New Analytical Solutions of Mathematical Models of Heat Shock of Local Non-Equilibrium Heat Transfer

Abstract

The article is devoted to practically new model representations of locally nonequilibrium heat transfer in terms of nonstationary heat conduction for hyperbolic type equations (wave equations), as well as dynamic models of heat shock based on wave equations. The results presented in the article practically open up an independent scientific direction in analytical thermal physics and in the theory of thermal shock, namely: the study of the thermal response of solids of a canonical form of finite sizes to intense heating and cooling under conditions of a locally nonequilibrium heat transfer process. This direction required the development of a special apparatus of operational calculus due to the appearance in analytical solutions of model problems in the image space according to Laplace of non-standard operational images, the originals of which are unknown and are not available in reference books on operational calculus. The presented images are typical for operational solutions of a wide class of generalized boundary value problems for equations of hyperbolic type in the theory of heat conduction, diffusion, hydrodynamics, vibrations, propagation of electricity, thermomechanics and other areas of science and technology. Illustrative examples of analytical solutions of specific model problems of locally nonequilibrium heat transfer and the theory of thermal shock for a finite region are given in both classical and generalized formulations (the latter taking into account the finite rate of heat propagation). The characteristic features of functional structures as analytical solutions of the considered mathematical models are revealed.