Data-driven dimensional analysis and modelling of two-phase heat-transfer in small-to-micro tubes*

The thermal design of electronic devices requires dissipation of large heat fluxes from small surface areas. This task can be accomplished by using two-phase flow boiling in small-to-micro diameter channels. The design of these compact heat exchangers requires accurate prediction of the two-phase heat transfer coefficient (HTC) as function of the operating conditions. Approaches to predict the HTC consist of empirical and semi-empirical correlations, and machine learning models, all of which involve performing complex nonlinear regressions on experimental data. However, it is challenging to identify the optimal dimensionless groups to be used as input for these regressions due to the complex interactions of key variables in phase-changing flows. To address this problem, we exploit data-driven dimensional analysis. First, starting from the dimensional input parameters, we estimate the active subspace of dimensionless groups, i.e., the dimensionless groups that have the greatest impact on the HTC. To do so, we use a Gaussian process regression (GPR) to model the function describing the HTC and its Jacobian. The GPR is trained with experimental data from the Brunel Two-Phase Flow database. Then, we express these optimal nondimensional groups in terms of products of powers of the Bond number, the Reynolds and Prandtl numbers of the liquid phase, and the reduced pressure and degree of subcooling at the entry to the channels. Our results show that working in nondimensional space is an effective way to avoid data overfitting and to obtain a realistic estimate of the data uncertainty.