Abstract
A series of boundary-value problems of local nonequilibrium heat transfer is considered in terms of the theory of transient heat conduction for hyperbolic-type equations (wave equations). The mathematical models for the generalized equation have been studied simultaneously in Cartesian, cylindrical (radial heat flux), and spherical (central symmetry) coordinate systems. The technique to determine analytical solutions to a broad class of practically important problems of transient heat conduction for canonical bodies (plate, solid cylinder, and solid sphere) and for partially bounded bodies (half-space bounded by a flat surface and spaces with an internal cylindrical cavity and an internal spherical cavity) has been developed. The obtained, exact analytical solutions to a series of model problems can be considered as radically new results of analytical thermal physics.
Similar content being viewed by others
REFERENCES
Kartashov, E.M., Analiticheskie metody v teorii teploprovodnosti tverdykh tel (Analytical Methods in the Theory of Thermal Conductivity of Solids), Moscow: Vysshaya Shkola, 2001.
Kartashov, E.M. and Kudinov, V.A., Analiticheskie metody teorii teploprovodnosti i ee prilozheniya (Analytical Methods of the Theory of Heat Conduction and Its Applications), Moscow: URSS, 2018.
Zarubin, V.S., Inzhenernye metody resheniya zadach teploprovodnosti (Engineering Methods for Solving Heat Conduction Problems), Moscow: Energoatomizdat, 1983.
Lykov, A.V., Teoriya teploprovodnosti (Heat Conduction Theory), Moscow: Vysshaya Shkola, 1967.
Lykov, A.V., Teploprovodnost’ i diffuziya (Thermal Conductivity and Diffusion), Moscow: Gizlegprom, 1941.
Cattaneo, C., Atti Semin. Mat. Fis. Univ. Modena, 1948, vol. 3, p. 83.
Vernotte, P., C. R. Acad. Sci., 1958, vol. 246, no. 22, p. 3154.
Maxwell, J.C., Philos. Trans. R. Soc. London, 1967, vol. 157, no. 1, p. 49.
Tissa, L., Nature, 1938, vol. 141, no. 3577, p. 913.
Landau, L.D., Zh. Eksp. Teor. Fiz., 1941, vol. 2, no. 6, p. 592.
Peshkov, V.P., Zh. Eksp. Teor. Fiz., 1946, vol. 16, no. 8, p. 744.
Ward, J.C. and Wilks, J., Philos. Mag., 1952, vol. 43, no. 336, p. 48.
Dinqle, R.B., Proc. Phys. Soc., 1952, vol. 65, no. 396A, p. 1040.
London, F., Superfluids 2, New York: Wiley, 1954.
Ackermann, C.C., Guyer, R.A., Bertman, B., and Fairbank, H.A., Phys. Rev. Lett., 1966, vol. 16, no. 18, p. 789.
Gurevich, V.L. and Shklovskii, R.P., Fiz. Tverd. Tela, 1966, vol. 8, no. 10, p. 3050.
Gurzhi, R.N. and Kontorovich, V.M., Sov. Phys. JETP, 1969, vol. 28, p. 577.
Gurzhi, R.N., Fiz. Tverd. Tela, 1965, vol. 7, no. 12, p. 3515.
Kashcheev, V.N., Izv. Akad. Nauk Latv. SSR, Ser. Fiz.-Tekh. Nauk, 1969, no. 2, p. 36.
Chester, M., Phys. Rev., 1963, vol. 131, no. 5, p. 2013.
Kaliski, S., Bull. Acad. Pol. Sci. Technol., 1965, vol. 13, no. 5, p. 409.
Herwiq, H. and Beckert, K., Heat Mass Transfer, 2000, vol. 36, p. 387.
Mitra, K., Kumar, S., Vedavars, A., and Mjallemi, M.K., J. Heat Transfer, 1995, vol. 117, no. 3, p. 568.
Kirsanov, Yu.A. and Kirsanov, A.Yu., Izv. Ross. Akad. Nauk, Energ., 2015, no. 1, p. 113.
Kirsanov, Yu.A., High Temp., 2017, vol. 55, no. 4, p. 535.
Kartashov, E.M., J. Eng. Phys. Thermophys., 2014, vol. 87, no. 5, p. 1116.
Formalev, V.F., Teploprovodnost’ anizotropnyh tel. Analiticheskie metody resheniya zadach (Thermal Conductivity of Anisotropic Bodies. Methods for Solving Analytical Problem), Moscow: Fizmatlit, 2014.
Formalev, V.F. and Kolesnik, S.A., High Temp., 2019, vol. 57, no. 4, p. 498.
Formalev, V.F., Kolesnik, S.A., and Kuznetsova, E.L., High Temp., 2019, vol. 57, no. 1, p. 58.
Kartashov, E.M., Tonkie Khim. Tekhnol., 2019, vol. 14, no. 4, p. 77.
Carslaw, H.S. and Jaeger, J.C., Operational Methods in Applied Mathematics, Oxford: Oxford Univ. Press, 1945.
Lavrent’ev, M.A. and Shabat, B.V., Metody teorii funkcij kompleksnogo peremennogo (Methods of the Theory of Functions of a Complex Variable), Moscow: Nauka, 1965.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by A. Sin’kov
Rights and permissions
About this article
Cite this article
Kartashov, E.M. Analytical Solutions to Models of Local Nonequilibrium Heat Transfer. High Temp 59, 259–267 (2021). https://doi.org/10.1134/S0018151X21020048
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0018151X21020048