Homogenization of the non-isothermal, non-Newtonian fluid flow in a thin domain with oscillating boundary

In this paper, we study the flow of a non-Newtonian fluid through a thin three-dimensional domain with an oscillating boundary. Starting from a nonlinear coupled system describing a non-isothermal regime of the flow, we rigorously derive three different effective models, depending on the period of the boundary roughness. We employ a homogenization technique based on the adaption of the unfolding method and deduce the roughness-induced effects on the fluid flow.