SOLUTION OF THE HEAT CONDUCTION EQUATION OF A CYLINDRICAL ROD

Abstract. The purpose of this paper is to investigate the thermophysical state of a cylindrical rod of constant cross-section and limited length. This paper is devoted to the automation of the study of the thermophysical state of a rod of constant cross-section and limited length. The process of automating research relies on the laws of conservation of energy. A three-dimensional body is considered, the constant cross section of which has the shape of a cylinder. However, due to the complexity of the studied phenomena, to solve analytically partial differential equations by modern mathematical methods. There are also many solution methods suitable for practical use. The problem is solved by reduction to a partial derivative equation in a cylindrical coordinate system, for the solution of which an appropriate algorithm is developed. The obtained results are translated into Cartesian coordinate system. This solves the original problem. A program for finding the temperature propagation along the rod has been developed, which puts the results of numerical calculations into several files. The results of numerical calculations in dynamics (by time) are output in the form of a table and displayed as one-dimensional graphs. A promising direction is the application of interval mathematics to the study of the heat conduction equation.

Keywords: thermal conductivity, thermal insulation, temperature, unsteady thermophysical process, energy.