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

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 caus...

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Bibliographic Details
Published inInternational journal of heat and mass transfer Vol. 44; no. 20; pp. 3883 - 3894
Main Authors Cole, Kevin D, Yen, David H.Y
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.10.2001
Elsevier
Subjects
Analytical and numerical techniques
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Green's functions
Heat conduction
Heat transfer
Laplace equation
Physics
Rectangle
Series convergence
Rectangle
Series convergence
Laplace equation
Green's functions
Finite element method
Temperature distribution
Rectangular configuration
Digital simulation
Series expansion
Heat flow
Green function
Numerical convergence
Thermal conduction
Finite difference method
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0017-9310
1879-2189
DOI:10.1016/S0017-9310(01)00040-0