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On One Method of Solving Nonstationary Boundary-Value Problems

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Journal of Engineering Physics and Thermophysics Aims and scope

An exact analytical solution of the problem on the heat conduction in an infinite plate with the first-kind symmetric boundary conditions has been obtained using the integral method of heat balance with an additional desired function and additional boundary conditions. The solution of the partial differential equation was reduced to the integration of the ordinary differential equation for the additional desired function. It is shown that the fulfillment of the differential equation at the boundary points of the computational region is equivalent to its fulfillment within this region. In the approach proposed there is no need to integrate the indicated equation with respect to the space variable because of the fulfillment of the integral condition of heat balance, which allows this approach to be applied to the solution of problems that are difficult to solve with the use of classical exact analytical methods.

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Authors and Affiliations

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

    I. V. Kudinov, V. A. Kudinov, E. V. Kotova & A. V. Eremin

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  1. I. V. Kudinov
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  2. V. A. Kudinov
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  3. E. V. Kotova
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  4. A. V. Eremin
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Correspondence to A. V. Eremin.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 90, No. 6, pp. 1387–1397, November–December, 2017.

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Kudinov, I.V., Kudinov, V.A., Kotova, E.V. et al. On One Method of Solving Nonstationary Boundary-Value Problems. J Eng Phys Thermophy 90, 1317–1327 (2017). https://doi.org/10.1007/s10891-017-1689-4

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  • DOI: https://doi.org/10.1007/s10891-017-1689-4

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