Integral model and numerical method determination of temperature at linear heat transfer

The work deals with the measurement problem associated with the problem of determining the temperature inside the object exposed to external heat. At each point of the surface, the thermal effect is the same and only changes over time. In this case, the temperature measurement problem has the form of a heat transfer problem in a linear object, one end of which corresponds to a point on the surface of the body, and the other end corresponds to the internal control point. The initial data of the problem are formed on the basis of temperature measurements near the object surface. In this recearsh, the problem of heat transfer is reduced to an integral model using the direct and inverse Laplace transform. The obtained integral equation is a Volterra equation of the first kind and characterizes the direct dependence of the unknown temperature functions at the control point on the initial data. To construct a numerical solution of an integral equation that is stable with respect to the error of the initial data, a computational scheme based on a regularizing approach including a multipara-meter algorithm is proposed. In order to obtain experimental estimates of the errors of the solutions to the measurement problem, a computational experiment was carried out on the basis of simulation modeling. During the experiment, the values of temperature functions at the control point of the object were determined and, on the basis of the obtained boundary functions, the temperature values were found at the internal points of the object. Also, in the course of the experiment, a comparative analysis of the temperature functions found in the test point with test values was performed. The results of the computational experiment are presented in the work and testify to the sufficient accuracy of the proposed computational method for determining the temperature during linear heat transfer.