Penetrative ferroconvection in a heterogeneous Brinkman porous medium

Abstract

This study aims at finding the linear theory for the onset of ferromagnetic convective flow in a heterogeneous Brinkman porous layer with uniformly distributed internal heat source in the presence of vertical magnetic field. The resulting critical values are obtained numerically using the Galerkin technique for isothermal/insulated rigid-ferromagnetic boundaries for different forms of vertical heterogeneity permeability function [Formula: see text]. The results converge for six terms in the Galerkin expansion. The effect of types of [Formula: see text] and [Formula: see text] is found to either delay or speedup the flow of the ferrofluids. The stability of the system for the model [Formula: see text] is more stable and least stable for the model [Formula: see text] in the presence of [Formula: see text]. For different forms of [Formula: see text], the results show that the critical Rayleigh number increases with increasing [Formula: see text], while decreases with increasing [Formula: see text] and [Formula: see text]. The values of [Formula: see text] increase with [Formula: see text], but they decrease with increasing [Formula: see text] and [Formula: see text]. Besides, isothermal boundaries are found to be more stabilizing when compared to insulated boundaries.