Asymptotic analysis of the thermomicropolar fluid flow through a thin channel with cooling

In this paper, we consider a steady-state flow the thermomicropolar fluid through a thin straight channel. The flow is governed by the prescribed pressure drop between channel's ends. The heat exchange between the fluid inside the channel and the exterior medium is allowed through the upper wall, whereas the lower wall is insulated. Using the asymptotic analysis with respect to the thickness of the channel, we derive a first-order asymptotic solution acknowledging the effects of the fluid's microstructure. A rigorous justification of the proposed effective model is provided by proving the error estimates in suitable norms.