A stochastic phase transfer process including dual random moving domains and variable thermal properties

The free boundary phase transfer problems may involve stochastic nature due to uncertain material properties, random heat sources, etc. In practical scenarios, the majority of the phase transfer processes consist of fluctuations in thermal properties. The deterministic phase transfer models often fail to predict the behavior of phase transfer processes accurately. Thus, a comprehensive investigation is needed to precisely capture the stochastic behavior of phase transfer processes. We present a detailed study of a random Stefan problem with variable thermal conductivity and random heat source term. This study presents a collocation method based on the transformed form of Vieta Luca polynomials (VLPs) and Monte Carlo simulations to tackle the stochastic phase transfer problem with random dual moving interfaces. We have also extended the front-fixing method for the stochastic Stefan problem with dual moving interfaces. The accuracy of the aforementioned methods is validated through their applications in two illustrative examples: the solidification problem and the freeze-drying problem. We found that the deviations in the temperature flow and the moving interfaces decrease with an increasing number of Monte Carlo realizations, which shows that the solutions for the temperature flow and the position of the moving interfaces become more stable with an increasing number of sample size.