Simultaneous estimation of boundary heat flux and convective heat transfer coefficient of a curved plate subjected to a slot liquid jet impingement cooling

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to simultaneously estimate the unknown boundary heat flux and convective heat transfer coefficient in a curved plate cooled by an impinging slot jet from the knowledge of temperature measurements taken within the plate. Subsequently, the distributions of temperature in the plate can be determined. It is assumed that no prior information is available on the functional forms of the heat flux and convective heat transfer coefficient; hence 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, and the effect of the errors and locations in these measurements upon the precision of the estimated results is also considered. Results show that an excellent estimation on the heat flux and convective heat transfer coefficient and temperature distributions can be obtained for the two test cases considered in this study.