Impact of heat transfer in a duct composed of anisotropic porous material: A non-linear Brinkman-Forchheimer extended Darcy's model: A computational study

Abstract

Forced convective heat transport in a rectangular porous channel with anisotropic permeability is investigated in this study. A fully developed flow field is assumed, and the Brinkman-Forchheimer extended Darcy's equation is adopted to model the fluid flow. The thermal field is developing. A weak formulation of the momentum equation has been obtained. The existence and uniqueness of the solution for the weak momentum equation are proved using the Browder-Minty theorem. The finite difference approach has been utilized to solve these coupled differential equations . Non-equidistant grids are implemented in the axial direction to reduce computational time and space. The effect of anisotropic parameters, such as permeability ratio and orientation angle, on the hydrodynamic and thermal characteristics of the flow has been discussed. An increase in the permeability ratio ( K ) causes an increase in the local Nusselt number . Anisotropy has been identified as crucial in heat transmission for the Darcy numbers less than 0.75. The anisotropic phenomenon of the channel contributed to a more than 13 % increase in the heat transmission rate compared to the isotropic scenario. Also, as the anisotropic parameters increase, the amount of heat transferred from the walls to the fluid up to any desired axial distance increases. Validation of numerical solutions is done using existing literature. • This study has addressed forced convective heat transport in a rectangular anisotropic porous channel. • The flow field is assumed to be governed by the non-linear Darcy – Brinkman – Forchheimer equations. • A weak form of the governing equations is derived, and the existence and uniqueness have been shown. • A finite difference approach based on a successive acceleration replacement (SAR) scheme has been implemented.