Flow Governed by Generalised Brinkman’s Equation through an Inclined Porous Channel

Abstract

The unidirectional flow of a fluid with pressure-dependent viscosity through a porous structure is considered when the viscosity–pressure relationship is an exponential function of a pressure power function in order to investigate effects of the viscosity–pressure relation on the flow characteristics. The flow is governed by the generalized Brinkman’s equation with constant permeability, and a model flow domain of flow down an inclined porous channel is chosen for the sake of studying flow behaviour. Although the current work considers flow in a constant permeability porous structure, it does represent the first step in studying the more general flow through a variable permeability porous channel. The arising governing equations are solved numerically using MATLAB (version R2022a) and the flow is simulated to illustrate the effects of fluid properties, as well as flow and medium parameters, on the velocity profiles and shear stress. The results obtained should represent a baseline and a benchmark with which future experimental and theoretical work can be compared.

Keywords

• pressure-dependent viscosity
• generalized brinkman equation