Modeling and optimization of properties of domestic mullite–corundum composites

Mathematical modeling of spectral-kinetic, thermal, and electrophysical characteristics, which are difficult to determine experimentally, has been carried out based on the available experimental data for a promising class of the latest high-temperature composite materials consisting of mullite–corundum fibers. The model based on the concept of a representative element makes it possible to take into account not only the structural regularities of the materials and the thermal and electrical properties of its constituents, but also the features (in particular, anisotropy) of radiation in their volume and a wide range of external conditions. After the model is adjusted to the experimental data (thermophysical or spectral), it is possible to calculate the necessary characteristics of materials as a whole and to study the physical processes in heterogeneous, highly porous structures on different spatial and temporal scales. In this study, the model was adjusted to the published results of a thermophysical experiment, which made it possible to determine over a wide temperature range the key parameters to take into account cooperative effects when the fragments of the material interact with electromagnetic radiation. New, important data on the thermal conductivity of materials and its conductive and radiative components, heat capacity, electrical resistivity, and dielectric permittivity have been obtained. A study on those external conditions that make experimentation substantially difficult has been carried out, and specific recommendations regarding the optimization of the properties of the materials are given. The results of the work clearly demonstrate the effectiveness of mathematical materials science as a tool that significantly expands the capabilities of experimental methods.