The theory of the method of Green’s functions in solving boundary-value problems of nonstationary heat conduction in domains with moving boundaries has been developed. A modification of the thermal-potential method for a uniform law of motion of the boundary has been proposed, which leads to integral relations of a new (simplest) form compared to the existing results; this makes it possible to consider numerous particular cases that are of practical interest for many applications. A number of special features of model representations of nonstationary heat transfer in domains with moving boundaries have been revealed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. G. Martynenko, A. V. Luikov’s scientific legacy (on the 90th anniversary of his birth), Inzh.-Fiz. Zh., 73, No. 5, 883–892 (2000).
A. V. Luikov, Some analytical methods of solving nonstationary heat-conduction problems, Izv. Akad. Nauk SSSR, Énergetika Transport, No. 2, 3–27 (1969).
A. V. Luikov, Methods of solving nonlinear equations of nonstationary heat conduction, Izv. Akad. Nauk SSSR, Énergetika Transport, No. 5, 109–150 (1970).
É. M. Kartashov, Analytical methods of solution of boundary-value problems of nonstationary heat conduction in regions with moving boundaries, Inzh.-Fiz. Zh., 74, No. 2, 171–195 (2001).
É. M. Kartashov, Analytical Methods in the Theory of Heat Conduction of Solids [in Russian], Vysshaya Shkola, Moscow (2001).
A. A. Samarskii, Parabolic-type equations with discontinuous coefficients, Dokl. Akad. Nauk. SSSR, 121, No. 2, 225–228 (1958).
V. I. Kval’vasser and Ya. F. Rutner, A method for finding Green’s function of the boundary-value problems of the heat-conduction equation for a segment of a straight line with uniform moving boundaries, Dokl. Akad. Nauk. SSSR, 156, No. 6, 1273–1276 (1964).
É. M. Kartashov, The problem of thermal shock in the region with moving boundaries on the basis of new integral relations, Izv. Ross. Akad. Nauk, Énergetika, No. 4, 122–137 (1997).
A. V. Luikov, Application of the methods of thermodynamics of irreversible processes to the investigation of heat and mass transfer, Inzh.-Fiz. Zh., 9, No. 3, 287–304 (1965).
A. G. Shashkov, V. A. Bubnov, and S. Yu. Yanovskii, Wave Phenomena of Heat Conduction [in Russian], Nauka i Tekhnika, Minsk (1993).
V. L. Kolpashchikov and S. Yu. Yanovskii, Coupled dynamic thermoelasticity problem for a halfspace with thermal “memory,” Inzh.-Fiz. Zh., 36, No. 6, 1093–1099 (1979).
Author information
Authors and Affiliations
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 83, No. 4, pp. 645–661, July–August, 2010.
Rights and permissions
About this article
Cite this article
Kartashov, É.M. New integral relations for analytical solutions of parabolic-type equations in noncylindrical domains. J Eng Phys Thermophy 83, 688–706 (2010). https://doi.org/10.1007/s10891-010-0391-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-010-0391-6