In this study, the thermal properties of porous materials with the topology of triply periodic minimal surfaces (TPMS) of Schwarz are investigated. By generalizing the results of computational experiments, the dependencies of the thermophysical properties of TPMS materials on macrostructural parameters such as size and thickness of the elementary cell have been obtained. The properties of the most common thermoplastic polymers PETG, ABS, PLA, and PHP used in additive manufacturing have been explored. It is demonstrated that the thermal conductivity coefficients of the examined TPMS materials can be represented as a linear function of the dimensionless geometric parameter – the relative thickness of the elementary cell wall. By varying this parameter, and consequently the geometric structure of the porous medium, it is possible to obtain a material with desired thermophysical properties. Verification of the obtained finite element method results is conducted based on the analysis of mesh convergence of solutions.

Keywords: effective thermal conductivity; heat transfer; porous material; porosity; thermoplastic polymer; ordered macrostructure; Schwarz minimal surface; triply periodic surface

In this paper, we study the process of heat conduction in a flat wall with an internal heat source under boundary conditions of the first kind. Various numerical and analytical methods are used to solve heat transfer problems. Each method has a number of advantages and disadvantages. The paper proposes to use the numerical method of finite differences. The original differential equation, as well as the boundary conditions, are approximated using a finite difference scheme. The essence of the method is to apply a spatiotemporal grid to the computational domain. For each grid node, a difference relation is written (the original differential equation with boundary conditions is replaced by the corresponding expressions obtained using the difference scheme). Solving this scheme, we obtain the temperature values ​​in the plate for each step in time and coordinate. On the basis of the solution obtained, graphical dependences of temperature on time and coordinates are constructed, and their analysis is carried out.

Keywords: finite difference method, thermal conductivity, plate, internal heat source, boundary conditions of the first kind

the presented work is devoted to the study of the temperature state of a fuel element (fuel element) – a cylindrical solid body with an internal heat source of constant power. Using the integral method of heat balance with the introduction of an additional desired function, an approximate analytical solution of the corresponding boundary value problem of thermal conductivity is obtained. The conditions of external heat transfer at the boundary of the studied region were set according to the Newton-Richman law (a boundary condition of the third kind). When obtaining the solution, trigonometric coordinate functions were used. Their use made it possible to reduce the number of terms in the desired solution due to the a priori fulfillment of the boundary condition in the center of the fuel element. It is shown that when using only three terms in the analytical solution (the first approximation), an accuracy sufficient for engineering applications is achieved. The error of the developed method was estimated by comparing the results obtained with a numerical solution based on the finite difference method. The article presents graphs of the temperature distribution at different power values of volumetric fuel element heat sources. The developed method can be used to determine the time of the system's exit to the stationary mode, estimate the maximum fuel element temperature at various values of the dimensionless Bio and Pomerantsev numbers, and determine temperature stresses.

Keywords: internal heat sources, boundary conditions of the third kind, additional desired function, heat balance integral, heat-generating element, approximate analytical solution, numerical solution, heat conduction problem, Bio number, Pomerantsev number