Objective. The purpose of the study is to develop a mathematical model for constructing a matrix of thermal conductivity coefficients under low-temperature exposure to the multilayer epidermis of biological tissue. Method. The research is based on methods of thermo dynamic analysis, full-scale and computational modeling of processes under low-temperature influence. Result. A mathematical model of the matrix of thermal conductivity coefficients under low-temperature effects on biological tissue has been developed. Heat transfer in a multilayer medium under low-temperature influence on biological tissue is presented as a process with a discrete step in time and coordinate. Thermal properties are evenly distributed throughout the volume of layers of biological tissue. For exposure to cold, layers of the epidermis of biological tissue were used, divided into uniform identical cells, where the cell area of the biological tissue was taken to be equal to one. Conclusion. The results obtained in this work can be useful to specialists who deal with modeling problems with free boundaries.
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