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

Paul E. Crittenden, Kevin D Cole

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

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
Volume45
Issue number17
DOIs
StatePublished - Jun 10 2002

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parallelepipeds
Heat conduction
conductive heat transfer
Boundary conditions
boundary conditions
Green's function
Heat flux
heat flux
Green's functions
Fluxes
Fourier series
Temperature
temperature
Computer program listings
coverings
convection
computer programs
energy

Keywords

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

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Energy(all)
  • Mechanical Engineering

Cite this

Fast-converging steady-state heat conduction in a rectangular parallelepiped. / Crittenden, Paul E.; Cole, Kevin D.

In: International Journal of Heat and Mass Transfer, Vol. 45, No. 17, 10.06.2002, p. 3585-3596.

Research output: Contribution to journalArticle

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