Influence of Bypass on Flow Through Plate Fin Heat Sinks

Transcription

1 Influence of Bypa on Flow Through Plate Fin Heat Sink Rakib Hoain, J. Richard Culham and M. Michael Yovanovich Microelectronic Heat Tranfer aboratory (MHT) Department of Mechanical and Mechatronic Engineering Univerity of Waterloo Waterloo, Ontario, Canada N 3G Correponding author: mrhoai@engmail.uwaterloo.ca Abtract Forced air convection cooling of plate fin heat ink i typically ued a an effective mean of cooling microelectronic device becaue of it inherent implicity and cot effectivene. While the increaed urface area obtained by placing plate fin heat ink in cloe proximity to one another can ignificantly reduce the boundary reitance becaue of the added urface area, the added preure drop aociated with a contrained flow can lead to a decreae in inter-fin flow velocity along with a decreae in heat tranfer. The ability to accurately predict the ditribution of fluid flow between the fin of a heat ink and the fluid flow bypaing the heat ink i critical in the deign and effective operation of heat ink ued to cool electronic component. An analytical model for predicting air flow and preure drop acro the heat ink i developed by applying conervation of ma and momentum over the bypa region and in the flow channel etablihed between the fin of the heat ink. The model i applicable for the entire laminar flow range and any type of bypa (ide, top or both) or fully hrouded configuration. During the development of the model, the flow i aumed to be teady, laminar, developing flow. The model i found in good agreement with the experimental data over a wide range of flow condition, heat ink geometrie and bypa configuration, typical of many application found in microelectronic and related field. Data publihed in the open literature are alo ued to how the flexibility of the model to imulate a variety of application. The model i alo correlated to a imple equation within ±% confidence level for eay calculation of channel velocity through the heat ink when heat ink geometry, duct geometry and flow condition are known. Keyword Bypa, Compact model, Correlation, Experiment, Forced convection, Plate Fin Heat Sink, Preure drop, Velocity. Nomenclature a Ratio of bypa area and ingle channel area A b Area of bypa [m ] A b Area of ide bypa [m ] A bt Area of top bypa [m ] A ch Frontal area of channel [m ] A ch Frontal area of one channel [m ] A d Area of duct [m ] Al Aluminium B Width of heat ink [m] CB Width of duct [m] CH Height of duct [m] D hb Side bypa hydraulic diameter [m] D hbt Top bypa hydraulic diameter [m] D hch Channel hydraulic diameter [m] f app Apparent friction factor for channel [ ] f appb Apparent friction factor for ide bypa [ ] f appbt Apparent friction factor for top bypa [ ] H Fin height [m] K c Contraction coefficient [ ] K e Expanion coefficient [ ] ength of heat ink [m] Dimenionle length [ ] Duct dimenionle length [ ] ch Channel dimenionle length [ ] b Side bypa dimenionle length [ ] bt Top bypa dimenionle length [ ] N Number of fin [ ] P Channel inlet preure [N/m ] P Channel outlet preure [N/m ] P c Channel contraction preure drop [N/m ] P e Channel expanion preure drop [N/m ] P f Channel frictional preure drop [N/m ] P G Plexigla Re b Reynold number of ide bypa [ ] Re bt Reynold number of top bypa [ ] Re ch Channel Reynold number [ ] Re d Duct Reynold number [ ] Fin pacing [m] t Fin thickne [m] t b Bae plate thickne [m] V b Bypa velocity [m/] V ch Channel velocity [m/] Duct velocity [m/] Greek Symbol α ch Channel apect ratio [ ] α b Side bypa apect ratio [ ] α bt Top bypa apect ratio [ ] µ Vicoity of air [kg/m ] ρ Denity of air [ kg/m 3] σ Fraction of frontal free flow area of channel [ ] P b Preure drop acro bypa region [N/m ] P b Preure drop acro ide bypa region [N/m ] P bt Preure drop acro top[bypa region [N/m ] P h Preure drop acro heat ink [N/m ] P d Duct perimeter [m] 7 IEEE 3rd IEEE SEMI-THERM Sympoium

