Onset of Darcy–Brinkman Ferroconvection in a Rotating Porous Layer Using a Thermal Non-Equilibrium Model: A Nonlinear Stability Analysis

Abstract

This article presents a nonlinear stability analysis of a rotating thermoconvective magnetized ferrofluid layer confined between stress-free boundaries using a thermal non-equilibrium model by the energy method. The effect of interface heat transfer coefficient \({( {{\mathcal H}^{\prime}})}\), magnetic parameter (M3), Darcy–Brinkman number \({( {\hat{{\rm D}}{\rm a}})}\), and porosity modified conductivity ratio (γ′) on the onset of convection in the presence of rotation \({({T_{{\rm A}_1}})}\) have been analyzed. The critical Rayleigh numbers predicted by energy method are smaller than those calculated by linear stability analysis and thus indicate the possibility of existence of subcritical instability region for ferrofluids. However, for non-ferrofluids stability and instability boundaries coincide. Asymptotic analysis for both small and large values of interface heat transfer coefficient \({({{\mathcal H}^{\prime}})}\) is also presented. A good agreement is found between the exact solutions and asymptotic solutions.