Abstract
This study addresses the conjugate heat transfer problem of hydrodynamically developed turbulent flow in a circular pipe. An inverse method is used to estimate the time-varying inlet temperature and the outer-wall heat flux simultaneously on the basis of temperature measurements taken at two different locations within the pipe flow. The present approach rearranges the matrix forms of the governing differential equations and then applies a whole domain estimation with the function specification method and the linear least-squares-error method to determine the two boundary conditions of the pipe flow. The dimensionless temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of temperature measurement errors upon the precision of the estimated results is investigated. The proposed method provides several advantages compared to traditional methods: (1) it yields a solution within a single computational iteration, (2) no prior information is required regarding the functional form of the quantities of interest, (3) no initial guesses of the unknown parameter values are required, and (4) the inverse problem can be solved in a linear domain. This study also considers the influence of the location of the temperature measurement sensors upon the accuracy of the calculated results. The numerical results confirm that the proposed method provides an efficient, robust, and accurate means of estimating the inlet temperature and outer-wall heat flux simultaneously in turbulent pipe flow.
