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Dynamic boundary conditions and the Carslaw-Jaeger constitutive relation in heat transfer

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  • Niko Sauer

    (University of Pretoria)

Abstract

We study a dynamic boundary condition problem in heat transfer which represents the interaction between a conducting solid enclosed by a conducting shell. Both the solid and the shell are thermally inhomogeneous and anisotropic. Interaction is modelled by considering the solid as a source of thermal energy to the shell. A constitutive equation proposed by Carslaw and Jaeger establishes a relation between temperature in the shell and the boundary value of temperature in the solid. This gives rise to a dynamic boundary condition problem that has not been studied in the recent literature. The system of equations so obtained is presented as an implicit evolution equation which involves a pair of unbounded linear operators that map between two different spaces. We extend the operators to a jointly closed pair for which the implicit equation makes sense. The solution of the initial value problem is constructed by means of a holomorphic family of solution operators. The class of admissible initial states is surprisingly large.

Suggested Citation

  • Niko Sauer, 2020. "Dynamic boundary conditions and the Carslaw-Jaeger constitutive relation in heat transfer," Partial Differential Equations and Applications, Springer, vol. 1(6), pages 1-20, December.
    • Handle: RePEc:spr:pardea:v:1:y:2020:i:6:d:10.1007_s42985-020-00050-y
    DOI: 10.1007/s42985-020-00050-y
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