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Heat Conduction Problem in a Dilated Pipe: Existence and Uniqueness Result

Mediterranean Journal of Mathematics volume 14, Article number: 97 (2017) Cite this article

Abstract

We study the heat conduction through a pipe filled with incompressible viscous fluid. The goal of this paper is to take into account the effects of the spipe’s dilatation due to the heating. In view of that, we assume that the longitudinal dilatation of the pipe is described by a linear heat expansion law. We prove the existence and uniqueness theorems for the corresponding boundary value problem. The main difficulty comes from the fact that the flow domain changes depending on the solution of the heat equation leading to a nonlinear coupled governing problem.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Zagreb, Zagreb, Croatia

    Eduard Marušić-Paloka & Igor Pažanin

  2. Department of Mathematics, Faculty of Graphic Arts, University of Zagreb, Zagreb, Croatia

    Marija Prša

Authors
  1. Eduard Marušić-Paloka
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  2. Igor Pažanin
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  3. Marija Prša
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Corresponding author

Correspondence to Igor Pažanin.

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Marušić-Paloka, E., Pažanin, I. & Prša, M. Heat Conduction Problem in a Dilated Pipe: Existence and Uniqueness Result. Mediterr. J. Math. 14, 97 (2017). https://doi.org/10.1007/s00009-017-0898-6

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  • DOI: https://doi.org/10.1007/s00009-017-0898-6

Mathematics Subject Classification

  • 35J40
  • 35Q35
  • 76D03

Keywords

  • heat conduction
  • dilated pipe
  • linear heat expansion law
  • existence and uniqueness of the solution