Operator Method of Nonstationary Temperature Field Calculation in Environment With an Isolated Cylindrical Pipe

Abstract

The following research is important for the understanding of thermal conductivity processes in the setting typical for thermal pumps and for bringing calculations nearer to the real situation. Considering a non-stationary 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 rules out branching and provides an integral of an analytic function, is employed. Cauchy’s theorem is applied to the calculations. As a result, indefinite integrals have been derived for temperature estimation in the heat pipe coating and the surrounding environment, depending on the fluid temperature within the heat pipe.