Analysis of the Darcy-Brinkman flow with viscous dissipation and non-homogeneous thermal boundary condition

TL;DR

This paper derives a simplified mathematical model for steady Darcy-Brinkman flow in porous media considering viscous dissipation and non-homogeneous thermal boundary conditions, aiding engineering applications.

Contribution

It introduces a rigorous asymptotic analysis leading to a new coupled model that accounts for viscous dissipation and thermal boundary effects in porous media flow.

Findings

Derived sharp a priori estimates for the model

Proved compactness of rescaled functions

Presented a simplified coupled flow model

Abstract

This study investigates the steady-state Darcy-Brinkman flow within a thin, saturated porous domain, focusing on the effects of viscous dissipation and non-homogeneous boundary condition for the temperature. Employing asymptotic techniques with respect to the domain's thickness, we rigorously derive the simplified coupled model describing the fluid flow. The mathematical analysis is based on deriving the sharp a priori estimates and proving the compactness results of the rescaled functions. The resulting limit model incorporates contributions of viscous dissipation and thermal boundary conditions and thus could prove useful in the engineering applications involving porous media.