Green's functions, temperature and heat flux in the rectangle

Kevin D. Cole, David H.Y. Yen

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

Steady heat conduction in the rectangle is treated with the method of Green's functions. Single-sum series for the Green's functions are reported in terms of exponentials which have better numerical properties than hyperbolic functions. Series expressions for temperature and heat flux caused by spatially uniform effects are presented. The numerical convergence of these series is improved, in some cases by a factor of 1000, by replacing slowly converging portions of the series with fully summed forms. This work is motivated by high-accuracy verification of finite-difference and finite-element codes.

Original languageEnglish (US)
Pages (from-to)3883-3894
Number of pages12
JournalInternational Journal of Heat and Mass Transfer
Volume44
Issue number20
DOIs
StatePublished - Aug 21 2001

Keywords

  • Green's functions
  • Laplace equation
  • Rectangle
  • Series convergence

ASJC Scopus subject areas

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

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