Roughness-induced effects on the thermomicropolar fluid flow through a thin domain
Igor Pažanin, Francisco J. Suárez-Grau
TL;DR
This work analyzes the asymptotic behavior of steady thermomicropolar flow in a thin channel with a rough boundary. By adapting the unfolding method to a thin-domain setting, it derives homogenized models in two regimes: a critical case where the roughness wavelength and thickness scale jointly, and a subcritical case with smooth-effective behavior. The macroscopic flow and microrotation are governed by two-pressure homogenized problems with coefficients a_λ and b_λ determined by local cell problems, yielding explicit expressions or computable cell formulas for the averaged quantities U^{av}, W^{av}, and T^{av}. The results quantify the impact of roughness on the mean velocity and microrotation and provide practical, numerically accessible effective models for engineering applications.
Abstract
In this paper, we study the asymptotic behavior of the thermomicropolar fluid flow through a thin channel with rough boundary. The flow is governed by the prescribed pressure drop between the channel's ends and the heat exchange through the rough wall is allowed. Depending on the limit of the ratio between channel's thickness and the wavelength of the roughness, we rigorously derive different asymptotic models clearly showing the roughness-induced effects on the average velocity and microrotation. To accomplish that, we employ the adaptation of the unfolding method to a thin-domain setting.