Maxwell-Cattaneo law of heat conduction through porous ferroconvection with magnetic field dependent viscosity

Abstract

The problem of convective instability in a ferromagnetic fluid saturated porous medium with magnetic field dependent (MFD) viscosity and Maxwell-Cattaneo law is studied using the method of small perturbation. Darcy model is used to describe the fluid motion. The horizontal porous layer is heated from below and cooled from above. Convection is caused by a spatial variation in magnetization which is induced when the magnetization of the ferrofluid is a function of temperature. The non-classical Maxwell-Cattaneo heat flux law involves a wave type of heat transport and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. For a fluid layer contained between magnetically responding and isothermal boundaries, approximate solutions for stationary instability are obtained by using the higher order Galerkin technique. It is shown that the ferromagnetic fluid is distinctly influenced by the effect of magnetic forces and is prone to instability in the presence of second sound and MFD viscosity. It is found that the second sound mechanism works in tandem with the effect of magnetic forces. It is also established that the effects of second sound and MFD viscosity are mutually antagonistic towards influencing the stability of the system and that an increase in MFD viscosity attenuates the threshold of porous ferroconvection.