Nonstationary Heat-Conduction Problem for a Half-Space with a Multilayer Coating Upon Cyclic Change in the Ambient Tempe
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Journal of Engineering Physics and Thermophysics, Vol. 93, No. 6, November, 2020
NONSTATIONARY HEAT-CONDUCTION PROBLEM FOR A HALF-SPACE WITH A MULTILAYER COATING UPON CYCLIC CHANGE IN THE AMBIENT TEMPERATURE V. A. Shevchuk and A. P. Gavris′
UDC 536.12:620.198
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. Keywords: heat conduction, half-space, multilayer coating, generalized boundary conditions, thermal cycling. Introduction. A widespread method to harden metals, alloys, and parts of machines and mechanisms (including products with multilayer coatings for various functional purposes) is their thermal treatment in the regime of multiple heating and cooling with optimum rates without holdings in the case of maximum heating temperatures with cyclic change in the ambient temperature [1]. Experimental studies of the states of products with multilayer coatings in heat treatment and of the influence of the change in temperature regimes on their operating characteristics have been made in [2–5]. Analytical and numerical solutions to the problems of nonstationary heat-conduction of multilayer bodies and bodies with single-layer and multilayer coatings under the conditions of the time dependence of the ambient medium have been the focus of [6–14] and [15–21] respectively. In [22], consideration has been given to the heating of simply shaped bodies in a medium whose temperature is a linear, exponential, cosinusoidal, or harmonic function of time. In [23], analytical solutions to the boundary-value heat-conduction problems with inhomogeneous cyclic boundary conditions of the third kind have been obtained for the periods of heating and cooling of simply shaped bodies and coated bodies of the same and varying duration within one cycle. To solve the problems of heat conduction of thin coatings whose thermal resistance and heat capacity are substantially lower than the thermal resistances and heat capacities of the substrate, an approach based on the use of generalized boundary conditions [16, 17, 24–36] enabling one to considerably simplify the solution of the indicated problems by the existing analytical methods is efficient. It is either the heat capacity [16, 17, 24, 28, 30] or just the thermal resistance [25, 27, 29] of a coating that usually appear in such generalized boundary conditions. In [26], generalized boundary conditions have been obtained with account of only one of these properties in an individual coating layer. The approach based on the operator method [37, 38], which enables us not to accept a priori hypotheses for the lateral distribution of the sought function in the coating, makes it possible to obtain more general generalized bounda
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