Analysis of the process OF non-stationary heat transfer through the wall of a cylindrical container

Abstract

The process of constructing a mathematical model of the heat exchange process between two media through the wall of a cylindrical container is described. In engineering, there are many problems of calculating the heat exchange process through the wall of a cylindrical tank (heat exchangers, heat supply systems, water tanks, etc.). There are usually no difficulties with the stationary process, while a unified calculation method has not yet been developed for the problems of non-stationary thermal conductivity due to the complexity of their mathematical description. Most of the problems encountered when using heat and mass transfer processes are reduced to solving partial differential equations. Differential equations describing real physical processes are usually very complex, and it is possible to obtain their solution in the form of a finite formula only in the simplest cases. With a strict formulation of the problem, assuming a minimum number of assumptions, these studies are comparable to the best physical experiments. In addition, numerical experiments have a number of advantages in comparison with physical ones: they allow relatively simple and wide-range variation of the problem parameters and boundary conditions, as well as obtaining comprehensive information about the process under study. The paper describes one of the possible ways to construct a method for calculating non-stationary heat transfer through the wall of a cylindrical container. A mathematical model has been developed that allows calculating thermal processes in cylindrical tanks.