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Asymptotic analysis of the thermomicropolar fluid flow through a thin channel with cooling. (English) Zbl 1504.35357

Summary: 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
76A05 Non-Newtonian fluids
80A19 Diffusive and convective heat and mass transfer, heat flow
35C20 Asymptotic expansions of solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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