Mathematical modeling and numerical analysis of heat transfer in solids of complex shape

Abstract

Introduction. Problem Statement. Modeling of heat exchange in solid bodies of complex shape is an urgent task. Explosions may occur as a result of emergency situations. Explosions are accompanied by pressure waves that destroy structures in their path. Also, explosions are accompanied by the release of heat. This in turn leads to fires. Forecasting the distribution of temperature fields can be used in the design of protective structures. Therefore, the creation of a new mathematical model that adequately describes transient thermal processes in solids, the development of an effective method for solving the problem and its implementation in the form of a modern information system that can be used for engineering purposes for analysis and forecasting is an acute problem. Purpose. The purpose of this study is to use mathematical modelling to obtain non-stationary temperature fields in solids in the region of significant temperature gradients that occur during emergency explosions of gas mixtures. Materials and Methods. Numerical modelling of unsteady heat transfer processes in multiconnected solid bodies of complex shape, surrounded by a heat-conducting gaseous medium, is performed based on a single finite-difference algorithm. Results. The joint direct problem of the flow of a continuous gaseous medium, heat transfer between a gas and a solid body, and thermal conductivity inside a solid body is considered. The mathematical model takes into account the spatial nature of the transfer of mass, momentum and energy, as well as the complex shape of streamlined solid bodies. The mathematical model is validated by comparison with analytical solutions of test problems for an infinite steel plate. Three-dimensional temperature fields in spatial solids of the form of various primitives, as well as their combinations, are obtained. Calculations of heat transfer in a turbine blade with a solid section and equipped with cooling cavities are carried out. Conclusions. Three-dimensional temperature fields can be used to assess the thermally stressed state of solids, as well as the strength characteristics of structures located in the zone of shock-pulse action of high overpressure due to an accident explosion of gas mixtures at industrial facilities.