Application of the inverse method to the estimation of heat flux and temperature on the external surface in laminar pipe flow

This study addresses the inverse problem of a finite cooled/heated length on the heat transfer characteristics of laminar flows through thick-walled circular tubes. Using temperature measurements taken at several different locations within the fluid, the inverse method is used to estimate the unknown heat flux and temperature on the external surface of the circular pipe. The present approach rearranges the matrix forms of the governing differential equations, and then combines the reverse matrix method and the linear least-squares-error method to determine the unknown boundary conditions of the pipe flow. The temperature data obtained from the direct problem are used to simulate the temperature measurement, and the influence of errors in these measurements upon the precision of the estimated results is also considered. This study also considers the influence of the locations and number of sensors used upon the accuracy of the estimated results. The results indicate that the accuracy of the estimated results is improved by taking temperature measurements in locations close to the inner-wall. Finally, the results confirm that the proposed method is capable of yielding accurate results even when errors in the temperature measurements are present.