The effects of heterogeneity on Darcy-Benard convection saturated with a ferrofluid

Abstract

This study investigates how the vertical magnetic field influences the stability of the ferrofluid in a heterogeneous porous layer with the vertical flow. The layer, confined between two impermeable walls, is subject to different heat flux conditions on each side. The behavior of the ferrofluid governed by Darcy’s law and the Oberbeck-Boussinesq approximation, while the magnetic field is modeled using Maxwell’s equations. A dimensionless formulation and linear stability analysis are employed to derive an ordinary differential equation, which is solved using the shooting method and a Runge-Kuttasolver. The results indicate that the transition of the wave number from zero to a nonzero value is connected to the Peclet number and other magnetic parameters.