A physics-constrained surrogate model for rapid prediction of microscale attached droplet evaporation in porous media under coupled radiative and conductive heating

The evaporation of microscale droplets attached to porous media surfaces is widely encountered in radiation assisted porous evaporation and evaporative thermal management. Droplet evaporation is jointly governed by substrate conduction, gas side convective heat exchange, and external radiation, while the local heat transfer and phase change process exhibits strong transient behavior, multiparameter coupling, and moving interface evolution. Consequently, detailed numerical simulations are computationally expensive, and rapid prediction methods are required for engineering analysis. In this study, a rapid prediction method was developed for microscale attached droplet evaporation under coupled conductive and radiative heating. High fidelity data were generated using a coupled LBM-FDM-FDTD framework. Based on these data, a surrogate model was constructed under the constraint of energy closure to predict droplet radius decay and evaporation lifetime. The substrate heat input was represented by a parameterized correlation with droplet radius and thermal boundary conditions, while the radiative heat input was separately parameterized using the radius dependent absorptivity. Latent heat consumption, sensible heat accumulation, and the residual influence of gas side heat exchange were incorporated into a calibrated effective latent heat. The results show that the proposed model reproduces the evolution of the principal energy terms and droplet radius with good overall agreement. Under varying radiation powers, the maximum error in the predicted substrate heat input was 6.7%. Under varying substrate heat fluxes, the maximum radius prediction error was approximately 16% for the nickel substrate, while the corresponding maximum error remained below 20% for the alumina substrate. Comparable predictive performance was obtained for both substrate materials, demonstrating the applicability of the parameterized model under different operating conditions. The proposed method provides an efficient tool for rapid local evaporation assessment in radiation assisted porous evaporation and high heat flux thermal management systems.