Advances and Applications in Fluid Mechanics

An analytical investigation is carried out to examine the stability of a horizontal, fluid-saturated, rotating anisotropic porous layer that is heated from below and cooled from above. The analysis is conducted under the assumption that the fluid and solid phases are not in local thermal equilibrium. The momentum equation is based on Darcy’s model, modified to include the Coriolis term to account for rotational effects. The energy equations are formulated using a two-field model, representing the thermal behavior of the solid and fluid phases separately, with each incorporating anisotropic thermal conductivity. It is assumed that the temperatures of the solid and fluid phases are equal at the bounding surfaces. Linear stability theory is employed to determine the critical Rayleigh number and wave number for the onset of convection. Through graphical analysis, the effects of anisotropic permeability and rotation on convective instability are illustrated. The results reveal that thermal anisotropy and rotation act to stabilize the system, while mechanical anisotropy and an increased conductivity ratio have a destabilizing influence.