Estimation of flow temperature in horizontal pipe using analytical inverse heat transfer

Pipeline systems are widely used in gas refineries, oil factories chemical power plants. It is important to measure the fluid temperature in this pipeline. Numerous cases, however, exist where the internal fluid temperature is not available and only an outside wall temperature measurement is feasible. Recently inverse heat transfer problems have been analyzed for the situations where a direct measurement of boundary/initial conditions, or thermophisical properties are difficult, or indeed impossible, to carry out. Various numerical approaches have been proposed to estimate fluid temperature in the pipes. In this study, the analytical method is applied to solve the one-dimensional inverse heat conduction problem, in order to estimate fluid temperature in the pipes, based on the exact outer wall temperature. The fluid temperature is assumed to be a polynomial. The unknown polynomial coefficients are found by combining the method of Duhamel's theorem and the least squares method. The results show that the fluid temperature in the pipes can be accurately estimated by using the inverse heat transfer method.