The heat conduction problem for a half-space with a multilayer coating under nonstationary heating

Based on the mathematical model with generalized boundary conditions of heat exchange of the bodies with ambient medium via thin multilayer coatings, the statement of heat conduction problem for a half-space with a multilayer coating under nonstationary heating at the arbitrary function of temperature of ambient medium is formulated. Applying the method of Laplace integral transformation with the use of Duhamel integral relation, we obtain an analytical solution of this problem and write the specific expressions for temperature in body and coating’s layers for the cases of linear, exponential, logarithmic, and periodic functions of temperature of ambient media. The influence of heat exchange condition with ambient medium on the contact temperature and temperature distribution across the spatial coordinate is analyzed