Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Eremin A. V., Zinina S. A., Bragin D. M., Popov A. I. On a method for investigating heat transfer processes in porous media with ordered macrostructures. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2026, vol. 26, iss. 2, pp. 211-224. DOI: 10.18500/1816-9791-2026-26-2-211-224, EDN: NEJOCV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
01.06.2026
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
536.21
DOI: 
10.18500/1816-9791-2026-26-2-211-224
EDN: 
NEJOCV

On a method for investigating heat transfer processes in porous media with ordered macrostructures

Autors: 
Eremin Anton V., Samara State Technical University
Zinina Sofya Alekseevna, Samara State Technical University
Bragin Dmitry M., Samara State Technical University
Popov Andrey I., Samara State Technical University
Abstract: 

This paper proposes a mathematical modeling method for the heat conduction process in a porous medium with an ordered macrostructure. Based on the combined use of the minimal representative volume method and computational homogenization, a dependence of the effective thermal conductivity of the porous medium on the geometric characteristics (thickness, height) of the elementary cell — the unit structural element of the studied medium — is obtained. The elementary cell is considered as a triply periodic minimal surface (TPMS) of the Schwarz P type. The derived dependence for determining the values of the effective thermal conductivity coefficient was used in formulating the boundary value problem of heat conduction in a thin porous plate under first-kind boundary conditions. Using an approximate analytical method based on the introduction of additional boundary characteristics and a new unknown function, a simple analytical solution to the formulated problem was obtained. The analysis of the obtained solutions led to the conclusion that TPMS cells can be used for designing materials with specified thermophysical properties. In particular, it is shown that by adjusting the porosity of the plate, the intensity of heat transfer can be increased or decreased, and the required values of the plate’s thermal resistance can be achieved.

Key words: 
effective thermal conductivity
minimal surface
TPMS
Schwarz minimal surface (Schwarz P)
approximate analytical method
additional unknown function
additional boundary characteristics
heat flux
porosity
Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 23-79-10044, https://rscf.ru/project/23-79-10044/).
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Received: 
21.03.2025
Accepted: 
07.02.2026
Published: 
01.06.2026
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