Inverse Estimation of Cooling Heat Flux in Spray Cooling of Hot Surface Based on Dual-Phase-Lag Model

An inverse analysis technique based on the conjugate gradient method (CGM) and the discrepancy principle is employed to estimate the time-wise variation of the unknown cooling heat flux in the spray cooling of a hot surface. In contrast to previous studies, the heat conduction equation of the cooled surface is formulated using a dual-phase-lag (DPL) model. In addition, no assumptions are made regarding the functional form of the cooling heat flux. The simulation data required to conduct the inverse analysis are generated by adding random errors to the calculated exact temperatures at the boundaries and interior of the hot body. The validity of the inverse solutions is demonstrated numerically by means of two illustrative examples. Moreover, the sensitivity of the estimation results to the measurement error and measurement location is systematically explored. Overall, the results show that the proposed method provides a robust and accurate approach for estimating the unknown time-dependent cooling heat flux in typical industrial spray cooling applications.