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TVT, 2017, Volume 55, Issue 4, Pages 556–563 (Mi tvt9737)  

This article is cited in 5 scientific papers (total in 5 papers)

Heat and Mass Transfer and Physical Gasdynamics

Additional boundary conditions in unsteady-state heat conduction problems

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

Samara State Technical University

Abstract: Using some additional sought function and boundary conditions, a precise analytical solution of the heat conduction problem for an infinite plate was obtained using the integral heat balance method with symmetric first-order boundary conditions. The additional sought function represents the variation of temperature with time at the center of a plate and, due to an infinite heat propagation velocity described with a parabolic heat conduction equation, changes immediately after application of a first-order boundary condition. Hence, the range of its time and temperature variation completely incorporates the ranges of unsteadystate process times and temperature changes. The additional boundary conditions are such that their fulfilment is equivalent the fulfilment of a differential equation at boundary points. It has been shown that the fulfilment of an equation at boundary points leads to its fulfilment inside the region. The consideration of an additional sought function in the integral heat balance method provide a possibility to confine the solution of an equation in partial derivatives to the integration of an ordinary differential equation, so this method can be applied to the solution of equations, which do not admit the separation of variables (nonlinear, with variable physical properties of a medium, etc.).

Funding Agency Grant Number
Russian Foundation for Basic Research 16-38-00059 мол_а


DOI: https://doi.org/10.7868/S004036441704010X

Full text: PDF file (365 kB)
References: PDF file   HTML file

English version:
High Temperature, 2017, 55:4, 541–548

Bibliographic databases:

UDC: 536.2 (075)
Received: 13.04.2015
Accepted:14.06.2016

Citation: I. V. Kudinov, V. A. Kudinov, E. V. Kotova, “Additional boundary conditions in unsteady-state heat conduction problems”, TVT, 55:4 (2017), 556–563; High Temperature, 55:4 (2017), 541–548

Citation in format AMSBIB
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\paper Additional boundary conditions in unsteady-state heat conduction problems
\jour TVT
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\vol 55
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\pages 556--563
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\crossref{https://doi.org/10.7868/S004036441704010X}
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\jour High Temperature
\yr 2017
\vol 55
\issue 4
\pages 541--548
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. F. Formalev, S. A. Kolesnik, E. L. Kuznetsova, “On the wave heat transfer at times comparable with the relaxation time upon intensive convective-conductive heating”, High Temperature, 56:3 (2018), 393–397  mathnet  crossref  crossref  isi  elib  elib
    2. A. S. Askarova, S. A. Bolegenova, Symbat A. Bolegenova, V. Yu. Maksimov, M. T. Beketayeva, “Modeling of heat mass transfer in high-temperature reacting flows with combustion”, High Temperature, 56:5 (2018), 738–743  mathnet  crossref  crossref  isi  elib
    3. V. F. Formalev, S. A. Kolesnik, E. L. Kuznetsova, “Wave heat transfer in the orthotropic half-space under the action of a nonstationary point source of thermal energy”, High Temperature, 56:5 (2018), 727–731  mathnet  crossref  crossref  isi  elib
    4. V. F. Formalev, S. A. Kolesnik, “On thermal solitons with wave heat transfer in restricted areas”, High Temperature, 57:4 (2019), 498–502  mathnet  crossref  crossref  isi  elib
    5. V. F. Formalev, S. A. Kolesnik, E. L. Kuznetsova, “Effect of components of the heat conductivity tensor of heat-protection material on the value of heat fluxes from the gasdynamic boundary layer”, High Temperature, 57:1 (2019), 58–62  mathnet  crossref  crossref  isi  elib
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