Forced convection in a fluid saturated anisotropic porous channel with isoflux boundaries

Abstract

Fully developed forced convective flow inside a channel filled with a porous material bounded by two impermeable walls subject to a constant heat flux is considered. We consider the Brinkman-Forchheimer equation to govern the flow inside the porous medium, which accounts for the presence of the inertial term. We assume that the porous medium is anisotropic in nature and the permeability is varying along all the directions so that it appears as a positive semidefinite matrix in the momentum equation. We have obtained velocity, temperature, and Nusselt number numerically due to the presence of the nonlinear quadratic term in the momentum equation. Asymptotic solutions for small Darcy number (∼10−3) and high Darcy number (∼10) are obtained. The asymptotic behavior of the Nusselt number is discussed. The key purpose of this paper is to study the effect of anisotropic permeability ratio, anisotropic angle, and inertial parameter on the hydrodynamic quantities and heat transfer for the configuration considered. In particular, we observe that for the moderate range of Darcy number, 10−2 to 102, inertia plays a significant role in the Nusselt number. We observe that inclusion of anisotropic permeability enhances the relative heat transfer rate by almost 20% compared to the corresponding isotropic situation. We present a detailed analysis about the inclusion of the permeability matrix in the Brinkman-Forchheimer extended Darcy momentum equation.