Determination of the Temperature in a Homogeneous Half-Plane with an Inclined Rectilinear Crack Approaching the Boundary of the Half-Plane According to the Magnitude of the Heat Flux Through the Boundary of the Half-Plane and the Magnitude of the Temperature and Heat Flux Jumps on the Crack

Abstract

Statement of the problem. The study is devoted to determining the temperature in a homogeneous half-plane with a finite rectilinear crack approaching the boundary of the half-plane, provided that the magnitude of the heat flux through the boundary of the half-plane as well as the jumps in temperature and heat flux on the crack are known. Results. A mathematical model is set forth that describes the stationary distribution of heat in a homogeneous half-plane with a rectilinear crack approaching the boundary of the half-plane, for the case when the magnitude of the heat flux through the boundary of the half-plane and the jumps in temperature and heat flux on the crack are known. The mathematical correctness of the proposed model is proved; a technique for constructing a solution to the model, as well as a whole class of related problems, is shown; a formula for representing the solution of the model is obtained. Conclusions. The formula obtained in the article can be used to study the temperature distribution in a material with a crack, including in the vicinity of a crack, as well as to determine what effect the presence of a crack has on the heat distribution.