Online proceedings - EDA Publishing Association

24-26 September 2008, Rome, ItalyInitial attempts to achieve the goals set by MACE werewith constant diameter staggered pin fins. This was notsuccessful. Another parameter was introduced by allowing thepins to be tapered. The results are shown in Figs. 5 and 6,Figure 6. Pin Fin Geometry with pin tip diameter of0.958mm and pitch to pin base diameter of 2.0A Fin base ThicknessB Fin tip thicknessC Pitch/Fin base thicknessE Reynolds numberFigure 7. Model Term Ranking Pareto Chart For Plane Finsoutput from Fusion Pro. Figure 5 is a Pareto Diagram showingthe relative importance of the different parameters. Theparameter that is conspicuously absent is the base thickness. Itis only hwne it becomes very thin that it becomes important.Figure 6 is the trajectory of the temperature at the midplane ofthe heatsink (TMID), the temperature at the heatsink exit(TMAX) and the effectiveness as a function of pin basediameter and Reynolds number. These results were achievedwith a staggered array of pins having a pin base diameter of2.2mm, a pin tip diameter of 1.0mm and a pitch to pin basediameter of 2.0 at a Reynolds number of 43,000. This result isnot fully optimized because the author is not yet skilledenough at the use of DoE. It is, nevertheless, remarkable.A similar effort was made to design an optimum heatsinkusing plane fins. This was not as successful as for the pin fins.The Pareto Diagram. Fig. 7, shows that the first threeparameters are almost equal in importance making the searchfor an optimum even more difficult. An effectiveness of 15was achieved, however, with tip thickness of 0.1mm, pitch tobase diameter of 4.0 and base thickness of 1mm at a Reynoldsnumber ranging from 1150 to 2000, see Fig. 8. Note the strongdependence on the base diameter. The reason is the need formore metal to conduct heat to the fluid-solid interface as theheat transfer coefficient increases with increasing velocity.CONCLUSIONSA preliminary study of micro heat sink optimization wascarried out. The problem was kept manageable by assumingthe morphologies evaluated were relatively simple. The heatflux to the heat sink was assumed to be uniform.The design of a micro channel heat sink for 4 inch by 4inch base was optimized for a uniform 1000W heat load withtwo constraints; first, the midpoint of the base temperaturemust be below 65 0 C and the overall heat sink height is limitedto 1 inch. Statistical design of experiment was used to find theoptimum performance variables. The VAT governingequations were solved with the proper closure to describe fluidflow and heat transfer in micro channels in lieu of experiment.DOE is shown to be a useful tool in both achieving an optimaldesign and in determining the importance of the geometricparameters describing the micro channel.Table 1. Optimal DesignsStaggered Pin Fins Plane finsBase Dimension 2.2 mm 0.2 mmTip Dimension 1.0 mm 0.1 mmPitch/BaseDimension2.0 4.0Reynolds Number 41,000 1000EffectivenessQ/PP50 20Mass Flow 0.027CFM 57.40Pressure Drop -13300The major conclusion that can be drawn from this study isthat optimization is difficult to accomplish. With each value ofthe Reynolds number having a different "best geometry",©EDA Publishing/THERMINIC 2008 181ISBN: 978-2-35500-008-9