We consider a mathematical model for the evaluation of temperature of a surface covered with a thin heat-insulating layer according to the data of measurements of temperature on the free surface of the coating and in the ambient medium. The model involves the mechanisms of conductive and radiation energy transfer in the volume of the layer, conductive and radiation heat exchange with the surface covered by the layer, convective and radiation heat exchange with the ambient medium on the free surface of the coating capable of emission, absorption, and reflection of thermal electromagnetic radiation. We also present the results of numerical analysis of the solutions of nonlinear problem based on the developed iterative procedure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. V. Borodai, I. D. Kolomiets, and D. M. Borodai, “Study of the influence of temperature on the optical characteristics of the heatresistant insulation of reusable space vehicles,” Vymir. Obchysl. Tekh. Tekhnol. Prots., No. 1, 29–34 (2011).
I. A. Gusarova and T. A. Man’ko, “Investigation of the heat-insulating properties of heat-resistant materials for reusable space vehicles,” Visn. Dnipr. Univ., Ser. Raket.-Kosm. Tekh., Issue 17, 1, 35–41 (2014).
M. N. Özisik, Radiation Transfer and Interactions with Conduction and Convection, Wiley, New York (1973).
V. A. Rozenenkova, N. A. Mironova, S. S. Solntsev, and S. V. Gavrilov, “Ceramic coatings for gradient high-temperature heatprotective materials,” Steklo Keram., No. 1, 29–32 (2013).
V. F. Chekurin and Yu. V. Boichuk, “Mathematical model for the radiation infrared tomography of the temperature field in an isotropic layer,” Mat. Met. Fiz.-Mekh. Polya, 59, No. 1, 171–182 (2016); English translation: J. Math. Sci., 229, No. 3, 320–334 (2018); 10.1007/s10958-018-3680-9.
Yu. E. Sheludyak, L. Ya. Kashporov, L. A. Malinin, and V. N. Tsalkov, Thermal Properties of the Components of Combustible Systems: A Handbook [in Russian], Inform TÉI, Moscow (1992).
V. K. Bityukov and V. A. Petrov, “Absorption coefficient of molten aluminum oxide in semitransparent spectral range,” Appl. Phys. Res., 5, No. 1, 51–71 (2013); https://doi.org/10.5539/apr.v5n1p51.
V. Chekurin and Yu. Boichuk, “An iterative method for solving of coupled equations for conductive-radiation heat transfer in dielectric layers,” Adv. Math. Phys., 2017, Article ID 9139135 (2017); https://doi.org/10.1155/2017/9139135.
K. Daryabeigi, G. R. Cunnington, and J. R. Knutson, “Combined heat transfer in high-porosity high-temperature fibrous insulation: Theory and experimental validation,” J. Thermophys. Heat Transfer, 25, No. 4, 536–546 (2011); https://doi.org/10.2514/1.T3616.
M. Dehghan, Y. Rahmani, D. D. Ganji, S. Saedodin, M. S. Valipour, and S. Rashidi, “Convection-radiation heat transfer in solar heat exchangers filled with a porous medium: Homotopy perturbation method versus numerical analysis,” Renew. Energy, 74, 448– 455 (2015); 10.1016/j.renene.2014.08.044.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 1, pp. 161–172, January–March, 2020.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Chekurin, V.F., Boichuk, Y.V. Mathematical Model for the Evaluation of Temperature of the Surface Covered with a Heat-Insulating Layer. J Math Sci 270, 191–204 (2023). https://doi.org/10.1007/s10958-023-06340-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06340-1