Transient heat diffusion in multilayered materials with thermal contact resistance

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A further extension to the method of recursive images is presented to obtain solutions of the transient diffusion equation in multilayered materials, based on the recursive superposition of Green functions for a semi-infinite material. This extension enables one to find the solution also when thermal contact resistance exists between the layers. Through a sequential sum of image Green functions, a temperature solution is initially built for a structure of one layer over a substrate. These functions are chosen in order to satisfy in sequence the boundary conditions, first at the front interface then at the back interface then again at the front interface and so on until the magnitude of the added functions becomes negligible. This present scheme is now valid for boundary conditions of the first, second and third kind. Four different heat diffusion problems are solved, illustrating how the method works. The first three are diffusion problems of a layer over a substrate while the last one is a three layer over a substrate structure with thermal resistance between layer 2 and 3.

Original languageEnglish
Pages (from-to)1001-1009
Number of pages9
JournalInternational Journal Of Heat And Mass Transfer
Publication statusPublished - 1 Jun 2016


  • Multilayer materials
  • Recursive images
  • Thermal resistance
  • Transient heat diffusion


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