The onset of convection in a gravity-modulated viscoelastic fluid-saturated anisotropic porous layer

Abstract

This study presents a linear stability analysis of thermal convection in a porous layer saturated with viscoelastic fluid subjected to harmonic vertical vibrations so that the gravity varies periodically with time. The fluid obeys an Oldroyd-B constitutive relationship. The porous layer is considered to be densely packed and to possess vertical anisotropy in both mechanical and thermal properties. The onset threshold in terms of correction to a critical Rayleigh number is computed using the regular perturbation method based on small amplitude of modulation. Due to the imposed gravity modulation, there is a shift in the onset criteria. It is found that the low-frequency gravity modulation advances the convection, while for moderate and large frequencies stabilization occurs. The thermal anisotropy, normalized porosity, Darcy-Prandtl number, and relaxation parameter reinforce-while the mechanical anisotropy and retardation parameters suppress-the stabilizing effect of g-jitter. © 2013 by Begell House, Inc.