Analytical Modeling of Forced Convection in Slotted Plate Fin Heat Sinks

Transcription

1 Analytical Modeling of Forced Convection in Slotted Plate Fin Heat Sinks P. Teertstra, J. R. Culham & M. M. Yovanovich Department of Mechanical Engineering Waterloo, Ontario, Canada Future Challenges in Electronic Packaging International ME 99 Congress and Exposition Nashville, TN Novemer 17, 1999

2 Introduction: Plate Fin Heat Sinks Heat transfer enhancement for air cooled applications: increase effective surface area decrease thermal resistance control operating temperatures Plate fin heat sinks: most common configuration convection in channels etween fins 1

3 Introduction: Slotted Fin Heat Sinks Enhanced thermal performance: new thermal oundary layers initiated at each fin section increase in average heat transfer coefficient decrease in surface area Performance of slotted fin heat sinks function of slot size and spacing Optimal slotted fin heat sink design alances enhancement of h with reduction of A 2

4 Introduction: Heat Sink Selection Heat sink selection depends on many factors: performance dimensional constraints availale airflow cost Quick and accurate design tools are required: predict performance early in design perform parametric studies alternative to numerical simulations, experiments 3

5 Ojectives Develop analytical models for average heat transfer rate for slotted fin heat sinks: laminar, forced convection flow full range of developing and fully-developed flow non-isothermal fins Perform experimental measurements to validate proposed models: range of slot sizes and spacing inline and staggered slot arrangement 4

6 Prolem Definition: Slotted Heat Sinks 5 Uniformly sized and spaced slots in fins fins slotted from tip to aseplate fin sections connected only y aseplate Slot size and spacing descried y dimensionless parameters: pitch, width, Slot arrangement: inline P S staggered L P ( 0 < P L 1) ( 0 S P < 1)

7 Prolem Definition: Plate Fin Heat Sink 6 Array of N plates on a single, flat aseplate Baseplate assumptions: fins in perfect thermal contact isothermal adiaatic lower surface, edges Uniform velocity in all channels with no ypass: shrouded heat sink with flow ypass model for un-shrouded heat sinks Heat sink modeled as N-1 parallel plate channels

8 Prolem Definition: Parallel Plate Channel 7 Assume << H 2D channel flow neglect aseplate, shroud effects Isothermal oundary conditions ynolds numer: U ν Nusselt numer: Q Nu, A 2 L H k A ( T T ) s a

9 Parallel Plate Channel Model Composite solution of 2 limiting cases (Teertstra et al, 1999) Fully Developed Flow Nu Pr 2 2 U L ν L fd Nu i n Nu + Nu fd n dev 1/ n 8 Developing Flow Nu dev Pr

10 Plate Fin Heat Sink Model Fin effects included in heat sink model: high aspect ratio heat sinks for power electronics dense arrays of tall, thin fins increased surface area for convection efficiency reduced Fin efficiency: η Nu Nu i Assume adiaatic condition at fin tip: η tanh m H ( m H ), m h P k A c, h Nu i k f 9

11 10 10 Plate Fin Heat Sink Model Plate Fin Heat Sink Model Model Summary ( ) i a s f T T A k N Q Nu η Pr Pr Nu + + i + + η 1 2 Nu 1 2 Nu tanh L t t H H k k L t t H H k k f i f i

12 Slotted Fin Heat Sink - Model Bounds Complex prolem where exact solution not possile Upper and lower ounds from plate fin heat sink model: 11

13 Slotted Fin Heat Sink - Lower Bound No new oundary layers formed Modeled using equivalent fin length: L LB L N S L 1 Lower ound expressions: LB 1 S P S Nu i ( S P) t L LB 1 t L S P η 12

14 Slotted Fin Heat Sink - Upper Bound New thermal oundary layer formed at each fin section with no upstream effects Modeled using equivalent fin length: L UB Upper ound expressions: t L UB ( P L)( S P) P S L 1 ( P L)( 1 S P) t ( P L)( S P) UB 1 L Nu η i 13

15 Experimental Apparatus High aspect ratio, H 20 Various slot configurations Back-to-ack arrangement Mounted in Plexiglas shroud Approach velocity measured with hot wire anemometer P L S P Slots inline inline inline inline staggered staggered Temperatures measured at 4 locations on aseplate Radiation losses measured in separate experiment 14

16 Experimental sults 15

17 Model Validation 16

18 Model Validation Arithmetic mean of ounds within 12% RMS of data Nu Nu LB + Nu 2 UB P S P L

19 Summary and Conclusions Models developed for upper and lower ounds for slotted fin heat sinks Experimental data within ounds for full range of test conditions Arithmetic mean of ounds predicts Nu 12% RMS over range of test conditions within liale optimization procedure cannot e determined from the limited range of S P values Additional study and data are required 18

20 Acknowledgements The authors gratefully acknowledge the continued financial support of R-Theta Inc. and Materials and Manufacturing Ontario. 19