Fast-converging steady-state heat conduction in a rectangular parallelepiped |
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| Authors: | Paul E Crittenden |
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| Affiliation: | a Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0323, USA
b Mechanical Engineering Department, College of Engineering and Technology, University of Nebraska, P.O. Box 880656, Lincoln, NE 68588-0656, USA |
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| 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. |
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| Keywords: | Green's functions Laplace equation Temperature Series convergence Parallelepiped |
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