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THE USE OF VOLUME AVERAGING THEORY TO ADDRESS HEAT TRANSFER WITHIN ENGINEERED HETEROGENEOUS HIERARCHICAL STRUCTURES

DOI: 10.1615/ICHMT.2012.CHT-12.30
pages 19-50

Ivan Catton
Morin, Martinelli, Gier Memorial Heat Transfer Laboratory, Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science, University of California, Los Angeles, USA

Abstract

Optimization of Heat Sinks (HS) and Heat Exchangers (HE) by design of their basic structure is the focus of this work. Consistant models are developed to describe transport phenomena within the porous structure that take into account the scales and other characteristics of the medium morphology. Equation sets allowing for turbulence and two-temperature or two- concentration diffusion are obtained for non-isotropic porous media with interface exchange. The equations differ from known equations and were developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in the space of every pore. The transport equations are shown to have additional integral and differential terms. The description of the structural morphology determines the importance of these terms and the range of application of the closure schemes. A natural way to transfer from transport equations in a porous media with integral terms to differential equations with coefficients that can be experimentally or numerically evaluated and determined is described. The relationship between CFD, experiment and closure needed for the volume averaged equations is discussed. Mathematical models for modeling momentum and heat transport based on well established averaging theorems are developed. Use of a 'porous media' length scale is shown to be very beneficial in collapsing complex data onto a single curve yielding simple heat transfer and friction factor correlations. It was also found that properly defining and using the closure expressions leads to a heat transfer coefficient that is independant of the mode of heating and is constant even within the thermal development region.

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