Estimation of fouling profile in a heat exchanger pipe applying the conjugate gradient method based on the inverse algorithm

One of the factors reducing the efficiency of the heat exchanger during its operation is fouling. Fouling takes place as a layer on one side or both sides of surface heat transfer and the resistances of the heat transfer that it shows cause the decrease in heat transfer through the surface. The measuring scale of fouling is most important. Because accurate measurement of fouling and to ensure that the limit is higher, fouling removal and cleaning operations is essential. A conjugate gradient method (CGM) based on the inverse algorithm is used to estimate the unknown fouling-layer profile on the inner wall of a pipe system using simulated temperature measurements taken within the pipe wall. It is assumed that no prior information is available about the functional form of the unknown profile. Therefore, the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The accuracy of the inverse analysis is examined using the simulated exact and inexact temperature measurements. The results show that the excellent estimation of the fouling-layer profile can be obtained for the test case considered in this study. The technique presented in this study can be used in a warning system to call for pipe maintenance when the thickness of fouling exceeds a predefined criterion.