Mathematical Model of Nonlocal Thermal Viscoelastic Medium. Part 2. Heat Equation

Modern structural and functional materials presenting an aggregate of micro-and nanostructured elements are named structure-sensitive materials. A general methodology for construction of mathematical models allowing the behavior of these materials to be described in a wide range of change in environmental exposure effects is still far from being complete. A mathematical model of heat conduction of structure-sensitive materials is considered which takes into account temporal effects during the heat accumulation and emission and while deforming. For deducing the heat equation, relationships of rational thermodynamics of irreversible processes with internal state parameters are used. The proposed equation of heat conduction with the assumptions relative to material structure opens broad possibilities of the detailed analysis of thermal deforming of materials in some practically important cases.

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