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Convective Transport in Nanofluids: Regularity of Solutions and Error Estimates for Finite Element Approximations

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Abstract

We study the stationary version of a thermodynamically consistent variant of the Buongiorno model describing convective transport in nanofluids. Under some smallness assumptions it is proved that there exist regular solutions. Based on this regularity result, error estimates, both in the natural norm as well as in weaker norms for finite element approximations can be shown. The proofs are based on the theory developed by Caloz and Rappaz for general nonlinear, smooth problems. Computational results confirm the theoretical findings.

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Acknowledgements

Pedro Morin was partially supported by Agencia Nacional de Promoción Científica y Tecnológica, through grants PICT-2014-2522, PICT-2016-1983, by CONICET through PIP 2015 11220150100661, and by Universidad Nacional del Litoral through grants CAI+D 2016-50420150100022LI. A research stay at Universität Erlangen was partially supported by the Simons Foundation and by the Mathematisches Forschungsinstitut Oberwolfach as well as by the DFG–RTG 2339 IntComSin.

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Authors and Affiliations

  1. Applied Mathematics III, University Erlangen–Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Eberhard Bänsch

  2. Facultad de Ingeniería Química, Universidad Nacional del Litoral and CONICET, Santiago del Estero 2829, S3000AOM, Santa Fe, Argentina

    Pedro Morin

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  1. Eberhard Bänsch
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  2. Pedro Morin
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Correspondence to Pedro Morin.

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Communicated by Y. Maekawa.

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Bänsch, E., Morin, P. Convective Transport in Nanofluids: Regularity of Solutions and Error Estimates for Finite Element Approximations. J. Math. Fluid Mech. 23, 42 (2021). https://doi.org/10.1007/s00021-020-00554-y

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