Theoretical study of non-linear heat conduction in multi-layer medium with phase transformation in the layers

The heat conduction is an important part of heat transfer processes in power engineering, civil engineering, chemical technologies, etc. Variety of researches is devoted to theoretical and experimental study of the heat transfer by the heat conduction. At present, the main attention is concentrated on the non-linear heat conduction when the material properties change with the temperature variation, and the outside conditions change with time. One of the reasons of non-linearity appearance is the phase transformation in the material due to its melting, or drying. The problems of modeling of such processes are also set up and solved in many works. However, the overwhelming majority of such works is related to single-layer materials but not to multi-layer once. Modeling of the heat conduction in a multi-layer medium with phase transformation in its separate layers requires additional investigation, which is the objective of the present paper. In order to solve the problem, the method of mathematical modeling is used. The model uses the mathematical tools of the theory of Markov chains. It is adapted to the case of multi-layer medium, the phase transformation can occur in separate parts of which. The heat transfer by heat conduction and heat processes during the phase transformation are described by the classical equations of heat balance. The numerical experiments were used to investigate the influence of parameters on the process behavior. A mathematical model that allows describing transient heat processes in a multi-layer medium with the possibility of phase transformation in its separate layers is developed. The results of heat process calculation for heating up the three-layer wall with the low-melt intermediate layer surrounded by high-melting layers are presented. The obtained results are consistent physically and validate workability of the model. The developed model of non-linear heat conduction in multi-layer medium with phase transformation in its layers can be successfully used to calculate various physicochemical processes in the layers: drying, freezing and defrosting, pyrolysis, and others.