Geodesic
Numerical solution of the nonlinear problem of thermal conductivity in a porous plate with an ordered macrostructure
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2024), pp. 53-67

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In this paper, the process of thermal conductivity in a porous plate with an ordered macrostructure is investigated. The boundary value problem of heat transfer with symmetric boundary conditions of the first kind is considered, taking into account the dependence of the effective coefficient of thermal conductivity on temperature. When deriving the differential equation of heat transfer, the dependence of the thermophysical properties of the porous medium on the geometric characteristics of the elementary cells was also taken into account. The solution of the boundary value problem was obtained using widely used numerical methods (finite difference method, finite element method). The paper presents graphs of the distribution of temperature and heat flux density in a porous plate with an ordered macrostructure at various points of a spatial variable depending on the values of the porosity coefficient. The analysis of the influence of the geometric characteristics of a porous medium on the distribution of the desired functions is performed.
Keywords: ordered macrostructure, thrice periodic minimum surfaces (TPMS) Schwarz P, nonlinear thermal conductivity problem, finite difference method, finite element method, porosity, minimum representative volume method. 
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     author = {S. A. Zinina and A. I. Popov and A. V. Eremin},
     title = {Numerical solution of the nonlinear problem of thermal conductivity in a porous plate with an ordered macrostructure},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {53--67},
     publisher = {mathdoc},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2024_1_a3/}
}
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S. A. Zinina; A. I. Popov; A. V. Eremin. Numerical solution of the nonlinear problem of thermal conductivity in a porous plate with an ordered macrostructure. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2024), pp. 53-67. http://geodesic.mathdoc.fr/item/VTPMK_2024_1_a3/