Online proceedings - EDA Publishing Association

24-26 September 2008, Rome, ItalyMicro-Channel Heat Sink OptimizationIvan CattonMorrin-Martinelli-Gier Memorial Heat Transfer LaboratoryDepartment of Mechanical and Aerospace EngineeringSchool of Engineering and Applied ScienceUniversity of California, Los AngelesABSTRACTAn increasing demand for a higher heat flux removalcapability within a smaller volume for high power electronicsled us to focus on micro channels in contrast to the classicalheat fin design. A micro channel can have various shapes toenhance heat transfer, but the shape that will lead to a higherheat flux removal with a moderate pumping power needs to bedetermined. The micro channel geometries explored are pinfins (staggered) and parallel plates. The problem solved hereis a conjugate problem involving two heat transfermechanisms; 1) porous media effective conductivity and 2)internal convective heat transfer coefficient. VolumeAveraging Theory (VAT) is used to rigorously cast the pointwise conservation of energy, momentum and mass equationsinto a form that represents the thermal and hydraulicproperties of the micro channel (porous media) morphology.Using the resulting VAT based field equations, optimization ofa micro channel heated from one side is used to determine theoptimum micro channel morphology. A standard commercialsize and design is chosen for analysis and to demonstrate theutility of the VAT based process.NOMENCLATUREC d drag coefficient [--]H z fin height [m]P f fin pitch per fin thickness [--]Pr Prandtl number [--]R thermal resistance [ o K/W]Re Reynolds number [--]S w specific surface [m -1 ]T temperature [ o K]X L heat sink length [m]Y L heat sink width [m]b kinetic turbulent energy [m 2 /s 2 ]c p specific heat coefficient [J/kg K]d f sphere and pin fin diameter [m]f friction factor [--]m porosity [--]p pressure [Pa]t f fin thickness [m]t b heat sink base plate thickness [m]u velocity (x-dir.) [m/s]α heat transfer coefficient [W/m 2 K]ν viscosity [m 2 /s]ρ density [kg/m 3 ]( ) f fluid phase( ) p particle( ) por pore( ) s solid phase( ) sph sphere( ) T turbulentINTRODUCTIONDespite the crucial role of heat sinks in thermal managementof microelectronic microstructures and electronic parts ingeneral, there is still a great deal of empiricism in their design.Although current guidelines provide an ad-hoc solution totheir design, a unified approach based on simultaneousmodeling of thermal hydraulics and thermal-structuralbehavior has not been proposed beyond direct numericalsimulation and direct numerical simulation is too costly toconsider optimization of a design. As a consequence, designsare often overly constrained with a resulting economic penalty.In this work we will demonstrate a more scientific procedurefor the design and optimization of heat sink geometries.The method of modeling heat sinks that will be developedand used in this work is general and can be applied to any typeof heat sink. Its present use has been limited to heat sinksalthough the equations have been developed for much morecomplex configurations. Transport phenomena inheterogeneous hierarchical media includes many types ofproblems, only one of which is a heat sink.A majority of past investigations focus on solutions to aspecific optimization task with a very limited number ofspatial parameters being varied, usually a fixed geometricconfiguration that they tune in their search for a maximumlevel of heat exchange (see, for example, Bejan and Morega,1993). This approach is a "single-scale" approach yielding anoptimum for a certain morphology and flow intensity withoutgiving an explanation for why it was achieved. Without anexplanation, there is little guidance on how to change thedesign to improve its performance. For each new morphology,the experiment, whether experimental or numerical, needs tobe performed again. In the heat exchanger industry there arecountless research studies devoted to this problem.Travkin et al. (1994) used Volume Averaging Theory(VAT) to develop a mathematical basis and models foroptimization of a heterogeneous, hierarchical scaled media.The treatment of the optimization process can be applied to©EDA Publishing/THERMINIC 2008 177ISBN: 978-2-35500-008-9