Simultaneous estimation of heat-transfer rate and coolant fluid velocity in a transpiration cooling process

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent heat-transfer rate on the heated surface and coolant fluid velocity in a transpiration cooling process using temperature measurements of the porous medium and coolant fluid. It is assumed that no prior information is available on the functional forms of the unknown heat-transfer rate and coolant fluid velocity; hence the procedure is classified as the function estimation 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 by using simulated exact and inexact temperature measurements. Results show that an excellent estimation on the time-dependent heat-transfer rate and coolant fluid velocity can be obtained for the test case considered in this study.