Generalized model representations of the theory thermal shock for local non-equilibrium processes heat transfer

An open problem of the theory of thermal shock in terms of a generalized model of dynamic thermoelasticity under conditions of a locally nonequilibrium heat transfer process was considered. The model simultaneously includes three coordinate systems: Cartesian coordinates - a massive body bounded by a flat surface; spherical coordinates - a massive body with an internal spherical cavity; cylindrical coordinates - a massive body with an internal cylindrical cavity. Three types of intensive heating and cooling are considered: temperature, thermal, medium. The task is set: to obtain an analytical solution, to carry out numerical experiments and to give their physical analysis.
As a result, generalized model representations of thermal shock in terms of dynamic thermoelasticity have been developed for locally nonequilibrium heat transfer processes simultaneously in three coordinate systems: Cartesian, spherical, and cylindrical. The presence of curvature of the boundary surface of the thermal shock area substantiates the initial statement of the dynamic problem in displacements using the proposed corresponding 'compatibility' equation. The latter made it possible to propose a generalized dynamic model of the thermal reaction of massive bodies with internal cavities simultaneously in Cartesian, spherical and cylindrical coordinate systems under conditions of intense thermal heating and cooling, thermal heating and cooling, heating and cooling by the medium. The model is considered in displacements on the basis of local non-equilibrium heat transfer. An analytical solution for stresses is obtained, a numerical experiment is carried out; the wave nature of the propagation of a thermoelastic wave is described. A comparison with the classical solution is made without taking into account local non-equilibrium. On the basis of the operational solution of the problem, design engineering relations important in practical terms for the upper estimate of the maximum thermal stresses are proposed.