Numerical Investigations of Thermal Convection in Rotating Micropolar Fluid in Hydromagnetics Saturating a Porous Medium

Abstract

The thermal convection in a layer of electrically conducting micropolar fluid heated from in the presence of a uniform magnetic field and rotation in a porous medium is considered. Using Boussinesq approximation, the linearized stability theory and normal mode analysis method for perturbation equations relevant to the problem, the dispersion relation is derived and the exact solutions are obtained for the case of two free boundaries.The presence of coupling between thermal and micropolar effects, uniform rotation , magnetic field and medium permeability may bring overstability in the system. The critical Rayleigh number for the onset of ordinary cellular convection and the onset of overstability are computed numerically using Newton-Raphson method through the software FORTRAN-95. It is found that these critical Rayleigh numbers increase with the increase in magnetic field , rotation and micropolar coefficients (dynamic microrotation viscosity and the coefficient of angular viscosity )implying thereby their stabilizing effect on the system , whereas critical Rayleigh numbers decrease with increase in medium permeability. It is evident from graphs that overstability is dominant parameter accounting for low wave numbers, however reverse occur for large wave numbers.