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Heat Conduction in a Semi-infinite Body with Power-Type Initial and Boundary Conditions

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Abstract

Heat conduction problems in a semi-infinite body with constant thermal properties are investigated. Firstly, two types of basic problems are studied. One type considers the medium with an initial temperature a power function of position subject to zero surface temperature, surface flux, or ambient temperature; the other type considers the medium with zero initial temperature subject to boundary conditions that vary as a power of time. Closed-form analytical solutions for these basic problems are constructed. Using these basic solutions and the supposition principle, analytical solutions for problems with polynomial-type initial and boundary conditions are obtained. The procedure can also be applied to obtain solutions for other types of initial and boundary conditions that can be expanded into power series with an infinite radius of convergence. An illustrative example is presented and discussed. Theoretical proof for the convergence of the series form solution is conducted.

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou, 221008, Jiangsu, People’s Republic of China

    Yang Zhou

  2. School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Yang Zhou

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  1. Yang Zhou
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Correspondence to Yang Zhou.

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Zhou, Y. Heat Conduction in a Semi-infinite Body with Power-Type Initial and Boundary Conditions. Int J Thermophys 33, 2390–2406 (2012). https://doi.org/10.1007/s10765-012-1341-7

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  • DOI: https://doi.org/10.1007/s10765-012-1341-7

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