Using the integral Laplace transformation and generalized boundary conditions, the authors have obtained the analytical solution to a one-dimensional nonstationary heat-conduction problem for a half-space with a multilayer coating on piecewise uniform change in the ambient temperature. A study has been made and regularities have been established of thermal processes occurring in the body and the coating in thermal cycling.
Similar content being viewed by others
References
A. S. Tikhonov, V. V. Belov, I. G. Leushin, V. I. Eremenko, and S. F. Zabelin, Thermocyclic Treatment of Steels, Alloys, and Composite Materials [in Russian], Nauka, Moscow (1984).
L. B. Getsov and A. I. Rybnikov, Mechanisms of deformation and fracture of multilayer coatings during thermal cycling, Mater. Sci., 29, No. 6, 604–611 (1993).
L. V. Kravchuk, R. I. Kuriat, K. P. Buiskikh, E. A. Zadvornyi, and S. G. Kiselevskaya, Investigation of the kinetics of damage to refractory alloys under cyclic thermal loading in a gas flow, Strength Mater., 38, No. 4, 386–391 (2006).
R. C. Hendricks, G. McDonald, R. L. Mullen, M. J. Braun, B. T. Chung, and J. Padovan, Thermomechanical loading of multilayered cylindrical geometries in thermal cycling from 300 to 1300 K, Proc. ASME/JSME Thermal Engineering Joint Conf., New York (1983), Vol. 3, pp. 329–340.
A. I. Rybnikov, L. B. Getsov, A. A. Tchizhik, I. S. Malashenko, and A. S. Osyka, Service life of heat-resistant alloys with protective coatings in thermocyclic loading, Sur. Coat. Technol., 78, Nos. 1–3, 103–112 (1996).
V. C. Ivanov and L. V. Karaseva, Radiative-convective heating of multilayer bodies on ideal and nonideal thermal contacts, Izv. Vyssh. Uchebn. Zaved., Severo-Kavkazskii Region, Tekh. Nauki, No. 4, 34–37 (2017).
O. T. Il’chenko, Temperature field of a two-layered plate with time-varying heat-transfer conditions, J. Eng. Phys. Thermophys., 19, No. 6, 1567–1570 (1970).
V. A. Kudinov, Analytical methods of solution of boundary-value problems for multilayer structures, Izv. Ross. Akad. Nauk, Énergetika, No. 5, 85–106 (1999).
V. V. Mel’nikov, Temperature field of a three-layered sphere, Prikl. Mekh. Tekh. Fiz., 50, No. 1, 78–84 (2009).
X. Lu and P. Tervola, Transient heat conduction in the composite slab — Analytical method. J. Phys. A: Math. Gen., 38, No. 1, 81–96 (2005).
X. Lu and M. Viljanen, An analytical method to solve heat conduction in layered spheres with time-dependent boundary conditions, Phys. Lett. A, 351, Nos. 4–5, 274–282 (2006).
M. N. Ozisik, Heat Conduction, John Wiley, New York (1993).
U. Siedlecka, Radial heat conduction in a multilayered sphere, J. Appl. Math. Comput. Mech., 13, No. 4, 109–116 (2014).
S. Singh, P. K. Jain, and Rizwan-uddin, Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions, Nucl. Eng. Des., 241, No. 1, 144–154 (2011).
A. V. Attetkov, N. S. Belyakov, and I. K. Volkov, Temperature field of a solid body containing a cylindrical channel with a multilayer coating under the conditions of nonstationary heat transfer, Vestn. MGTU im. N. É. Baumana, Ser. Mashinostroenie, No. 3, 37–50 (2006).
A. V. Attetkov, P. A. Vlasov, and I. K. Volkov, Temperature field of a half-space with a thermally thin coating in pulse modes of heat exchange with the environment, J. Eng. Phys. Thermophys., 74, No. 3, 647–655 (2001).
A. V. Attetkov, L. N. Vlasova, I. K. Volkov, and E. A. Zagoruiko, Formation of temperature fields in a region containing a thin-walled coating, Vestn. MGTU im. N. É. Baumana, Ser. Mashinostroenie, No. 2, 3–10 (1999).
V. B. Veselovskii, Solution of nonstationary-heat-conduction problems for multilayer thermal protection coatings, in: Applied Problems of Aerogasdynamics [in Russian], Naukova Dumka, Kiev (1987), pp. 95–100.
