MAXWELL-CATTANEO LAW OF HEAT CONDUCTION THROUGH POROUS FERROCONVECTION WITH MAGNETIC FIELD DEPENDENT VISCOSITY

Abstract

The problem of convective instability in a ferromagnetic uid saturated porous medium with magnetic eld dependent (MFD) viscosity and Maxwell-Cattaneo law is studied using the method of small perturbation. Darcy model is used to describe the uid 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 ferro uid is a function of temperature. The non-classical Maxwell-Cattaneo heat ux law involves a wave type of heat transport and does not su er from the physically unacceptable drawback of in nite heat propagation speed. For a uid 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 uid is distinctly in uenced by the e ect 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 e ect of magnetic forces. It is also established that the e ects of second sound and MFD viscosity are mutually antagonistic towards in uencing the stability of the system and that an increase in MFD viscosity attenuates the threshold of porous ferroconvection.