Oscillatory porous medium ferroconvection with Maxwell-Cattaneo law of heat conduction

Abstract

The scheme of small perturbation is used to address the problem of buoyancy driven convection of Darcy-Brinkman type in a ferromagnetic fluid invoking the Maxwell-Cattaneo law. An analytical solution of the eigenvalue problem involved, encompassing stationary and overstable modes, is obtained by adopting simplified boundary conditions. The mathematical application package MATHEMATICA is adopted to determine the eigenvalue expressions and the critical numbers. It is established that the threshold of Darcy-Brinkman ferroconvection is amplified through the stresses of magnetic and second sound mechanisms and the opposite influence is found to be true due to the presence of porous medium. It is delineated that both the critical frequency of oscillations and aspect ratio of cells of convective heat transfer are susceptible to the different parameters of the study. It is also shown that, as long as the Cattaneo and Prandtl numbers are pretty high, the oscillatory mode of instability is preferred to the stationary mode of ferroconvection.