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

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

Based on the use of additional boundary conditions (characteristics) and the integral method of heat balance, a numerical and analytical solution of the heat conduction problem for an infinitely extended plate is obtained under symmetric boundary conditions of the third kind with constant internal heat sources in time. Considering the heat flux on the plate surface as a new sought function, a simple analytical form of the specified problem is obtained. Using the proposed approach is possible for solving partial differential equations that do not allow separation of variables.

Keywords: analytical solution, internal heat sources, non-stationary thermal conductivity, boundary value problem, boundary conditions of the third kind, additional function, integral of heat balance

Based on Dual-Phase-Lag theory a mathematical model of heat transfer in a rod was developed. During the derivation of the differential equation, the modified Fourier law was used. Analysis of the calculation results made it possible to determine the dependence of the optimal rod length on the intensity of heat transfer from its side surface.

Keywords: heat transfer intensification, third kind boundary conditions, temporal nonlocality, Dual-Phase-Lag theory, finite-difference method