Numerical Solution to the Problem of Thermal Conductivity in a Porous Plate with a Topology of Triply Periodic Minimal Surfaces

Introduction. Thermal performance of materials based on triply periodic minimal surfaces (TPMS) is becoming increasingly important in view of the growing interest in materials with special thermophysical properties and their applications in engineering, energy, and other fields. Since these materials have unique structural and functional characteristics, understanding the relationship between their geometry and thermal parameters plays a key role in optimizing their use. Despite the considerable attention paid to the problem, the study of the relationship between the geometry of porous structures and their thermal characteristics remains incomplete. Existing scientific papers cover only individual options, and a complete understanding of the effect of complex micro- and macrostructure on thermal conductivity requires further study. The current gap in scientific knowledge is the lack of systematization and generalization of existing data, which complicates the development of universal approaches to calculating thermal conductivity in such materials. The objective of this study was to develop simplified formulas for calculating the effective thermal conductivity of porous structures based on S-type TPMC cells proposed by Fisher and Koch. The authors also set the task of analyzing the heat-conducting process in a plate with given porosity parameters. This will improve the understanding of the thermodynamic processes occurring in such systems. Materials and Methods . To achieve the stated objectives, mathematical modeling was performed, including the solution to the boundary value problem taking into account the identified correlations. A cellular structure made of PETG plastic and having pores consisting of identical repeating elements was considered. These elements formed a three-dimensional minimal surface that corresponded to the Fisher-Koch model. The analysis was performed using two methods: calculations in MathCAD based on the finite difference method, and modeling in ANSYS using the finite element method. In this case, the effect of the geometric parameters of the porous structure on its thermal characteristics was taken into account. Results. The research results represented a numerical solution to the thermal conductivity problem for a porous plate, taking into account the symmetrical boundary conditions of the first kind, and the presence of internal heat sources that remained constant in time and considered the topological features of the material. In the course of the study, temperature distributions were obtained, both in the spatial coordinate and in time. The change in heat flow depending on variations in the plate porosity coefficient was estimated. The graphs of isotherm distribution and their speed of movement were constructed and analyzed, which allowed for a deeper understanding of the heat transfer dynamics in the system under consideration. Discussion and Conclusion. The obtained mathematical dependences demonstrate the degree and nature of the effect of porosity on the distribution of heat flux density. It has been found that changes in the porosity of the plate can both increase and decrease the intensity of heat transfer, which provides reaching the required values ​​of thermal resistance of the material. The obtained results are consistent with the findings presented in other studies on similar topics, which opens up opportunities for their application in further research. These results can be useful in designing thermal protection systems for heat-generating equipment, as well as for heat and mass transfer paths of heat-mechanical equipment and other applications. The solutions are presented in an accessible and understandable form, which makes them easy to use for a wide range of researchers and engineers, and does not require expensive software or specialized computing equipment.