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ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

# A volume averaging theory and its sub-control-volume model for analyzing heat and fluid flow within complex heat transfer equipment

Akira Nakayama
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561, Japan; School of Civil Engineering and Architecture, Wuhan Polytechnic University, Wuhan, Hubei 430023, China

Fujio Kuwahara
Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561 Japan

Atsuhiro Naoki
Dept. of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432 Japan

Guoliang Xu
Dept. of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432 Japan

DOI: 10.1615/IHTC12.4770
6 pages

## Аннотация

In this paper, a local volume-averaging theory has been introduced to derive a set of macroscopic governing equations, namely the two individual sets of continuity and momentum equations for hot and cold fluids and also the two individual energy equations for the two fluids and one energy equation for a solid structure. These macroscopic equations are coupled together with a macroscopic turbulence model to analyze flow and heat transfer within complex heat transfer equipment, consisting of small-scale heat exchanging surfaces. In order to close the set of these macroscopic equations, the idea of sub-control volume modeling has been proposed to account for heat and fluid flow around sub-scale elements such as fins, ribs and any other obstructions, which are too small to grid. Following a procedure similar to Nakayama and Kuwahara (2000), the permeability tensor, Forchheimer tensor and interfacial heat transfer coefficient needed in the macroscopic momentum and energy equations have been determined by conducting a series of numerical experiments, using the corresponding structural models of individual passage elements.

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