Inverse Radiation Problem in Determination of the Inlet Temperature Profile for Two-Phase Laminar Flow in a Channel

An inverse thermal problem is considered for two-phase laminar flow in a parallel-plate duct where there is conductive, convective and radiative heat transfer involved. The inlet temperature distribution is estimated when only measured gas temperatures are available at downstream of the duct. The inverse problem is solved through a minimization of an objective function by using two regularization methods, i.e., the iterative conjugate gradient method (CGM) and the Tikhonov regularization method (TRM). The effects of the functional form of inlet temperature profile, the number of the measurement points, and the measurement errors are investigated and discussed. The computational accuracy and efficiency of these two regularization methods are compared and discussed. Both CGM and TRM are found to work well for finding the inlet temperature, even when radiation is involved. However, usually the TRM requires a longer computational time than the conjugate gradient method because of nonlinearity in estimating the sensitivity coefficient.