Onset of Darcy-Brinkman double-diffusive convection in a magnetized ferrofluid layer using a thermal non-equilibrium model: A nonlinear stability analysis

Abstract

This paper presents a nonlinear stability analysis of a double-diffusive convection in a magnetized ferrofluid layer confined between stress-free boundaries using a thermal non-equilibrium model by the energy method. A Darcy-Brinkman model is used for the momentum equation and a two-field model is used for the energy equation, each representing the solid and fluid phases separately. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. The effects of the interface heat transfer coefficient (H), magnetic parameter (M3), Darcy-Brinkman number (D̂a) and porosity-modified conductivity ratio (γ') on the onset of ferroconvection in the presence of solute (S') have been analysed. For all the cases studied, it is found that solute gradient enhances the stability of the system. A comparison with linear instability theory shows that there is a difference between the critical Rayleigh numbers and thus indicates the possibility of the existence of a subcritical instability region for ferrofluids. However, for non-ferrofluids stability and instability boundaries coincide. ©2010 Nanjing Geophysical Research Institute Printed in the UK.