On the basis of the weighted temperature method, an algorithm of generalized solution of boundary-value problems on the heat conduction in bodies canonical in shape with boundary conditions of general form has been constructed. It is shown that this problem is equivalent, in the limit, to the infinite system of identities including n-fold integral operators for the temperature function, initial and boundary conditions, and internal heat source as well as an additional boundary function (the temperature at one of the boundary points or its derivative with respect to the coordinate of this point). High approximation accuracy of the approach proposed is demonstrated by the example of solving a number of boundary-value problems on nonstationary heat conduction with nonsymmetric and mixed boundary conditions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. A. Kot, Weighted temperature identities, J. Eng. Phys. Thermophys., 88, No. 2, 423–438 (2015).
V. A. Kot, Method of weighted temperature function, J. Eng. Phys. Thermophys., 89, No. 1, 192–211 (2016).
V. A. Kot, Integral identities for the heat-conduction equations, in: Heat and Mass Transfer–2014, Collect. sci. papers [in Russian], ITMO, Minsk (2015), pp. 221–230.
V. A. Kot, Determination of boundary functions on the basis of systems of integral identities for the weighted temperature function, in: Heat and Mass Transfer–2014, Collect. sci. papers [in Russian], ITMO, Minsk (2015), pp. 242–251.
E. A. Vlasova, V. S. Zarubin, and G. N. Kuvyrkin, Approximate Methods of Mathematical Physics [in Russian], Izd. MGTU im. N. É. Baumana, Moscow (2001).
C. A. Fletcher, Computational Galerkin Methods [Russian translation], Mir, Moscow (1988).
L. V. Kantorovich and V. I. Krylov, Approximate Methods of Highest Analysis [in Russian], Gostekhizdat, Moscow–Leningrad (1962).
M. G. Kogan, Use of the Galerkin and Kantorovich methods in the heat-conduction theory, in: Investigation of Nonstationary Heat and Mass Exchange, Collect, papers [in Russian], Nauka Tekhnika, Minsk (1966), pp. 42–51.
V. A. Kudinov, É. M. Kartashov, and V. V. Kalashnikov, Analytical Solutions of Problems on Heat and Mass Transfer and Thermoelasticity for Multilayer Structures [in Russian], Vysshaya Shkola, Moscow (2005).
V. A. Kudinov, B. V. Averin, and E. V. Stefanyuk, Heat Conduction and Thermoelasticity in Multilayer Structures [in Russian], Vysshaya Shkola, Moscow (2008).
É. M. Kartashov and V. A. Kudinov, Analytical Theory of Heat Conduction and Thermoelasticity [in Russian], Yurait, Moscow (2012).
P. V. Tsoi, System Methods for Calculating Boundary-Value Problems on Heat and Mass Transfer [in Russian], Izd. MÉI, Moscow (2005).
N. S. Koshlyakov, É. B. Gliner, and M. M. Smirnov, Equations of Mathematical Physics [in Russian], Vysshaya Shkola, Moscow (1970).
N. M. Tsirel’man, Direct and Inverse Problems on Heat and Mass Transfer [in Russian], Énergoatomizdat, Moscow (2005).
A. V. Luikov, Theory of Heat Conduction [in Russian], Vysshaya Shkola, Moscow (1967).
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids [Russian translation], Nauka, Moscow (1964).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 91, No. 4, pp. 1066–1088, July–August, 2018.
Rights and permissions
About this article
Cite this article
Kot, V.A. Generalized Solution of the Mixed Heat-Conduction Problem by the Weighted Temperature Method. J Eng Phys Thermophy 91, 1006–1028 (2018). https://doi.org/10.1007/s10891-018-1827-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-018-1827-7