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


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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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).

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Mathematics Subject Classification

  • 35J40
  • 35Q35
  • 76D03


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