2 P ch P b P bt P f Subcript app b b b bt c ch d e f h Channel perimeter [m] Perimeter of ide bypa [m] Perimeter of top bypa [m] Perimeter of fin baed on cro-ectional area of one fin [m] Apparent Bypa Side bypa One ide of bypa Top bypa Contraction Channel Duct Expanion Friction Heat ink. Introduction Plate fin heat ink are commonly ued to lower the operating temperature of electronic component thereby providing condition for reliable operation. Heat ink performance can be enhanced by increaing the convective heat tranfer coefficient ince the thermal conductance at the boundary i directly proportional to the product of the heat tranfer coefficient and the wetted urface area. In order to etimate the magnitude of the convective heat tranfer coefficient, it i neceary to have a thorough undertanding of the forced convection flow provided by a fan a it ditribute air through the parallel channel formed by plate fin and the baeplate a well a around the heat ink in the flow bypa region. Heat ink are typically attached to electronic component with ufficient clearance around the aembly to allow for free movement of an approaching air tream. A precie etimation of the air flow near the wetted region of the heat ink i often difficult becaue of the number of parameter influencing the ditribution of the air flow, including heat ink geometry, urrounding condition, approaching air flow velocity, thermal condition, etc. There are very few predictive model that allow for accuracy and eay of ue depite the importance of having a good undertanding of flow condition in order to obtain accurate thermal prediction. The purpoe of thi paper i to provide a implified model that allow for accurate etimation of flow condition in parallel plate heat ink with bypa, given relevant deign information uch a geometry, approach velocity and thermofluid propertie. The performance of heat ink ha been the focu of many invetigation in recent year, and the ubject ha been treated analytically, numerically, and experimentally. Mot of the work ha dealt with fully hrouded heat ink [-]; heat ink in ducted flow with tip [9-] or lateral clearance [] or both [7-] are alo addreed by ome reearcher. Deign of a heat ink with a clearance around it i achieved motly through experimental and numerical method, but both of thee method are time conuming and expenive for deigning an optimized heat ink. No complete analytical model for meauring the channel velocity of a heat ink with bypa i available for ue in an optimization procedure. ee [7], and Simon and Schmidt [] propoed a hydrodynamic model to predict the inter-fin velocity of a plate fin heat ink by applying ma and momentum balance between fin and bypa area by ignoring preure drop (large bypa approximation) in the bypa area that can prove to be ignificant for mall bypa clearance. They did not provide a model to etimate preure drop inide the heat ink. Moreover, their tudy doe not provide a clear undertanding of the flow phenomena around the heat ink, and therefore, doubt remain regarding the validity of the model. Butterbaugh and Kang [9] invetigated the effect of tip and lateral bypa on a heat ink with mall fin pacing uing compact modelling. Intead of balancing total energy (kinetic and preure) of the fluid, they only balanced the preure drop aociated with the heat ink and bypa area in their iterative procedure to calculate the channel velocity. The prediction of their flow model were within % of mot of their experimental data. Jonon and Mohfegh [] developed an empirical bypa correlation [Eq.] baed on experimental data to predict the preure drop not the channel velocity of a plate fin heat ink under variable bypa condition. The correlation ha an agreement of ± % with their experimental data, but the correlation i limited to a certain range of duct Reynold number, bypa to heat ink area ratio, fin pacing to height ratio and fin thickne to height ratio. Therefore, a compact model i needed to provide the neceary flow information for deigning a plate fin heat ink of optimal thermal performance.. Experiment An experimental program wa conducted to provide inight for the development of an analytical model and data for evaluating the ability of the model to accurately predict the hydraulic behavior of heat ink with bypa under a range of deign condition. The ample heat ink (Fig. ) of Table were ued during the experimental invetigation. y x z Figure : Geometry of a Plate Fin Heat Sink B t t b 3rd IEEE SEMI-THERM Sympoium N H

