Modeling of Thermal Conductivity in a Medium with Phase Transition with a Moving Boundary of Phase Change

Abstract

This work is devoted to the theoretical study of the effect of the phase interface motion on thermal conductivity in a liquid-solid nonlinear medium with a phase transition. The problem under consideration deals with the Stefan problems. Its most significant feature is the jump in the phase properties at separation of their moving boundaries. The objective was achieved by solving the following tasks: the construction of the process mathematical model based on its cell representation and with the use of the Markov chain theory mathematical apparatus, performing numerical experiments with the developed model, demonstrating its operability and the possibility to achieve the set goal. The most significant scientific results were as follows. First was an algorithm for the construction of a cell mathematical model of nonlinear thermal conductivity in a phase transitions medium with a moving phase interface for domains of a canonical shape (plane wall, cylinder, ball). Second, the results of the numerical experiments, showing that the jump of properties affected greatly the kinetics of the process. The significance of the results obtained consisted in the development of a simple but informative mathematical model of the media heat treatment kinetics with phase transformations, available for a direct use in the engineering practice. The proposed algorithm for constructing the model can be effectively used in prediction the open water pipes freezing in cold regions, in modeling the heat treatment of metals, in choosing the freezing modes of food products for a long-term storage, and other thermo-physical processes.