Porous ferroconvection with local thermal nonequilibrium temperatures and with Cattaneo effects in the solid

Abstract

The influence of local thermal nonequilibrium with Cattaneo effects in the solid on the onset of thermal-convective instability in a horizontal layer of Darcy porous medium saturated by a ferrofluid in the presence of a uniform vertical magnetic field is investigated. The presence of the Cattaneo effect is to instill instability via oscillatory motion as well which is not reminiscent of the observed instability phenomenon in its absence. Increase in the value of the solid thermal relaxation time parameter τ is found to advance the onset of oscillatory ferroconvection. The onset of stationary ferroconvection is delayed, while the onset of oscillatory convection is accelerated with an increase in the value of the interphase heat transfer coefficientHt. The threshold value of Ht, at which the transition from stationary to oscillatory convection takes place, decreases with increasing τ noticeably and marginally with increasing magnetic parameter M3, while it increases with increasing ratio of conductivities α and magnetic number M1. The critical wave number for stationary convection is found to be higher than for oscillatory convection.