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ISSN Online: 2377-424X

ISBN Print: 978-1-56700-421-2

International Heat Transfer Conference 15
August, 10-15, 2014, Kyoto, Japan

Towards a General Spatial Averaging Procedure for Multi-Scale Flow Modeling in Heat Transfer Devices with Repetitive Fin Structures

Get access (open in a dialog) DOI: 10.1615/IHTC15.pmd.009108
pages 6899-6912

Résumé

This paper presents spatially averaged flow equations for computationally efficient simulation of the macroscale flow in heat transfer devices with repetitive fin structures. The weighted averaging technique of Quintard and Whitaker [1] is used in order to simplify the determination of the closure terms in the macro-scale flow equations. It is shown that an appropriate choice of the weighting function ensures that the closure terms are constant for periodically developed flow. Therefore they can be determined by solving a simple local closure problem on a unit cell of the periodic fin structure. Furthermore, it is proven that this local closure problem is fully equivalent to the periodically developed flow equations in which a constant pressure gradient over a fin unit is imposed. Finally, the macro-scale flow through an array of cylindrical fins is investigated as a case study. This case study illustrates the theoretical framework of the weighted spatial averaging technique and reveals the shortcomings of the volume averaging technique.