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Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type

Abstract

A number of problems for the interaction of laser radiation with a heat-conducting half-space and a layer are considered. The obtained solutions are compared with each other and with the solutions of the classic heat equation and the wave equation. A laser impulse is modelled by defining the heat flux at the boundary for the opaque medium, or by defining the distribution of heat sources in the volume for the semitransparent medium. The power of the laser pulse depends on time as the Dirac delta function or as the Heaviside function do. It allows for the simulation of instant and continuous laser exposure on the medium. Temperature distributions are obtained by using Green’s functions for a half-space and a layer with the Dirichlet and Neumann boundary conditions.

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Correspondence to Mikhail B. Babenkov.

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Communicated by Andreas Öchsner.

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Babenkov, M.B., Ivanova, E.A. Analysis of the wave propagation processes in heat transfer problems of the hyperbolic type. Continuum Mech. Thermodyn. 26, 483–502 (2014). https://doi.org/10.1007/s00161-013-0315-8

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  • DOI: https://doi.org/10.1007/s00161-013-0315-8

Keywords

  • Hyperbolic heat conduction
  • Heat flux relaxation constant
  • Heat propagation speed
  • Heat transport in nanosystems
  • Heat pulse