Geodesic
Analytical solutions to the heat conduction problems for a cylinder and a ball based on determining the temperature perturbation front
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 681-692

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Analytical solutions to the heat conduction problems for a cylinder and a ball are obtained by the integral method of heat balance. To improve the accuracy of the solutions, the temperature function is approximated by polynomials of high degrees. Their coefficients are determined via introducing additional boundary conditions, which are found from the governing differential equation and the basic boundary conditions, including those specified at the temperature perturbation front. It is shown that the additional boundary conditions, even in the second approximation, lead to a considerable improvement in the solution accuracy. 
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     title = {Analytical solutions to the heat conduction problems for a~cylinder and a~ball based on determining the temperature perturbation front},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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M. S. Antimonov; V. A. Kudinov; E. V. Stefanyuk. Analytical solutions to the heat conduction problems for a cylinder and a ball based on determining the temperature perturbation front. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 681-692. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a11/