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Multiphase Science and Technology
SJR: 0.183 SNIP: 0.483 CiteScore™: 0.5

ISSN Imprimer: 0276-1459
ISSN En ligne: 1943-6181

Multiphase Science and Technology

DOI: 10.1615/MultScienTechn.v25.i2-4.120
pages 311-338

EFFICIENT HYDRAULIC AND THERMAL ANALYSIS OF HEAT SINKS USING VOLUME AVERAGING THEORY AND GALERKIN METHODS

Krsto Sbutega
University of California, Los Angeles, UCLA MAE, Box 951597, 48-121 E4, Los Angeles, California 90095-1597, USA
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

RÉSUMÉ

Air- and water-cooled heat sinks are still the most common heat rejection devices in electronics, making their geometric optimization a key issue in thermal management. Because of the complex geometry, the use of finite-difference, finite-volume, or finite-element methods for the solution of the governing equations becomes computationally expensive. In this work, volume averaging theory is applied to a general heat sink with periodic geometry to obtain a physically accurate, but geometrically simplified, system model. The governing energy and momentum equations are averaged over a representative elementary volume, and the result is a set of integro-partial differential equations. Closure coefficients are introduced, and their values are obtained from data available in the literature. The result of this process is a system of closed partial differential equations, defined on a simple geometry, which can be solved to obtain average velocities and temperatures in the system. The intrinsic smoothness of the solution and the simplified geometry allow the use of a modified Fourier−Galerkin Method for efficient solutions to the set of differential equations. Modified Fourier series are chosen as the basis functions because they satisfy the boundary conditions a priori and lead to a sparse system of linear equations for the coefficients. The validity of the method is tested by applying it to model the hydraulic and thermal behavior of an air-cooled pin-fin and a water-cooled micro-channel heat sink. The convergence was found to be O(N-3.443), while the runtime was ~0.25 s for N = 56. The numerical results were validated against the experimental results, and the agreement was excellent with an average error of ~4% and a maximum error of ~5%.


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