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Rigorous derivation of the asymptotic model describing a steady thermomicropolar fluid flow through a curvilinear channel

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Abstract

In this paper, we consider the steady flow of a thermomicropolar fluid through a thin curvilinear channel. The flow is governed by the prescribed pressure drop between the channel’s ends. The heat exchange between the fluid inside the channel and the exterior medium is allowed through the upper curved wall, while the lower wall is insulated. Using asymptotic analysis with respect to the domain’s thickness, we compute the asymptotic approximation of the solution. The derived solution is obtained in explicit form, allowing us to clearly observe the effects of the curvature of the domain as well as the micropolarity of the fluid. A boundary layer analysis is provided for the microrotation. The proposed effective model is rigorously justified via error estimates in suitable norms.

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Acknowledgements

The authors of this work have been supported by the Croatian Science Foundation under the project MultiFM (IP-2019-04-1140). We thank the Reviewers for their valuable remarks and comments that helped to correct and improve our paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

    Igor Pažanin, Marko Radulović & Borja Rukavina

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  1. Igor Pažanin
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  2. Marko Radulović
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  3. Borja Rukavina
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Correspondence to Marko Radulović.

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Pažanin, I., Radulović, M. & Rukavina, B. Rigorous derivation of the asymptotic model describing a steady thermomicropolar fluid flow through a curvilinear channel. Z. Angew. Math. Phys. 73, 195 (2022). https://doi.org/10.1007/s00033-022-01831-8

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  • DOI: https://doi.org/10.1007/s00033-022-01831-8

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