A numerical study of solid–vapor phase conversion process with size-dependent thermal conductivity and variable boundary condition

Abstract

In this study, we present a mathematical model for a two phase sublimation process in a moving domain which involves the thermal conductivity as a function of size of the regions, mass density as a function of molar concentration and a boundary temperature as a function of time. Since analytical solution to this problem is not possible, therefore, we investigate the temperature movement and mass density by utilizing a boundary-fixing explicit finite difference approach. The stability and consistency of the numerical scheme are theoretically analyzed. A comparison between the obtained numerical results and exact solution for a specific case reveals that both results are nearly identical. It is observed that sublime particles need additional energy to break inter molecular bonds whenever thermal conductivity depends on the size of the domain, which slows down the conversion of solid particles into vapor phase. In this case, the heat flux coefficient (Formula presented.) and Peclet coefficient Pe can be utilized to accelerate the speed of sublimation process. The consequences of size depending nature of thermal conductivity are highlighted graphically. The outcomes from this analysis suggest some techniques to enhance the heat flow between sublime particles for phase transition with minimal energy absorption during sublimation process. © 2025 Taylor & Francis Group, LLC.