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Information × Registration Number 0217U001759, 0110U004791 , R & D reports Title Mathematical modeling of the thermal and mechanical fields during phase transitions of materials popup.stage_title Head Vladimir Yachmenyov, Registration Date 12-05-2017 Organization Sumy State University popup.description2 The object of study: differential equation with fractional derivatives, which describe the thermal conductivity processes in fractal media and materials with memory. The research method - analytical methods of the theory of differential equations in partial derivatives, methods of operational calculus. Aim of the study design and calculation methods of thermal fields in materials having a complex structure (in particular, thin films and nanomateriyah) given the presence in them of moving boundaries. Initially set and two minor problems have been solved: the problem of calculating thermal fields in a limited bar in the conditions of the anomalous thermal conductivity and the problem of calculating thermal fields in the composite semi-infinite rod. Both problems described by differential equations with fractional derivatives. In both cases, solutions are obtained in closed form. In conclusion, the work is formulated and delivered to the Stefan problem for the two-phase medium (that is, the problem with moving boundary) in the case of the anomalous thermal conductivity and the ways of its solution. PDR results can be used to create new materials with complex structures and design processes of their manufacture. Forward-looking assumptions concerning the further development of PDR - the solution of optimization problems for equations with fractional derivatives. Product Description popup.authors Клименко Володимир Андрійович Ніколенко Валентина Володимирівна popup.nrat_date 2020-04-02 Close