Analytical solution of heat conduction problem for a multilayer assembly arising in photothermal reliability testing

T. Elperin, G. Rudin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

An analytical solution of a two-dimensional heat conduction problem is obtained for a multilayer thin coating-substrate assembly irradiated by a laser beam. A method of solution is based on expansion of Laplace and Hankel transforms of temperature distribution in terms of a small parameter which is equal to the ratio of a coating thickness to a laser beam radius. It is shown that the boundary value problem of the second kind reduces to a generalized characteristic equation. It includes as particular cases the known in heat conduction theory characteristic equations which have been obtained for the one-dimensional boundary value problems of the second and third kinds. Also an asymptotic expression for a temperature distribution in a substrate is derived for the case of small values of Fourier number.

Original languageEnglish
Pages (from-to)95-104
Number of pages10
JournalInternational Communications in Heat and Mass Transfer
Volume21
Issue number1
DOIs
StatePublished - 1 Jan 1994

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • General Chemical Engineering
  • Condensed Matter Physics

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