Based on the generalized law of wave heat transfer, a wave equation of parabolic type is obtained, for which the problem of heating an anisotropic half-space under the action of a point nonstationary source of thermal energy of exponential character is posed and solved analytically. The anisotropic half-space has anisotropy of heat transfer in planes parallel to the plane bounding the body, whereas the body is isotropic in the direction of the axis perpendicular to these planes. Therefore, the isotherms moving in time have the form of elliptical paraboloids, at the fronts of which the first-kind discontinuous changes are observed in both temperatures and heat fluxes, which is a consequence of the wave nature of heat transfer. Numerical results are obtained and analyzed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. V. Luikov, Heat Conduction Theory [in Russian], Vysshaya Shkola, Moscow (1967).
A. G. Shashkov, A. V. Bubnov, and S. Yu. Yanovskii, Wave Phenomena of Heat Conduction [in Russian], URSS, Moscow (2004).
S. L. Sobol′, Transfer processes and running waves in locally nonequilibrium systems, Usp. Fiz. Nauk, 161, No. 3, 5–15 (1991).
P. Vernotton, La Nouvelle equation de la chaleur, J. de la Trans de la Chaleur, 1−12 (1961).
É. M. Kartashov, Mathematical models of heat conduction with a two-phase lag, J. Eng. Phys. Thermophys., 89, No. 2, 346–356 (1991).
O. N. Shablovskii and D. G. Krol′, Phenomenological assessment of the thermal relaxation time in explosive crystallization of amorphous germanium fi lms, Tepl. Prots. Tekh., No. 5, 203–208 (2010).
O. N. Shablovskii, Thermal hysteresis in nonlinear media, J. Eng. Phys. Thermophys., 59, No. 1, 944–950 (1990).
V. F. Formalev, É. M. Kartashov, and S. A. Kolesnik, Simulation of nonequilibrium heat transfer in an anisotropic semispace under the action of a point heat source, J. Eng. Phys. Thermophys., 92, No. 6, 1537–1547 (2019).
V. F. Formalev and S. A. Kolesnik, On thermal solitons during wave heat transfer in limited regions, Teplofi z. Vys. Temp., 57, No. 4, 543–547 (2019).
V. A. Kudinov and I. V. Kudinov, Mathematical simulation of the locally nonequilibrium heat transfer in a body with account for its nonlocality in space and time, J. Eng. Phys. Thermophys., 88, No. 2, 406–422 (2015).
É. M. Kartashov, Originals of operational images for generalized problems of nonstationary heat conduction, Tonk. Khim. Tekhnol., 14, No. 4, 77–86 (2019).
É. M. Kartashov, Analytical solutions of hyperbolic heat-conduction models, J. Eng. Phys. Thermophys., 87, No. 5, 1116–1125 (2014).
V. F. Formalev, On thermal shock waves in nonlinear media, Teplofi z. Vys. Temp., 50, No. 6, 799–803 (2012).
V. F. Formalev and S. A. Kolesnik, Analytical investigation of heat transfer in an anisotropic band and with heat fluxes assigned at the boundaries, J. Eng. Phys. Thermophys., 89, No. 4, 975–984 (1016).
V. F. Formalev and S. A. Kolesnik, Heat transfer in a half-space with transversal anisotropy under the action of a lumped heat source, J. Eng. Phys. Thermophys., 92, No. 1, 51–59 (2019).
V. F. Formalev, S. A. Kolesnik, and E. L. Kuznetsova, Influence of the thermal conductivity tensor components of heat protecting material on the magnitude of heat fluxes of the gas-dynamical boundary layer, Teplofiz. Vys. Temp., 57, No. 1, 66–71 (2019).
V. F. Formalev, S. A. Kolesnik, and B. A. Garibyan, Heat transfer with absorption in anisotropic thermal protection of high-temperature products, Vestn. MGU im. N. É. Baumana, Ser. Estestv. Nauki, No. 5, 35–49 (2019).
A. V. Attetkov and I. K. Volkov, Temperature field of an anisotropic half-space with its moving boundary containing film coating, Izv. Ross. Akad. Nauk, Énergetika, No. 3, 39–49 (2015).
G. Korn and T. Korn, Handbook of Mathematics [Russian translation], Nauka, Moscow (1968).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 95, No. 2, pp. 373–380, March–April, 2022.
Rights and permissions
About this article
Cite this article
Formalev, V.F., Kartashov, É.M. & Kolesnik, S.A. Wave Heat Transfer in Anisotropic Half-Space under the Action of a Point Exponential-Type Heat Source Based on the Wave Parabolic-Type Equation. J Eng Phys Thermophy 95, 366–373 (2022). https://doi.org/10.1007/s10891-022-02490-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-022-02490-2