Temperature identification in the structural elements of non-contacting face seals by using Trefftz functions

Abstract

Phenomena of the heat transfer in non-contacting face seals was described by partial differential equation of the second order and boundary conditions. In this way, the mathematical model was developed for the sealing rings. The distributions of temperature in the structural elements was obtained by the Trefftz method. It is a simple method of solving direct and inverse problems described by a homogeneous or an inhomogeneous partial differential equation. The main idea of the method is to determine functions satisfying a given differential equation (Trefftz functions) and to fit the linear combination of them to the governing boundary conditions.