Linear Stability Analysis of Convection of a Maxwell Fluid in a Rotating Anisotropic Porous Layer with Oblique Principal Axes

Abstract

An analytical method is carried out to investigate linear stability analysis of convection in a rotating anisotropic porous layer heated from below. For the accurate modeling of the anisotropic porous matrix, both mechanical anisotropy about the rotating axis in the vertical direction and hydrodynamical anisotropy prevailing in the horizontal plane whose principal axes oriented in a direction non-coincident with the gravity force are considered. On the basis of the generalized Darcy’s law and the modified Darcy-Maxwell- Jeffrey model employed to take into account the properties of the viscoelastic fluid saturating the porous matrix and to include the time derivate and Coriolis terms, the linear stability theory related to the normal mode method has been followed to conduct this analysis. Moreover, the criteria for both stationary and oscillatory convection is derived analytically. The rotation inhibits the onset of convection in both stationary and oscillatory modes. It has been demonstrated that each physical parameter involved in the present analysis has an important effect on the system.