Mathematical Modeling of Heat Transfer in a Plate During Plasma Spraying of Thermal Protection on It

The article considers non-stationary heat transfer in a plate under conditions of high-temperature aerosol spraying during the formation of thermal protection on this plate. To solve such a problem in a domain with a moving boundary, which increases the computational domain, a substitution is used that reduces the domain with a moving boundary to a domain with fixed boundaries. The finite cosine Fourier transform was applied to the obtained problem, for which the problem for eigenvalues and eigenfunctions with boundary conditions of the third kind was previously solved. A new analytical solution and results on the thermal state of the entire system with a complex temperature pattern at the moving boundary are obtained.