Finite element modeling of heat propagation of a complete rod of constant cross-section

Abstract

In this paper, the definition of the temperature distribution field for a rod made of heat-resistant alloy EI48 is introduced. The authors consider for the study a complete rod of circular cross-section of radius R, of limited length L. Studied body is under the influence of a heat flow q from the surface over the entire cross-sectional area of the left end, and heat exchange with the environment occurs on the cross-sectional area of the right end. The rod is thermally insulated along the side surface. The authors consider two cases: the first is the heat flow with intensity q can be set on the area of a small circle with radius r <R, the second is the heat flow can be set on its part, that is, on the area 2 2   R     . During the study, the authors showed that during the thermomechanical process, the strength of each section of the load-bearing structural elements is significantly influenced by the temperature distribution field. The influence of high temperature on the morphology of heat-resistant alloys is also shown. This leads to the fact that in some parts of the structural elements the temperature will be acceptable, and in some — critical. As a result, rapid wear of structural elements and loss of their physical qualities occur. Therefore, mathematical modeling of temperature distribution field for a body of various configurations is an urgent problem. The article presents a method for constructing a mathematical model and a corresponding computational algorithm that allows solving a class of problems to determine the regularities of the temperature distribution field in the elements of rod-shaped structures. To do this, the authors used the energy-variation principle in combination with the finite element method.