Local thermal nonequilibrium perspective of heat transfer and fluid flow in a slender anisotropic porous cavity due to lateral uniform heat flux

Abstract

The influence of the local thermal nonequilibrium (LTNE) state on steady-state natural convection due to the heating and cooling of the side walls of the slender porous cavity has been addressed analytically and numerically. The porous medium is assumed to be hydrodynamically anisotropic. The Darcy model has been adopted. A closed-form solution, based on a parallel hypothesis, is reported for a slender cavity. The combined impact of media anisotropy and LTNE state on the heat transfer rate, as well as flow dynamics, have been analyzed. The help of boundary layer analysis is taken to report the boundary layer thickness and heat transfer rate of fluid flow analytically. It has been found that the maximum (minimum) heat transfer rate of the fluid phase as well as solid phase takes place at orientation angle, ϕ , equal to π / 2 when permeability along the horizontal (vertical) direction is higher than the same along vertical (horizontal) direction.