Study of the Heat Transfer Process in a Flat Fuel Element

This article discusses an approximate analytical solution to the problem of heat transfer in a plate fuel element with internal energy sources under boundary conditions of the first kind. Modeling the heat transfer process in fuel elements is of great interest, since it allows you to control the heating / cooling modes of elements, determine temperature stresses, etc. The appearance of heat inside the body can be caused by the work of an electric current, chemical or nuclear reactions. In this case, the power of the internal source is given by the quadratic dependence on the coordinate. The solution to this problem is sought in the form of a trigonometric series. The solution is carried out by the joint method of integral heat balance and the introduction of additional boundary conditions. The advantage of this method is to obtain a simple analytical solution that simplifies further analysis of the original problem. In the course of the solution, the dependence of the temperature distribution over the thickness of the plate was obtained, from which it can be seen that with an increase in the Fourier time, the value of the dimensionless temperature increases. Also, the temperature dependence on time was obtained for different values of the Pomerantsev criterion, from which it can be seen that, regardless of the power of the internal source, the process of stabilization of the temperature field is observed at a level that depends on the Pomerantsev number. In the course of the analysis of the research results, it was revealed that with an increase in the number of members of the initial trigonometric series, the obtained solution approaches the exact solution, which indicates the convergence of the proposed method.