Upper Limits to the Complex Growth Rate in Magneto-Thermal Instability in a Couple-Stress Fluid in a Porous Medium

Abstract

A layer of couple-stress fluid heated from below in a porous medium is considered in the presence of  uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the paper through mathematical analysis of the governing equations of couple-stress fluid convection with a uniform vertical magnetic field in porous medium, for any combination of perfectly conducting free and rigid boundaries of infinite horizontal extension at the top and bottom of the fluid, established that the complex growth rate  of oscillatory perturbations, neutral or unstable, must lie inside a semi-circle...........