Penetrative ferroconvection in a heterogeneous Brinkman porous medium

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 F(z). The results converge for six terms in the Galerkin expansion. The effect of types of F(z) and N-s is found to either delay or speedup the flow of the ferrofluids. The stability of the system for the model F4 is more stable and least stable for the model F1 in the presence of N-s. For different forms of F(z), the results show that the critical Rayleigh number increases with increasing Da, while decreases with increasing R-m and M-3. The values of a(c) increase with R-m but they decrease with increasing M-3 and Da. Besides, isothermal boundaries are found to be more stabilizing when compared to insulated boundaries.

Automated summary

This study aims to find 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 a vertical magnetic field. Numerical results show that the type of vertical heterogeneity permeability function and N-s parameter can either delay or speed up the flow of ferrofluids. Additionally, the critical Rayleigh number increases with increasing Da but decreases with increasing R-m and M-3 for different forms of the permeability function. Furthermore, isothermal boundaries are more stabilizing compared to insulated boundaries.