We first consider the partial differential equation that governs one-dimensional heat flow in a homogeneous medium. This equation is reduced to a difference equation, and the problem of difference equation stability and convergence is discussed and examples of the breakdown of each are given. Next, the above analysis is extended to a three-dimensional space with spherical symmetry. Several interesting problems are programmed and the solutions are displayed in graphical form. The accuracy of the numerical difference technique is checked by comparison with exact Fourier series solutions. The paper is mainly intended for beginning students of physics and engineering, and also for college teachers who have not had a formal course in numerical solutions of partial differential equations.
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April 1973
PAPERS|
April 01 1973
Numerical Solution to Transient Heat Flow Problems
Ronald A. Kobiske;
Ronald A. Kobiske
Department of Physics, Milwaukee School of Engineering, Milwaukee, Wisconsin 53201
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Jeffrey L. Hock
Jeffrey L. Hock
Department of Physics, Milwaukee School of Engineering, Milwaukee, Wisconsin 53201
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Am. J. Phys. 41, 517–525 (1973)
Article history
Received:
June 24 1972
Citation
Ronald A. Kobiske, Jeffrey L. Hock; Numerical Solution to Transient Heat Flow Problems. Am. J. Phys. 1 April 1973; 41 (4): 517–525. https://doi.org/10.1119/1.1987281
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