Abstract
A mathematical model of heat transfer is constructed for a composite inhomogeneous body of arbitrary shape, which includes elements of anisotropic materials. Thermal contact between these elements can generally be imperfect. A dual formulation of the variational problem of stationary heat transfer is used in obtaining two-sided estimates for the thermal resistance of the body.
Similar content being viewed by others
References
Mal’kov, V.A., Favorskii, O.N., and Leont’ev, V.N., Kontaktnyi teploobmen v gazoturbinnykh dvigatelyakh i energoustanovkakh (Contact Heat Transfer in Gas Turbine Engines and Energy Units), Moscow: Mashinostroenie, 1978.
Favorskii, O.N. and Kadaner, Ya.S., Voprosy teploobmena v kosmose (Problems of Heat Transfer in Space), Moscow: Vysshaya Shkola, 1972.
Zarubin, B.C., Temperaturnye polya v konstruktsii letatel’nykh apparatov (Temperature Fields in Aircraft Design), Moscow: Mashinostroenie, 1966.
Madkhusudina, K.V. and Fletcher, L.S., Aerokosm. Tekh., 1987, no. 3, p. 103.
Karnozhitskii, V.N., Kontaktnyi teploobmen v protsessakh lit’ya (Contact with Heat Transfer during the Casting Process), Kiev: Naukova Dumka, 1978.
Zhuravlev, V.P. and Kitaev, E.M., Teplofizika formirovaniya nepreryvnogo slitka (Thermal Physics of the Formation of a Continuous Ingot), Moscow: Metallurgiya, 1974.
Dozhdikov, V.I., Teplofizicheskie osobennosti formirovaniya nepreryvnogo slitka v kristallizatore MNLZ (Thermal and Physical Characteristics of the Formation of a Continuous Ingot Mold in the Continuous Casting Machine), Lipetsk: Lipetsk State Technical University, 2007.
Fokin, K.F., Stroitel’naya teplotekhnika ograzhdayushchikh konstruktsii (Architectural Thermal Engineering of Building Envelopes), Moscow: Stroiizdat, 1973.
Zarubin, B.C., Raschet i optimizatsiya termoizolyatsii (Calculation and Optimization of the Thermal Insulation), Moscow: Energoatomizdat, 1991.
Popov, B.M., Teploobmen v zone kontakta raz”emnykh i neraz”emnykh soedinenii (Heat Transfer in the Contact Region of the Detachable and Permanent Connections), Moscow: Energiya, 1971.
Shlykov, Yu.P., Ganin, E.A., and Tsarevskii, S.N., Kontaktnoe termicheskoe soprotivlenie (Contact Thermal Resistance), Moscow: Energiya, 1977.
Zarubin, B.C. and Rodikov, A.V., High Temp., 2007, vol. 45, no. 2, p. 243.
Formalev, V.F., Kolesnik, S.A., and Kuznetsova, E.L., High Temp., 2009, vol. 47, no. 2, p. 228.
Yasinsky, J.B. and Kaplan, S., Nucl. Sci. Eng., 1968, vol. 31, no. 1, p. 80.
Arthurs, A.M., Complementary Variational Principles, Oxford: Clarendon, 1970.
Finlayson, B.A., The Method of Weighted Residuals and Variational Principles, New York: Academic, 1972.
Zarubin, B.C., Inzhenernye metody resheniya zadach teploprovodnosti (Engineering Methods for Solving Problems of Heat Conduction), Moscow: Energoatomizdat, 1983.
Zarubin, B.C. and Kuvyrkin, G.N., Matematicheskie modeli mekhaniki i elektrodinamiki sploshnoi sredy (Mathematical Models of Mechanics and Electrodynamics of Continuous Media), Moscow: Bauman Moscow State Technical University, 2008.
Efremov, V.P. and Potapenko, A.I, High Temp., 2010, vol. 48, no. 6, p. 881.
Gorskii, V.V. and Zlonkevich, F.V., High Temp., 2012, vol. 50, no. 4, p. 556.
Zinchenko, V.I., Efimov, K.N., and Yakimov, A.S., High Temp., 2011, vol. 49, no. 1, p. 81.
Gorsky, V.V., Zabarko, D.A., and Olenicheva, A.A., High Temp., 2012, vol. 50, no. 2, p. 286.
Kruglov, A.B., Kruglov, V.B., and Tenishev, A.V., High Temp., 2010, vol. 48, no. 1, p. 136.
Mustafina, D.A. and Skibin, A.P., High Temp., 2010, vol. 48, no. 2, p. 291.
Brykin, M.V., Son, E.E., and Sheindlin, M.A., High Temp., 2011, vol. 49, no. 6, p. 841.
Akopov, F.A. and Borovkova, L.B., High Temp., 2011, vol. 49, no. 6, p. 862.
Kuznetsova, E.L., High Temp., 2011, vol. 49, no. 6, p. 881.
Lepeshkin, A.R., Bychkov, N.G., and Pershin, A.V., High Temp., 2010, vol. 48, no. 5, p. 699.
Borzenko, V.I., Dunikov, D.O., and Malyshenko, S.P., High Temp., 2011, vol. 49, no. 2, p. 249.
Zalkind, V.I. and Schigel, S.S., High Temp., 2011, vol. 49, no. 4, p. 598.
Ivanov, P.P., High Temp., 2011, vol. 49, no. 4, p. 608.
Tsydypov, B.D. and Simakov, P.G., High Temp., 2011, vol. 49, no. 5, p. 642.
Ivanov, P.P., Kovbasyuk, V.I., and Medvedev, Yu.V., High Temp., 2012, vol. 50, no. 6, p. 779.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.S. Zarubin, G.N. Kuvyrkin, 2013, published in Teplofizika Vysokikh Temperatur, 2013, Vol. 51, No. 4, pp. 578–585.
Rights and permissions
About this article
Cite this article
Zarubin, V.S., Kuvyrkin, G.N. Two-sided estimates for thermal resistance of an inhomogeneous solid body. High Temp 51, 519–525 (2013). https://doi.org/10.1134/S0018151X1304024X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0018151X1304024X