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Approximate analytic solution of heat conduction problems with a mismatch between initial and boundary conditions

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Abstract

We consider a heat conduction problem for an infinite plate with a mismatch between initial and boundary conditions. Using the method of integral relations, we obtain an approximate analytic solution to this problem by determining the temperature perturbation front. The solution has a simple form of an algebraic polynomial without special functions. It allows us to determine the temperature state of the plate in the full range of the Fourier numbers (0≤F<∞) and is especially effective for very small time intervals.

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Reference

  1. A. V. Lykov, Theory of Heat Conduction (Vysshaya Shkola, Moscow, 1967) [in Russian].

    Google Scholar 

  2. T. Gudmen, “Application of Integral Methods in Nonlinear Problems of Nonstationary Heat Exchange,” in Heat Transfer (Atomizdat, Moscow, 1967), pp. 41–96.

    Google Scholar 

  3. N. M. Belyaev and A. A. Ryadno, Methods of Nonstationary Heat Conduction (Vysshaya Shkola, Moscow, 1978) [in Russian].

    Google Scholar 

  4. Yu. S. Postols’nik, “Methods of Averaging Functional Corrections in Heat-Conduction Problems,” Teplo-i Massoperenos 8 23–29 (1972).

    Google Scholar 

  5. M. Biot, Variational Principles in Heat Transfer (Oxford University Press, Oxford, 1970; Energiya, Moscow, 1975).

    MATH  Google Scholar 

  6. A. I. Veinik, Approximate Calculation of Heat-Conduction Processes (Gosenergoizdat, Moscow-Leningrad, 1959) [in Russian].

    Google Scholar 

  7. V. A. Kudinov, B. V. Averin and E. V. Stefanyuk, “Solutions of Heat-Conduction Problems under Time-Variable Boundary Conditions Based on the Determination of the Temperature Perturbation Front,” Izv. RAN. Ser. Energetika, No. 1, 55–68 (2007).

    Google Scholar 

  8. V A. Kudinov and E. V Stefanyuk, “Heat Conduction Problems Based on the Determination of the Temperature Perturbation Front,” Izv. RAN. Ser. Energetika, No. 5, 141–157 (2008).

    Google Scholar 

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Authors and Affiliations

  1. Samara State Technical University, ul. Molodogvardeiskaya 244, Samara, 443100, Russia

    E. V. Stefanyuk & V. A. Kudinov

Authors
  1. E. V. Stefanyuk
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  2. V. A. Kudinov
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Correspondence to E. V. Stefanyuk.

Additional information

Original Russian Text © E.V. Stefanyuk and V. A. Kudinov, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 4, pp. 63–71.

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Stefanyuk, E.V., Kudinov, V.A. Approximate analytic solution of heat conduction problems with a mismatch between initial and boundary conditions. Russ Math. 54, 55–61 (2010). https://doi.org/10.3103/S1066369X10040079

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  • DOI: https://doi.org/10.3103/S1066369X10040079

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