Genocchi operational matrix of the differentiation method for phase change process with size-dependent thermal conductivity and mass diffusivity

Abstract

The study of variable heat conductivity shows significant contribution in the fields of heat and mass transfer. When phase-change materials (PCMs) experience a temperature difference, they change their original state. This causes a change in thermal conductivity at each instant. In connection with this, the study of a phase change sublimation that accounts for size-dependent thermal conductivity and mass diffusivity is essential to optimizing the sublimation rate, which is still absent and being considered in this work. Modeling accounts for internal heat generation as a function of space and time. A time-dependent flux-type heat source drives sublimation. The Genocchi operational matrix of differentiation method is employed successfully to obtain the numerical results and verified with finite-difference method in the case of full model. The condition for the limitation of the sublimation is derived in the case of full model, and shown that sublimation can take place within the region under the sublimation curve. It is found that with an internal heat source, a greater rate of sublimation is achieved. Moreover, a sublimation model that accounts for fixed heat conductivity, convection, and an internal heat source has a faster sublimation rate than a sublimation model with size-dependent thermal conductivity and the standard sublimation model.