Proposed Modification to Whole Domain Function Specification Method to Improve Accuracy of Its Estimations

This paper investigates the inverse heat transfer problem of laminar forced convection within a circular pipe. The performances of two classical algorithms used in the whole domain function specification method (WDFSM) to obtain simultaneous estimates of the time-varying inlet temperature and outer-wall heat flux are compared. Additionally, this study proposes a modification to the linear assumption employed in the conventional WDFSM to improve its estimation performance. The WDFSM solution procedure is based on future temperature measurements at two different locations within the pipe flow. In the modified algorithm, the variations of the estimations at all time steps for various values of the future-time parameter are investigated, and if large variations in the slope of the function are detected at some time steps, the originally linear assumption for the variation of the unknowns is replaced with the assumption of a constant function at these time steps. Otherwise, the estimates at the other time steps are calculated using the linear assumption. The numerical results confirm that the proposed algorithm yields slightly more accurate estimates of the unknowns than the two classic algorithms.