New derivations of the fundamental solution for heat conduction problems in three-dimensional general anisotropic media

Rogério José Marczak, Mitsunori Denda

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

This work presents two new methods to derive the fundamental solution for three-dimensional heat transfer problems in the general anisotropic media. Initially, the basic integral equations used in the definition of the general anisotropic fundamental solution are revisited. We show the relationship between three, two and one-dimensional integral definitions, either by purely algebraic manipulation as well as through Fourier and Radon transforms. Two of these forms are used to derive the fundamental solutions for the general anisotropic media. The first method gives the solution analytically for which the solution for the orthotropic case agrees with the well known result obtained by the domain mapping, while the fundamental solution for the general anisotropic media is new. The second method expresses the solution by a line integral over a semi-circle. The advantages and disadvantages of the two methods are discussed with numerical examples.

Original languageEnglish (US)
Pages (from-to)3605-3612
Number of pages8
JournalInternational Journal of Heat and Mass Transfer
Volume54
Issue number15-16
DOIs
StatePublished - Jul 1 2011

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Keywords

  • Fourier and Radon transforms
  • Fundamental solutions
  • General anisotropic solids
  • Heat transfer

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