RT Journal Article ID 1b2642a634c47393 A1 Sbutega, Krsto A1 Catton, Ivan T1 EFFICIENT HYDRAULIC AND THERMAL ANALYSIS OF HEAT SINKS USING VOLUME AVERAGING THEORY AND GALERKIN METHODS JF Multiphase Science and Technology JO MST YR 2013 FD 2014-07-08 VO 25 IS 2-4 SP 311 OP 338 K1 Galerkin method K1 volume averaging theory K1 pin-fin heat sink K1 micro-channel heat sink AB 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%. PB Begell House LK https://www.dl.begellhouse.com/journals/5af8c23d50e0a883,576264641be74a20,1b2642a634c47393.html