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

## TL;DR

This study investigates forced convection in an anisotropic porous channel with isoflux boundaries, analyzing how anisotropic permeability affects flow and heat transfer using a Brinkman-Forchhimer model.

## Contribution

First analysis of anisotropic permeability effects on forced convection in porous channels using the Brinkman-Forchhimer model with permeability matrix.

## Key findings

- Nusselt number varies significantly with anisotropic ratio and angle.
- Velocity and temperature profiles are affected by anisotropic permeability.
- Permeability matrix inclusion offers new insights into flow behavior.

## Abstract

Fully developed forced convective flow in a channel filled with porous material bounded by two impermeable walls subject to constant heat flux is considered. We consider Brinkman-Forchhimer equation to govern the flow inside the porous medium which accounts for the presence of inertial term. We assume that the porous medium is anisotropic in nature and permeability is varying along all the directions, correspondingly, permeability will be a matrix which appear as a positive semi-definite matrix in the momentum equation. The anisotropic nature of the porous medium is characterized by anisotropic ratio and angle. We have obtained the velocity, temperature and Nusselt number numerically, due to the presence of the non-linear quadratic term in the momentum equation. The effect of anisotropic permeability ratio and anisotropic angle on hydrodynamic and heat transfer is shown. We see that Nusselt number is altered significantly with the anisotropic ratio and angle. We present a fresh analysis about the inclusion of the permeability matrix in the Brinkman-Forchhimer extended Darcy momentum equation. To the best of the authors knowledge, this is the first attempt to analyze general anisotropy corresponding to Brinkman-Forchhimer extended Darcy model.