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 language | English (US) |
|---|---|
| Pages (from-to) | 3585-3596 |
| Number of pages | 12 |
| Journal | International Journal of Heat and Mass Transfer |
| Volume | 45 |
| Issue number | 17 |
| DOIs | |
| State | Published - Jun 10 2002 |
Keywords
- Green's functions
- Laplace equation
- Parallelepiped
- Series convergence
- Temperature
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes