Three-Dimensional Inverse Heat Conduction Method to Estimate Boundary Heat Flux: Multiple-Droplet Impact Application

Estimating boundary conditions during spray cooling requires the solution of a transient heat conduction inverse problem in a three-dimensional space, so the heat dissipation caused by the impact of each droplet can be captured. In this paper, the quality of the heat flux estimate is evaluated for single and multiple droplet impact on a heated surface. We used classical integral transform to solve the heat equation and we employed Beck’s function specification method for regularization. Based on experimental results, two heat flux profiles were used to simulate the heat dissipation by droplet impact: one corresponding to the deposition regime and another corresponding to the Leidenfrost regime. The results show that the proposed inverse method succeeds in capturing the heat flux profile for both one- and two-droplet simulations, especially for the Leidenfrost regime. An analysis of the droplet size effect showed that estimates of the dissipated heat by the droplet are accurate if the diameter of the heat transfer area is larger than at least ten times the pixel size. Meanwhile, the spacing between two impacting droplets has minor effect. Finally, a Monte Carlo simulation allowed to estimate the accuracy of the estimated dissipated heat as 10% with 95% of confidence interval.