Mathematical model of the heat transfer process taking into account the consequences of nonlocality in structurally sensitive materials

Creation of new materials based on nanotechnology is an important direction of modern materials science development. Materials obtained using nanotechnology can possess unique physical-mechanical and thermophysical properties, allowing their effective use in structures exposed to high-intensity thermomechanical effects. An important step in creation and use of new materials is the construction of mathematical models to describe the behavior of these materials in a wide range of changes under external effects. The model of heat conduction of structural-sensitive materials is considered with regard to the medium nonlocality effects. The relations of the mathematical model include an integral term describing the spatial nonlocality of the medium. A difference scheme, which makes it possible to obtain a numerical solution of the problem of nonstationary heat conduction with regard to the influence of the medium nonlocality on space, has been developed. The influence of the model parameters on the temperature distributions is analyzed. (paper)