This article is cited in 1 paper

MECHANICS

Modeling of heat and mass transfer in the discontinuum approximation

S. I. Martynenko<sup>abc

a</sup> Joint Institute for High Temperatures of the Russian Academy of Sciences, ul. Izhorskaya, 13, Bd. 2, Moscow, 125412, Russia
^b Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry of the Russian Academy of Sciences, pr. Akademika Semenova, 1, Chernogolovka, Moscow region, 142432, Russia
^c Bauman Moscow State Technical University, ul. 2ya Baumanskaya, 5/1, Moscow, 105005, Russia

Abstract: The article presents a theoretical analysis of the governing equations expressing the fundamental conservation laws in the continuum and discontinuum approximations, and methods for solving problems of hydrodynamics as one of the most important subfields of continuum mechanics. This article is an attempt to more accurately describe physicochemical macro-processes. It is shown that the most suitable equations for computer modeling are the conservation laws under natural constraints on the minimum spatial and time scales, i.e., equations without partial derivatives and constraints on the solution smoothness. Using the continuity and thermal conductivity equations, a phenomenological method for constructing and numerically solving the governing equations is presented, and comparison with the traditional approach is given.

Keywords: continuum medium, Knudsen number, phenomenological approach, mathematical modeling, heat and mass transfer

UDC: 532.5.013

MSC: 76A02, 676D05, 76M12

Received: 24.12.2023
Accepted: 15.02.2024

DOI: 10.35634/vm240109

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