NDLI: Application of Fourier-Galerkin Method to Volume Averaging Theory Based Model of Heat Sinks

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Application of Fourier-Galerkin Method to Volume Averaging Theory Based Model of Heat Sinks

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Sbutega, Krsto Catton, Ivan
Copyright Year	2013
Abstract	Efficient analysis of heat sink performance is a crucial step in the optimization process of such devices. Accurate analysis of these complex geometric systems with CFD and FE methods requires fine meshes, which imply significant computational time. In this study, Volume Averaging Theory (VAT) is rigorously applied to obtain a geometrically simplified but physically accurate model for any periodic heat sink geometry. The governing equations are averaged over a Representative Averaging Volume (REV) to obtain a set of integro-differential equations. Some information about lower level phenomena is lost in every averaging process and a closure scheme is required to model these behaviors. Experimental data for friction factor and Nusselt number in an REV is used to close the set of PDEs. This mathematical process replaces the complex geometry of the heat sink with a fictitious continuous medium and smoothens the quantities of interest throughout the system. These system features allow the use of a global Fourier-Galerkin method to efficiently solve the resulting equations and accurately predict the performance of the system. The effectiveness of the method is proven by applying it to model thermal behavior for laminar flow over an air-cooled pin-fin heat sink and a water-cooled micro-channel heat sink. The convergence in the Nusselt number in the case of constant heat flux is found to be quadratic with respect to the number of basis functions. The accuracy of the method is validated by comparing the numerical results obtained to existing experimental data. The maximum difference between the predicted Nusselt number and the experimental measurements is found to be only 4% for both cases.
File Format	PDF
ISBN	9780791856369
DOI	10.1115/IMECE2013-65244
Volume Number	Volume 8C: Heat Transfer and Thermal Engineering
Conference Proceedings	ASME 2013 International Mechanical Engineering Congress and Exposition
Language	English
Publisher Date	2013-11-15
Publisher Place	San Diego, California, USA
Access Restriction	Subscribed
Subject Keyword	Geometry Water Computational fluid dynamics Friction Laminar flow Heat sinks Heat flux Optimization Microchannels
Content Type	Text
Resource Type	Article

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