A lot of heat-shielding materials used in engineering have porous structure. When there is an intensive thermal exposure, there occurs a necessity to consider thermal energy transfer by means of radiation in pores of such materials. We contructed a mathematical model describing heat exchange by radiation in a spherical cavity. Its form can be considered as an average statistical form in relation to forms of closed pores in solid bodies. For the quantitative analysis of this model we used the method of the least squares and introduced an equivalent coefficient of thermal conductivity in the conditional continuous environment filling a pore. This allows to regard the material with porous structure as a continuous non-uniform solid body.
Zarubin V., Pugachev O., Savelyeva I. Application of the least squares method to the problem of radiation transfer in a spherical cavity. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 53-65
On the basis of mathematical model of thermal interaction between inclusion and the matrix we estimated influence of inclusions deviations from spherical shape on the effective thermal conductivity coefficient of the composite and associated with such deviation a possible occurrence of the anisotropy of the composite with respect to the property of thermal conductivity. Using the dual variational formulation of the stationary problem of heat conduction in an inhomogeneous body we built bilateral estimates of effective thermal conductivity.
Zarubin V., Kuvyrkin G., Savelyeva I. Effective thermal conductivity of a composite in case of inclusions shape deviations from spherical ones. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 3-17
The mechanical analog, allowing qualitatively and quantitatively describe the main features of inelastic deformation of the structural material at varying temperatures is presented. Analog is constructed using physical conceptions of polycrystalline structural material microstructures and the micromechanism of deformation process in combination with known provisions of the phenomenological theory of plasticity and creep. In the context of the particular modes of thermal and mechanical impacts on a heat-stressed structure this approach allows choosing a rational option of the structural material model adequately describing the most essential effects specific for the process of inelastic non-isothermal deformation. A variant of such a model under material singleaxis loading is developed and an example of its parameter numerical values selection is presented.
Zarubin V., Kuvyrkin G., Savelyeva I. Mechanical analog modeling of the inelastic non-isothermal deformation processes. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 25-38