Fast-converging steady-state heat conduction in a rectangular parallelepiped

Paul E. Crittenden, Kevin D. Cole

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


A Green's function approach for precisely computing the temperature and the three components of the heat flux in a rectangular parallelepiped is presented. Each face of the parallelepiped may have a different, but spatially uniform, boundary condition. Uniform volume energy generation is also treated. Three types of boundary conditions are included: type 1, a specified temperature; type 2, a specified flux; or type 3, a specified convection boundary condition. A general form of the Green's function covering all three types of boundary conditions is given. An algorithm is presented to obtain the temperature and flux at high accuracy with a minimal number of calculations for points in the interior as well as on any of the faces. Heat flux on type 1 boundaries, impossible to evaluate with traditional Fourier series, is found by factoring out lower-dimensional solutions. A numerical example is given. This research and resulting computer program was part of a code verification project for Sandia National Laboratories.

Original languageEnglish (US)
Pages (from-to)3585-3596
Number of pages12
JournalInternational Journal of Heat and Mass Transfer
Issue number17
StatePublished - Jun 10 2002


  • Green's functions
  • Laplace equation
  • Parallelepiped
  • Series convergence
  • Temperature

ASJC Scopus subject areas

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


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