Operator Method for Nonstationary Temperature Field Calculation in Thick-walled Cylindrical Heat Pipe Environment

Abstract

The paper is dedicated to the exploration of one of the methods of renewable energy research. A significance lies in the economically efficient facilities; therefore, it is important to establish distribution of temperatures in the parts of facilities. Considering a nonstationary process, the temperature field is described in the polar coordinate system by using Laplace’s equation and corresponding mixed-type boundary data. The solution was obtained by the Laplace Transform Method, applying an integral function of complex variables. The inverse Laplace Transform and the original temperature are expressed as an integral. For the integration, a closed contour, which excludes branching and provides the integral of a function that is analytic, was employed. The Cauchy theorem was applied to the calculations. As a result, indefinite integrals were derived for the temperature estimate in the heat pipe cover and the surrounding environment, depending on the temperature of a fluid within the heat pipe.