3 HS Mat. t b H B t N mm mm mm mm mm mm Al 9.. Al PG PG 9. 3 PG Table : Specification of Heat Sink. Setup and Procedure An experimental etup for meauring the preure drop characteritic of a plate heat ink wa deigned and aembled. The general layout of the wind tunnel i hown in Fig. and 3. The wind tunnel wa fabricated from Plexigla. The heat ink wa intalled at the center of the wind tunnel, and air flow wa drawn into the wind tunnel through a honeycomb. The honeycomb in the chamber wa ued to traighten the flow inide the tet ection. Bypa wa enured by adjuting the ide and top wall (Fig. ) to obtain the deired clearance ratio. The duct configuration of Table were ued during the experiment. with a Betz water manometer prior to the experiment. The maximum error of the preure tranducer, according to the manufacturer, i ±.% of the full cale reading. The ambient temperature in the tet ection wa monitored uing two T- type thermocouple mounted jut inide the inlet and exit of the wind tunnel. The pecified accuracy of the thermocouple i ±.3 C, however, when calibrating the thermocouple, an accuracy of le than ±. C wa oberved. A abview data acquiition interface wa ued to record the data collected by a Keithley 7 data logger. An average of reading for each data point were recorded in order to reduce the preciion error aociated with the experiment. Adjutable Side Wall Adjutable Top Wall t B CB Adjutable Side Wall H CH Honeycomb Nozzle or Flow meter Fan Figure : Front View of Wind Tunnel Configuration Heat Sink Preure Tap Figure : Top View of Wind Tunnel Configuration Honeycomb Nozzle or Flow meter Figure 3: Side View of Wind Tunnel Configuration Preure Tap Preure tap were mounted in variou location of the duct to meaure the preure drop around the heat ink and bypa area (Fig. ). Heat ink preure drop wa meaured uing two preure tap located on the floor of the wind tunnel along the heat ink center line, and they were poitioned mm uptream and downtream of the heat ink. The air wa driven by a fan and the flow rate wa controlled by the frequency regulation of a motor driving the fan. Flow rate correponding to duct velocitie,.,,., 3 m/ were ued during the experiment. Flow rate wa meaured from the nozzle (flow meter) intalled at the back of the wind tunnel. The preure drop wa meaured uing preure tap connected to Omega (Model-PX3) preure tranducer. Three different preure tranducer were ued with full cale reading of., and inche H O (.3, 9, 9 Pa repectively) depending on the prevailing preure drop. Tranducer were calibrated CB/B x. x CH/H...7. x.7 x x Table : Duct Configuration for Experiment (Fig. ). Uncertainty of Experiment When etimating the uncertainty in meaured and calculated quantitie, both bia and preciion error were conidered. Thee elemental error are combined to give an overall uncertainty in a meaured quantity uing the root-umquare method. Thi method i expreed mathematically in Eq. : u x = ± [ e bia + e ] preciion () where u x repreent the uncertainty in the meaured quantity x. The etimation of bia error (e bia ) i baed on the accuracy of the intrument [3], while the etimation of preciion error (e preciion ) i baed on the tatitical analyi of the data []. To minimize the preciion uncertainty of a meaurement, multiple reading were taken, typically on the order of. The experimental uncertaintie in T a, P a, ρ air and P were the reult of uncertaintie in the experimental meaurement of temperature, preure, flow rate and uncertaintie in the propertie of the tet fluid. The reult of that analyi i ummarized in Table 3. 3rd IEEE SEMI-THERM Sympoium

4 Uncertainty Parameter Minimum Maximum % % T a ±.9 ±. P a ±. ±. ρ air ±. ±.3 P h ±. ±.3 Table 3: Uncertaintie of Experimental Parameter 3. Model Development Model are developed to predict the channel velocity and preure drop of a plate fin heat ink for fully hrouded, top bypa only, ide bypa only, and both bypa baed on the following aumption: -D flow through the heat ink channel Channel apect ratio (α ch /H) of le than.7 aminar developing flow Negligible leakage from the top of the heat ink Uniform approach velocity Contant fluid propertie (ρ, µ) Negligible contraction and expanion lo in bypa area 3. Fully Shrouded Configuration For the fully hrouded configuration, A bt and A b of Fig. are zero. The frictional preure drop, P c inide the channel i expreed uing the Fanning friction coefficient (f app ) a: P f = f app ρ V ch D hch (7) Uing conervation of ma, the heat ink channel velocity, V ch i given by: V ch = () σ where, the area ratio, σ i defined a: σ = (9) + t For laminar hydrodynamically developing flow, the apparent friction factor, f app can be obtained from the following form of Churchill-Uagi correlation []: ( ) f app Re ch = 3. + (fre ch) () ch where f Re ch i the laminar fully developed friction factor. From the combined olution of the Navier-Stoke Equation for wall hear tre and control volume analyi for one dimenional momentum flux of an arbitrary rectangular duct, f Re ch i reduced to the following expreion []: f Re ch = + α ch () After ubtitution of f Re ch, Eq. become: ( ) ( ) f app Re ch = 3. + ch + α ch () A b A bt A b where ch = Re ch D hch α ch = H Figure : Arrangement of Bypa The preure drop acro a heat ink can be expreed a: The contraction preure drop, P c i : P h = P c + P f + P e () P c = K c ( ρ V d where the contraction lo coefficient, K c i correlated from the graph of Kay and ondon [] for laminar flow: ) (3) K c =. +. σ.39 σ () The expanion preure drop, P e i: ( ) P e = K e ρ V ch where the expanion lo coefficient, K e i correlated from the graph of Kay and ondon [] for laminar flow: () K e =.7 σ + σ () Re ch = ρ V chd hch µ D hch = A ch P ch a H 3. Top Bypa For a heat ink with top bypa, A b of Fig. i zero. From conervation of momentum inide the control volume of the heat ink and the bypa flow area, the flow relationhip for the heat ink and top bypa area i expreed a: V bt V ch = ( P h P bt ) ρ From conervation of ma, V bt i given by: (3) V bt = A d A ch V ch A bt () P h can obtained by uing Eq. to. For laminar developing flow, P bt can be expreed a: P bt = f app bt ρ V bt D hbt () 3rd IEEE SEMI-THERM Sympoium

5 f appbt i obtained uing the form of Eq. : ( ) ( ) f appbt Re bt = 3. + bt + α bt where bt = Re bt D hbt α bt = CH H B Re bt = ρ V btd hbt µ D hbt = A bt P bt A bt = B (CH H) P bt = [B + (CH H)] 3.3 Side Bypa For a heat ink with ide bypa, A bt of Fig. i zero. () Uing conervation of momentum inide the control volume of the heat ink and the bypa flow area, the flow relationhip for the heat ink and the ide bypa area i expreed a: V b V ch = ( P h P b ) ρ From conervation of ma, V b i given by: (7) V b = A d A ch V ch A b () P h can be obtained uing Eq. to. For laminar developing flow, P b can be expreed a: P b = f app b ρ V b D hb (9) f appb i obtained uing the form of Eq. : ( ) ( ) f appb Re b = 3. + b + α b where b = α b = Re b D hb (CB B)/ H Re b = ρ V bd hb µ D hb = A b P b A b = CB B H [ ] CB B P b = + H = (CB B) + H () 3. Top and Side Bypa For a heat ink with both top and ide bypa, both A bt and A b of Fig. exit. From Eq. 3 and 7, the following relationhip can be obtained: ( V bt + Vb ) V ch = P h ( P bt + P b ) () ρ Vb Vbt = ( P bt P b ) () ρ A bt V bt + A b V b = A b V b (3) A b V b = A d A ch V ch () A b = A d A h () A d = CB CH () A h = N t H + (N ) H (7) A ch = (N ) H () P h, P bt and P b are obtained from Eq., and 9. The value of V ch, V bt and V b can be obtained by the imultaneou olution of Eq. -,, and 9 uing mathematical oftware uch a Maple or Mathematica. 3. Correlation for Channel Velocity The olution for the model decribed above can be obtained uing a oftware imulation tool uch a Maple or Mathematica. An approximation of the full olution can be obtained uing a imple correlation that include all variable (geometrie, flow condition and fluid propertie). The correlation i well uited for the iterative procedure ued in the parametric optimization of heat ink. The following correlation (Eq. 9) i developed to calculate the channel velocity (V ch ) through the heat ink with flow bypa. ( ) + t [ V ch = ( a ).] (9) = Re d D hd Re d = ρ D hd µ CB CH D hd = (CB + CH) a = A b A ch A b = CB CH A ch = H When bypa area (A b ) become zero, Eq. 9 take the form of conervation of ma for a ingle channel of the fully hrouded model. ( ) + t V ch = 3rd IEEE SEMI-THERM Sympoium

