On the effects of surface roughness in non-isothermal porous medium flow

TL;DR

This paper studies how surface roughness affects non-isothermal porous medium flow, deriving effective models that account for oscillatory boundary effects and viscous heating.

Contribution

It introduces a rigorous asymptotic analysis of non-isothermal Darcy-Brinkman flow over rough surfaces, revealing new coupled elliptic systems depending on roughness scale.

Findings

Effective models depend on roughness scale and show strong coupling effects.

Oscillatory geometry induces coupling not present in smooth boundary cases.

Convergence of velocity, pressure, and temperature fields established as roughness parameter tends to zero.

Abstract

We analyze a non-isothermal Darcy-Brinkman thin-film flow with a periodically oscillating boundary and viscous dissipation acting as a heat source. Using asymptotic analysis and the periodic unfolding method, we establish the convergence of velocity, pressure, and temperature fields as the small parameter (related to the film thickness and the period of the roughness) tends to zero. The limit problems depend on the relative scaling of the roughness wavelength and consist of coupled elliptic systems combining Reynolds-type equations with Darcy-Brinkman cell problems and reduced energy equation. In the critical roughness regime, the effective model exhibits a strong coupling induced by the oscillatory geometry, which does not occur in a smooth-boundary case.