different from effective viscosity. The boundaries of the vertical porous slab are assumed to be rigid-isothermal and electrically non-conducting. The resulting stability equations are solved numerically using Galerkin method. The critical Grashof number GcGc, the critical wave number αcαc and the critical wave speed cccc are computed for a wide range of porous parameter σpσp, the ratio of effective viscosity to the fluid viscosity ΛΛ, the Prandtl number PrPr and the Hartmann numberMM. Based on these parameters, the stability characteristics of the system are discussed in detail. The presence of advective inertia is to instill instability on the flow in a porous medium and found that the magnetic field, porous parameter and ratio of viscosities have a stabilizing effect on both stationary and oscillatory wave instabilities. Besides, the value of PrPr at which transition occurs from stationary to oscillatory mode of instability decreases with increasing M,σpandΛ.