Linear and weakly nonlinear stability analysis on a rotating anisotropic ferrofluid layer

Abstract

In this article, the linear and weakly nonlinear instability in a rotating anisotropic magnetic fluid layer when the layer is internally heated and the solid matrix and fluid are not in local thermal equilibrium is studied. The Darcy model for the permeable medium and Coriolis force term for rotation are considered in the momentum equation. For the linear stability analysis, normal mode has been performed while weakly nonlinear analysis is carried out with a truncated Fourier series. The Runge-Kutta-Gill numerical method is used for solving the finite-amplitude equation to study the transient behavior of the Nusselt number at the lower boundary. Effects of parameters on the Rayleigh number have been studied in gravitational as well as microgravity conditions. It was found that Taylor number Ta and thermal anisotropy parameter ηf had a stabilizing effect on the convection. Heat transport is decreased with the increase in Taylor number Ta and thermal anisotropy parameter ηf. When internal heat is less (ζ = 1.5), the heat transport rate is high, and when internal heat is sufficient (ζ = 0.3), the heat transfer rate is low.