Effect of Gravity Modulation on the Onset of Convection in a Horizontal Anisotropic Porous Layer

摘要

A linear stability theory is used to investigate the effect of gravity modulation on the onset of convection in a homogeneous anisotropic porous layer heated from above. The Brinkman model with anisotropic permeability is considered in the current analysis. The Oberbeck - Boussinesq approximation is employed and the corresponding governing equations are reduced to Mathieu's equation. Floquet theory is used to find the critical Rayleigh number and the corresponding wave number as a function of modulation amplitude and frequency. It is found that the onset of convection can be advanced or delayed by adjusting amplitude and frequency depending upon the Darcy number.