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

[+] Author Affiliations
Krsto Sbutega, Ivan Catton

UCLA, Los Angeles, CA

Paper No. IMECE2013-65244, pp. V08CT09A031; 10 pages
doi:10.1115/IMECE2013-65244
From:
  • ASME 2013 International Mechanical Engineering Congress and Exposition
  • Volume 8C: Heat Transfer and Thermal Engineering
  • San Diego, California, USA, November 15–21, 2013
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5636-9
  • Copyright © 2013 by ASME

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.

Copyright © 2013 by ASME
Topics: Heat sinks

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