Developing generalized model representations of thermal shock for local non-equilibrium heat transfer processes

Abstract

Objectives. Processes of energy transfer in solids and resultant thermal loads are widespread in nature and technology. This explains the scientific and practical significance of constructing a theory of these processes, as well as developing effective methods for studying the modeled concepts developed on this basis. The purpose of such studies is to determine basic flux patterns of complex processes occurring especially under conditions of powerful energy impacts in various technological operations. These include plasma-chemical processing of materials, their processing in infrared furnaces and solar plants, intense heating of materials carried out by laser or electron beams, and the use of powerful radiation emitters for thermal hardening and hardening of the surface of products. In these cases, the phenomenon of thermal shock arises, forming one of the central topics in thermomechanics and strength physics of solids. The present work considers an open theoretical problem of thermal shock in terms of a generalized model of dynamic thermoelasticity under conditions of a locally nonequilibrium heat transfer process. Depending on the type and curvature of the boundary surface of the considered massive body, the model can be used to study the problem in 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 are considered: temperature heating, thermal heating, and heating by medium. Following the development of an analytical solution, the results of conducted numerical experiments are presented along with their physical analysis.Methods. The study applies methods and theorems of operational calculus according to the theory of special functions.Results. Generalized model representations of thermal shock are developed in terms of dynamic thermoelasticity 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.Conclusions. 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 temperature heating, thermal heating, and heating by medium is proposed. The model is considered in terms of displacements based on local nonequilibrium heat transfer. A numerical experiment carried out according to the obtained analytical solution for stresses forms a basis for a description of the wave nature of the propagation of a thermoelastic wave. A comparison with the classical solution is made without taking into account local nonequilibrium. The calculation of engineering relations carried out on the basis of the operational solution of the problem is important in practical terms for the upper estimate of the maximum thermal stresses.