6 Correlated value are found to be within ±% of the model data.. Reult and Dicuion The preure drop obtained from the model for variou duct configuration are compared with the experimental data of variou heat ink at duct velocitie of,.,,., and 3 m/. Figure, 7, compare the model with the experimental data of the ample heat ink for variou ide, top and combination of top and ide bypa configuration. The model and experimental data are in excellent agreement for variou duct velocitie with an RMS difference ranging from. to.%,. to 9.% and 3. to.% repectively. The data for the other heat ink ample are alo found in good agreement with the model. Experimental data of Butterbaugh and Kang [9] are alo compared with the model for their heat ink geometry and duct configuration. The reult of the model how good agreement with their experimental data with overall RMS error ranging from % to 9% (Fig. 9). Figure how the velocity ditribution (obtained from model) inide the heat ink of ample and bypa (top and ide) region for variou duct velocitie and one particular bypa arrangement, and found that with the increae of duct velocity, velocity through the heat ink channel increae. The plot alo how that preure drop correponding to the channel velocity obtained from the model i alo in good agreement with the experimental data. The influence of the clearance region on channel velocity obtained from the model are hown in Fig., and the correponding preure drop i found in good agreement with the experimental data. The RMS error varie between 3.9% and.%. P h (pa) CB=.B; CH=H: Model CB=.B; CH=H: Experiment CB=.B; CH=H: Model CB=.B; CH=H: Experiment CB=.7B; CH=H: Model CB=.7B; CH=H: Experiment CB=.B; CH=H: Model CB=.B; CH=H: Experiment Heat Sink - Sample Max. Min. % % RMS Error =.. Uncertainty of Expreiment = Figure : Validation of Side Bypa Model. Concluion Thi reearch work preent the development of an analytical model for fluid flow through a heat ink by applying P (pa) CB=B; CH=.H: Model CB=B; CH=.H: Experiment CB=B; CH=.H: Model CB=B; CH=.H: Experiment CB=B; CH=.7H: Model CB=B; CH=.7H: Experiment CB=B; CH=.H: Model CB=B; CH=.H: Experiment Heat Sink - Sample Max. Min. % % RMS Error = Uncertainty of Expreiment = Figure 7: Validation of Top Bypa Model P (pa) CB=.B; CH=.H: Model CB=.B; CH=.H: Experiment CB=.B; CH=.H: Model CB=.B; CH=.H: Experiment CB=.7B; CH=.7H: Model CB=.7B; CH=.7H: Experiment CB=.B; CH=.H: Model CB=.B; CH=.H: Experiment Heat Sink - Sample Max. Min. % % RMS Error = Uncertainty of Expreiment = Figure : Validation of Combined Top and Side Bypa Model a control volume analyi for ma and momentum balance between heat ink and bypa area in order to accurately predict the air flow through the heat ink. The control volume analyi incorporate the flow and frictional drag aociated with the heat ink and bypa area for laminar developing flow. The model wa validated with experimental data for preure drop and found to have an RMS error ranging from. to 9.%. The model wa later validated with the experimental data of Butterbugh and Kang [9] uing their heat ink and duct geometry, and the RMS difference wa found within 9%. Their experimental procedure were imilar to thi reearch tudy. A correlation for channel velocity wa built with repect to flow condition, heat ink and duct geometry, and the RMS error wa found ± % with repect to the model data. Acknowledgement The author gratefully acknowledge the financial upport of the Natural Science and Engineering Reearch Council 3rd IEEE SEMI-THERM Sympoium

7 P (Pa) Top and Side Bypa - Model Top and Side Bypa - Experiment Side Bypa - Model Side Bypa - Experiment Top Bypa - Model Top - Experiment 3 V ch Channel Velocity - Model Preure drop - Model 9. Preure drop - Experiment Clearance Ratio = (A d - A h )/ A h 7. P h (Pa) Figure 9: Validation of Model with The Experimental Data of Butterbaugh and Kang Figure : Influence of bypa on channel velocity (V ch ) V 3 Max. (%) Min. (%) V app - Model Uncertainty of P h.77. V ch - Model RMS Error of P h V bt - Model V b - Model P h - Model P h - Experiment Heat Sink - Sample Duct Configuration - CB = B and CH =. H.. 3 Figure : Velocity Ditribution in Heat Sink and Bypa Region (NSERC) of Canada for thi reearch. Reference. Goldberg, N., Narrow Channel Forced Heat Sink, IEEE Tranaction on Component, Hybrid, and Manufacturing Technology, Vol. CHMT-7, No., 9, pp Azar, K., Mceod, R.S., and Caron, R.E., Narrow Channel Heat Sink for Cooling of High Powered Electronic Component, Proceeding of the Eighth Annual IEEE Semiconductor Thermal Meaurement and Management Sympoium (SEMI- THERM VIII), Autin, TX, 99, pp