The analytical solutions of nonlinear unsteady heat conduction equation are meaningful in theory. In addition, they are very useful to the computational heat conduction to check the numerical solutions and to develop numerical schemes, grid generation methods and so forth. However, very few explicit analytical solutions have been known for the unsteady nonlinear heat conduction. In order to develop the heat conduction theory, some algebraically explicit analytical solutions of nonlinear heat conduction equation have been derived in this paper, which include one-dimensional and two-dimensional unsteady heat conduction solutions with thermal conductivity, density and specific heat being functions of temperature.
Some Algebraically Explicit Analytical Solutions of Unsteady Nonlinear Heat Conduction
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division May 17, 2000; revision received March 5, 2001. Associate Editor: C. Beckermann.
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Cai , R., and Zhang , N. (March 5, 2001). "Some Algebraically Explicit Analytical Solutions of Unsteady Nonlinear Heat Conduction ." ASME. J. Heat Transfer. December 2001; 123(6): 1189–1191. https://doi.org/10.1115/1.1392990
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