A method of recursive images extended to solve diffusion in multilayer materials under convective boundary conditions

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Abstract

Abstract A method of recursive images applicable to diffusion in multilayer materials, is extended to cases where there is convection at the outer faces. Therefore this old/new method is now applicable to a wider, more diverse and real life diffusion problems. This objective is reached using a result by Bryan [1] who established that the Green function at a convection boundary involves adding a mirror reflecting thermal wave while subtracting a one-sided convolution, of a decreasing exponential with that same reflected wave. This is verified in the case of convection of heat, for a slab with its back face insulated. This method was then applied to find temperature solution for the diffusion in a slab having convection both at the front and at the back face of the slab. Finally the same rationale, of the recently proposed method of generalized method of images, was used to find the temperature solution for a three layered material with radiation convection at its front face. An alternative method is suggested which minimizes computation errors when the convection coefficient becomes very large. Finally a relationship is found between the semi-infinite solutions with and without convection radiation.

Original languageEnglish
Article number11528
Pages (from-to)1069-1074
Number of pages6
JournalInternational Journal Of Heat And Mass Transfer
Volume85
DOIs
Publication statusPublished - 2015

Keywords

  • Convection
  • Method of images
  • Multi-layer materials
  • Transient diffusion

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