Holahan, M.F., Kang, S.S., and Bar-Cohen, A., A Flow Stream Baed Analytical Model for Deign of Parallel Plate Heat Sink, ASME Proceeding of the 3 t National Heat Tranfer Conference (HTD-Vol. 39), Houton, TX, Vol. 7, 99, pp P h (pa). Copeland, D., Optimization of Parallel Plate Heat Sink for Forced Convection, Proceeding of the Sixteenth Annual IEEE Sympoium on Semiconductor Thermal Meaurement and Management (SEMI-THERM XVI), San Joe, CA,, pp Teerttra, P., Yovanovich, M.M., Culham, J.R., and emczyk, T., Analytical Forced Convection Modelling of Plate Fin Heat Sink, Proceeding of the Fifteenth Annual IEEE Sympoium on Semiconductor Thermal Meaurement and Management, San Diego, CA, 999, pp Saini, M., and Webb,.R., Validation of Model for Cooled Plane Fin Heat Sink Ued in Computer Cooling, Proceeding of the Eighth Interociety Conference on Thermal and Thermomechanical Phenomena in Electronic Sytem (I- THERM),, pp Naraimhan, S., and Bar-Cohen, A., Flow and Preure Field Characteritic in the Porou Block Compact Modelling of Parallel Plate Heat Sink, IEEE Tranaction on Component, Packaging and Manufacturing Technologie, Vol., No., 3, pp Knight, R.W., Goodling, J.S., and Gro, B.E., Optimum Thermal Deign of Cooled Forced Convection Finned Heat Sink- Experimental Verification, IEEE Tranaction on Component, Hybrid, and Manufacturing Technology, Vol., No., 99, pp ee, R.S., Huang, H.C., and Chen, W.Y., A Thermal Characteritic Study of Extruded-Type Heat Sink in Conidering Flow Bypa Phenomena, Proceeding of the Sixth Annual IEEE Sympoium on Semiconductor Thermal and Temperature Meaurement (SEMI-THERM VI), Phoenix, AZ, 99, pp Wirtz, R.A., Chen, W., and Zhou, R., Effect of Flow Bypa on the Performance of ongitudinal Fin Heat Sink, ASME Journal of Electronic Packaging, Vol., 99, pp. -. 3rd IEEE SEMI-THERM Sympoium

8 . Sparrow, E.M., and Beckley, T.J., Preure Drop Characteritic for a Shrouded ongitudinal Fin Array with and without Tip Clearance, ASME Journal of Heat Tranfer, Vol. 3, 9, pp au, K.S., and Mahajan, R.., Effect of Tip Clearance and Fin Denity on the Performance of Heat Sink for VSI Package, IEEE Tranaction on Component, Hybrid, and Manufacturing Technology, Vol., No., 99, pp eonard, W., Teerttra, P., and Culham, J.R., Characterization of Heat Sink Flow Bypa in Plate Fin Heat Sink, Proceeding of ASME International Mechanical Engineering Congre & Expoition (IMECE-39), New Orlean, ouiiana,.. Coetzer, C.B., and Vier, J.A., Compact Modeling of Forced Flow in ongitudinal Fin Heat Sink with Tip Bypa, ASME Journal of Electronic Packaging, Vol., 3, pp Min, J.Y., Jang, S.P., and Kim, S.J., Effect of Tip Clearance on the Cooling Performance of a Microchannel Heat Sink, International Journal of Heat and Ma Tranfer, Vol. 7,, pp Iwaaki, H., Saaki, T., and Ihizuka, M., Cooling Performance of Plate Fin for Multichip Module, IEEE Tranaction on Component, Packaging and Manufacturing Technology -Part A, Vol., No. 3, 99, pp ee, S., Optimum Deign and Selection of Heat Sink, IEEE Tranaction on Component, Packaging and Manufacturing Technologie, Vol., 99, pp Simon, R.E., and Schmidt, R.R., A Simple Method to Etimate Heat Sink Flow Bypa, Electronic Cooling, Vol.3, No., 997, pp Butterbaugh, M.A., and Kang, S.S., Effect of flow Bypa on the Performance of Heat Sink in Electronic Cooling, ASME Advance in Electronic Packaging, Vol. EEP--, 99, pp Jonon, H., and Mohfegh, B., Modeling of the Thermal and Hydraulic Performance of Plate Fin, Strip Fin, and Pin Fin Heat Sink- Influence of Flow Bypa, IEEE Tranaction on Component and Packaging Technologie, Vol., No.,, pp Moffat, R. J., Decribing the Uncertaintie in Experimental Reult, Experimental Thermal and Fluid Science, Vol., 9, pp Kay, W.M., and ondon, A.., Compact Heat Exchanger, New York: McGraw-Hill, Holman, J.P., Experimental Method for Engineer, New York: McGraw-Hill,.. Montgomery, D.C., Deign and Analyi of Experiment, New York: Wiley,.. Hoain, M.R., Optimization of a Plate Fin Heat Sink with Flow Bypa uing Entropy Generation Minimization, MASc Thei, Department of Mechanical Engineering, Univerity of Waterloo, Appendix A,, pp. -.. Churchil, S.W. and Uagi, R., A General Expreion for the Correlation of Rate of Tranfer and Other Phenomena, AIChE Journal, Vol., No., 97, pp. -. 3rd IEEE SEMI-THERM Sympoium