S. V. Kobel’skii, R. I. Kuriat, V. L. Kravchenko, and A. L. Kvitka, Procedure and analysis of three dimensional thermal stressed states of turbine blades with coatings subjected to thermal cycling, Strength Mater., 31, No. 6, 564–570 (1999). ЛKo
B. A. Lyashenko, V. A. Terletskii, N. A. Dolgov, and E. B. Soroka, Distribution of temperature in a plate with a single layer coating subjected to intense heating, Strength Mater., 30, No. 3, 787–792 (1998).
V. M. Samoilenko, Yu. V. Petrov, and O. A. Ratenko, Temperature distribution in multilayer cermet coatings under nonstationary thermal action, Nauch. Vestn. NGTU GA, 20, No. 04, 33–40 (2017).
G. N. Tret’yachenko and B. S. Karpinos, Strength and Durability of Materials under Cyclic Thermal Actions [in Russian], Naukova Dumka, Kiev (1990).
Yu. A. Kirsanov, Cyclic Thermal Processes and the Theory of Heat Conduction in Regenerative Air Heaters [in Russian], Fizmatlit, Moscow (2007).
A. A. Berezovskii, Nonlinear problems of heat-radiating bodies with a thermally thin coating, in: Problems of Nonstationary Heat Conduction [in Russian], Preprint No. 83.29, Inst. Matematiki AN USSR, Kiev (1983), pp. 6–11.
A. D. Gorbunov, Analytical calculation of the heating (cooling) of elemental bodies covered with a thin shell, Metallurg. Teplotekhnika, Issue 2 (17), 56–62 (2010).
V. S. Zarubin, Calculation and Optimization of Heat Insulation [in Russian], Énergoatomizdat, Moscow (1991).
I. A. Motovilovets and V. I. Kozlov, Mechanics of Coupled Fields in Structural Elements. Thermoelasticity, Vol. 1 [in Russian], Naukova Dumka, Kiev (1987).
M. A. Al Nimr and M. K. Alcam, A generalized thermal boundary condition, Int. J. Heat Mass Transf., 33, Nos. 1–2, 157–161 (1997).
F. Du, M. R. Lovell, and T. W. Wu, Boundary element method analysis of temperature fields in coated cutting tools, Int. J. Solid Struct., 38, Nos. 26–27, 4557–4570 (2001).
D. Moulton and J. A. Pelesko, Thermal boundary condition: An asymptotic analysis, Heat Mass Transf., 44, No. 7, 795–805 (2007).
Ya. S. Podstrigach (Pidstryhach) and P. R. Shevchuk, Temperature fields and stresses in bodies with thin coatings, Teplov. Napryazh. Élement. Konstruktsii, No. 7, 227–233 (1967).
Yu. M. Kolyano and M. E. Khomyakevich, Generalized heat conduction in coated bodies that accounts for the coating curvature, J. Eng. Phys. Thermophys., 65, No. 6, 1251–1256 (1993).
V. A. Shevchuk, Generalized boundary conditions to solving thermal stress problems for bodies with thin coatings: in Encyclopedia of Thermal Stresses, Springer, Dordrecht, Heidelberg, New York, London (2014), Vol. 4, pp. 1942–1953.
V. A. Shevchuk, Generalized boundary conditions for heat transfer between a body and the surrounding medium through a multilayer thin covering, J. Math. Sci., 81, No. 6, 3099–3102 (1996).
V. A. Shevchuk, Calculation of thermal state of bodies with multilayer coatings, Lect. Notes Comput. Sci., 2330, 500–509 (2002).
V. A. Shevchuk, Modeling and computation of heat transfer in a system “body–multilayer coating,” Heat Transf. Res., 37, No. 5, 412–423 (2006).
Ya. S. Podstrigach (Pidstryhach) and R. N. Shvets, Thermoelasticity of Thin Shells [in Russian], Naukova Dumka, Kiev (1978).
S. A. Lukasiewicz, Thermal stresses in shells: in Thermal Stresses III, Elsevier, North Holland (1989), pp. 355–553.
V. A. Shevchuk, Analytical solution of nonstationary heat conduction problem for a half-space with a multilayer coating, J. Eng. Phys. Thermophys., 86, No. 2, 450–459 (2013).
A. V. Luikov, Heat Conduction Theory [in Russian], Vysshaya Shkola, Moscow (1967).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 6, pp. 1543–1552, November–December, 2020.
Rights and permissions
About this article
Cite this article
Shevchuk, V.A., Gavris’, A.P. Nonstationary Heat-Conduction Problem for a Half-Space with a Multilayer Coating Upon Cyclic Change in the Ambient Temperature. J Eng Phys Thermophy 93, 1489–1497 (2020). https://doi.org/10.1007/s10891-020-02254-w
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-020-02254-w