This article presents the results of a study of the filtration flow in a porous material based on a thrice periodic minimum surface (TPMP) Neovius. The Brinkman model was used to determine the profile of the fluid flow velocity in the channel containing the TPMP insert. Based on computational experiments in ANSYS Fluent, the dependence of the permeability of the medium on its porosity is determined. The results of the study can be used to describe filtration processes in the oil and gas industry, hydrogeology and other fields related to filtration flows in rocks and other media.

Keywords: permeability, filtration, porous medium, minimum surface, TPMP, ANSYS, Brinkman model, numerical modeling, boundary value problem, velocity profile

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