The existing shortcomings of the models for determining the thermal conductivity of composite materials with dispersed spherical inclusions raise the issue of creating more advanced calculation methods. This paper proposes a model for determining the thermal conductivity of composite materials, taking into account influence of thermal resistance at the material-inclusion boundary. The analysis of numerical and theoretical calculations showed that the analytical dependence is consistent with the results of numerical modelling for relatively small values of thermal conductivity of the filler and inclusion diameter. This paper considers several models that have been recently developed and that allow calculating thermal conductivity of such materials. They are compared with the model that takes into account influence of thermal resistance of the phase boundary. Applicability intervals of the considered model for various ratios of the thermal conductivity of inclusion material and matrix material are given.
The undoubted importance of these problems allows us to conclude that the research aimed at creating and using a simple model of the flow of a two-phase medium is relevant and of interest not only from a scientific, but also from a practical point of view. Two approaches to their description can be distinguished: the study of flows of two-phase media taking into account relaxation processes between phases with a microscopic description of the interaction between phases, or the study of flows of two-phase media with a macroscopic description of the medium in the form of a one-speed one-temperature continuum. However, sometimes, when calculating, it is possible to ignore the structural two-phase medium and consider the medium as a one-speed one-temperature continuum. This proposal allows us to calculate the averaged flow parameters of a two-phase medium, which is required for engineering calculations. In this paper, the calculation of the flow of the gas-drop flow in the Laval nozzle is given. The method is described, which is based on integral energy equations for two-phase dispersed currents. In the calculations, the two-phase flow is considered as a single-speed, single-temperature continuum. When modeling in the ANSYS Fluent software package, a package of Euler equations is used to compare with analytical results obtained from integral energy equations.
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