Generalized Model Representation of the Thermal Shock Theory

Abstract

This article considers the open problem of the thermal shock theory in terms of a generalized model of dynamic thermoelasticity under conditions of a locally nonequilibrium heat transfer process. The model is used for a massive body in the cases of three coordinate systems: Cartesian coordinates for a body bounded by a flat surface; spherical coordinates for a body with an internal spherical cavity; and cylindrical coordinates for a body with an internal cylindrical cavity. Three types of intensive heating and cooling are considered: temperature, thermal, and heating by the 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 a thermal shock in terms of dynamic thermoelasticity are developed for locally nonequilibrium heat transfer processes simultaneously in three coordinate systems: Cartesian, spherical, and cylindrical. The presence of a 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, and heating and cooling by the medium. The model is considered in displacements on the basis of a local nonequilibrium heat transfer. An analytical solution for stresses is obtained and a numerical experiment is carried out; the wave nature of the propagation of a thermoelastic wave is described. A comparison is made with the classical solution without taking into account the local non-equilibrium. Based on the operational solution of the problem, design engineering relations that are important in practical terms for the upper estimate of the maximum thermal stresses are proposed.