Effect of gravity modulation on the onset of thermal convection in rotating viscoelastic fluid and porous layer

Abstract

The combined effect of gravity modulation and rotation on the onset of thermal convection in a viscoelastic horizontal fluid layer and a fluid-saturated porous layer is studied analytically using linear stability theory. The regular perturbation method based on small amplitude of modulation is employed to compute the critical value of Rayleigh number and wavenumber. The correction critical Rayleigh number is calculated as a function of Deborah number, Taylor number, Prandtl number, Darcy number, frequency of the modulation and normalized porosity. It is shown that in general the gravity modulation produces a stabilizing effect in case of viscous fluid and Darcy porous layer and both destabilizing and stabilizing effects in case of Brinkman porous layer. It is shown that the onset of convection can be advanced or delayed by proper tuning of various governing parameters. © 2012 Begell House, Inc.