Methodology to determine coefficients of effective thermal conductivity when heating porous bodies using fractal-like structures

Thermal insulation, porous composite, ceramic, charge materials are frequently used in the energy industry. The materials are heat treated to improve the structure and give them the desired properties required for specific production conditions. The important task is to assess the influence of geometric parameters of the fractal-like structure and radiation heat transfer on the thermophysical properties of porous bodies. For numerical description of porous bodies, the technique of replacing geometry of porous body with the bodies with a fractal-like structure having self-similarity properties is significant. The object under study is an array of blanks arranged chaotically, the structures that are called bulk cages. The porous body is replaced by a fractal cube structure of the 2nd rank of partitioning. The simulation has been performed in the COMSOL Multiphysics software based on a three-dimensional model of the Sierpinski carpet. Since the distribution of heat can be non-uniformed over the structure of the object, three variants of the fractal-like cubic structure cross section are considered. A method to determine the effective thermal conductivity coefficients based on the use of fractal-like structures has been developed. Depending on the cross sections, one-dimensional computational models with sufficient accuracy for engineering analysis are obtained. The effective thermal conductivity coefficients are determined. The results of data analysis have shown that the geometric parameters of the structure and radiation heat transfer significantly affect the effective coefficient of thermal conductivity at high temperatures. In comparison to the currently available approaches, the developed method allows solving the problem of determining thermophysical properties without physical experiments. The technique used in the study may be used for mathematical modeling of heat exchange processes of heat-power facilities when calculating temperature fields and determining heating modes.