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 language | English (US) |
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Pages (from-to) | 3883-3894 |
Number of pages | 12 |
Journal | International Journal of Heat and Mass Transfer |
Volume | 44 |
Issue number | 20 |
DOIs | |
State | Published - 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