Approximate approach to the problems of complex heat exchange simulating

The problems of complex heat exchange in engineering constructions and their analysis in the framework of specialized packages of multiphysics modelling have been considered. The mathematical model of heat exchange in the construction becomes more complicated if it is necessary to model the internal or external heat exchange with gas or liquid. If it is necessary to take into account heat exchange by radiation, the problem for the system of equations of thermal conductivity in the elements of the structure becomes nonlinear. It is impossible to construct an analytical solution for such problems, even for the simplest tasks in geometry.

On the basis of finite-element analysis of heat transfer problems, an approach has been suggested that essentially reduces the cost of computer resources for analysing such problems. For example, the modelling of a sealed electronic unit with a board inside has been carried out. The board has been considered as a source of heat. Heat exchange with the environment has been described by Newton’s law. Inside the unit, the heat exchange between the board and the case have been described by the thermal conductivity of the contact surfaces, convection in the air in the internal volume of the unit and the thermal radiation between the internal surfaces of the unit. In this formulation, the task has been modelled using COMSOL and Elmer multiphysical simulation packages. In the case of modelling by the Elmer package, the results visualization has been performed in the ParaView package. The suggested approximated approach consists in an approximate estimation of the heat exchange coefficients of the internal surfaces of the unit for con­vection and thermal radiation processes. In this case, the problem is reduced to the solution of the system of thermal conductivity equations for solids forming a block de­sign. It becomes linear and in calculations using the same packages it requires much less computer resources. In the paper, the modelling error for describing the problem in the framework of the suggested approach has been analysed.

Keywords: heat exchange, finite elements method, computer simulation.