thermal and hydrodynamic analysis of the … and hydrodynamic analysis of the experimental results...

Thermal and Hydrodynamic Analysisof the Experimental Results with 13

Wolverine Cold Plates

November, 2013

Ecole Polytechnique Fédérale de Lausanne / EPFLLaboratoire de Transfert de Chaleur et de Masse / LTCM

Prof. John Richard ThomeDr. Jackson Braz Marcinichen

Contents1. Cold Plates Geometry2. System of Equations (Thermal Analysis)3. Instrumentation and General Assumptions4. Results (Nominal Geometry)5. Analysis of Results6. ME Code Validation7. Local wall HTC results (2D conduction scheme)8. System of Equations (Hydrodynamic analysis)9. Results10. Analysis of Results11. ME Code Validation12. Water versus EG-Water (50%)13. Extrapolation/Generalization of Adjusted Correlations14. Nusselt versus Pressure Drop 15. Ongoing Activities and Final Remarks

2WolverineNovember, 2013

1. Cold Plates Geometry

• Base thickness: 3 mm• Fin Height: 4 mm• Manufacturer inputs:


Sample 1 2 3 4 5 6 7

Material Copper

Fin type straight straight straight in-line in-line staggered staggered

Fin per inch 12 25 40 12 25 12 25

Sample 8 9 10 11 12 13 14

Material Aluminum


Fin per inch 12 25 40 12 25 12 25

1. Cold Plates Geometry• Optical microscope-photo camera measurements versus nominal values (the

latter were used for the analysis)


Sample 1 2 3 4 5 6 7

Material Copper


Number of channels 11 24 38 11 23 10 22

MeasuredHydraulic diameter [mm] 1.701 0.874 0.521 1.531 0.641 1.621 0.746

Fin width [mm] 1.078 0.528 0.370 1.200 0.707 1.349 0.689

NominalHydraulic diameter [mm] 1.709 0.905 0.601 1.709 0.939 1.835 0.976

Fin and channel width [mm] 1.087 0.510 0.325 1.087 0.532 1.190 0.556

Sample 8 9 10 11 12 13 14

Material Aluminum


Number of channels 11 24 ----- 10 23 10 22

MeasuredHydraulic diameter [mm] 1.975 0.799 ----- 1.531 0.710 1.177 0.614

Fin width [mm] 0.839 0.554 ----- 1.405 0.665 1.641 0.766

NominalHydraulic diameter [mm] 1.709 0.905 ----- 1.835 0.939 1.835 0.976

Fin and channel width [mm] 1.087 0.510 ----- 1.190 0.532 1.190 0.556

Measured values depicted in the table were determined from measuredchannel cross sectional area (frontal view) and channel height

2. System of Equations• Reynolds𝑅𝑅𝑅𝑅 = �̇�𝑚 𝐷𝐷ℎ

𝑁𝑁𝑐𝑐ℎ 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝜇𝜇, it was applied for the 3 types of fin (pin fins were

considered as straight channels and the dimensions were based on the frontal view). 𝐷𝐷ℎ = 4𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴

𝑃𝑃𝐴𝐴𝐴𝐴𝑃𝑃𝑚𝑚𝐴𝐴𝑃𝑃𝐴𝐴𝐴𝐴

• Wall heat transfer coefficient

5WolverineOctober, 2013

Iterative loop to determine the wall heattransfer coefficient (αw).

𝑞𝑞𝑤𝑤 =𝑞𝑞𝑓𝑓𝑃𝑃𝑓𝑓𝑀𝑀𝐸𝐸𝑤𝑤𝑃𝑃𝑤𝑤𝑃𝑃ℎ

𝑛𝑛𝑐𝑐ℎ𝐴𝐴𝑐𝑐𝑐𝑐𝐴𝐴𝑐𝑐 𝐶𝐶𝑤𝑤 + 2 𝐶𝐶ℎ 𝜂𝜂𝑓𝑓

𝜂𝜂𝑓𝑓 =tanh(𝑚𝑚 𝐶𝐶ℎ)

𝑚𝑚 𝐶𝐶ℎ𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑚𝑚2 = 2 𝛼𝛼𝑤𝑤

𝐹𝐹𝑤𝑤 + 𝑀𝑀𝐸𝐸𝑐𝑐𝐴𝐴𝑐𝑐𝑙𝑙𝑃𝑃ℎ𝜆𝜆𝐶𝐶𝐶𝐶 𝑜𝑜𝐴𝐴 𝐴𝐴𝑐𝑐 𝑀𝑀𝐸𝐸𝑐𝑐𝐴𝐴𝑐𝑐𝑙𝑙𝑃𝑃ℎ 𝐹𝐹𝑤𝑤

Assumptions: Twall = Tftp

qftp = qbottom of TIM2

𝜶𝜶𝒘𝒘 =𝒒𝒒𝒘𝒘 𝜶𝜶𝒇𝒇𝒇𝒇𝒇𝒇𝒒𝒒𝒇𝒇𝒇𝒇𝒇𝒇

𝑇𝑇𝑤𝑤 = 𝑇𝑇𝐴𝐴𝑎𝑎𝑙𝑙 𝑐𝑐𝑜𝑜𝑓𝑓𝑓𝑓𝐴𝐴𝐴𝐴 − 𝑞𝑞𝑓𝑓𝑃𝑃𝑓𝑓𝑇𝑇𝑤𝑇𝑇𝑇𝑇𝑇𝑇2𝜆𝜆𝑇𝑇𝑇𝑇𝑇𝑇2

+𝑇𝑇𝑤𝑏𝑏𝐴𝐴𝑏𝑏𝐴𝐴 𝑐𝑐𝑜𝑜𝑐𝑐𝑤𝑤 𝑓𝑓𝑐𝑐𝐴𝐴𝑃𝑃𝐴𝐴𝜆𝜆𝑏𝑏𝐴𝐴𝑏𝑏𝐴𝐴 𝑐𝑐𝑜𝑜𝑐𝑐𝑤𝑤 𝑓𝑓𝑐𝑐𝐴𝐴𝑃𝑃𝐴𝐴

𝛼𝛼𝑓𝑓𝑃𝑃𝑓𝑓 =𝑞𝑞𝑓𝑓𝑃𝑃𝑓𝑓

𝑇𝑇𝑤𝑤 − 𝑇𝑇𝑓𝑓𝑐𝑐𝐶𝐶𝑃𝑃𝑤𝑤

3. Instrumentation and General Assumptions• For the energy balance the temperatures at the inlet and outlet pipes wereconsidered (it is closer of a real application, i.e. if one considers anexperimental validation of the correlations in a real application and with acompletely assembled cold plate, the inlet and outlet pipes temperatures willbe measured / I’d like to say that will not be possible to access the headers).• The heat losses remained in the range from 0 to 10 % of the total inputelectrical power (dependent of the fluid’s temperature).• The average of 3 temperatures measured below of the TIM and 1Dconduction were considered.• TIM2: 79 µm thickness and39.5 W m-1K-1 of thermalconductivity.• Torque of 32 cN m on 4 bolts• Uniform heat flux on the bottomof TIM2 (30 W cm-2).• Inlet fluid temperature(5, 10, 20, 30 and 40 oC)• Mass flow rate: 30 to 100 kg h-1

(steps of 10 kg h-1)• λCu: 380 W m-1K-1, λAl: 237 W m-1K-1


3. Instrumentation and General Assumptions


Experimental Facility

Mass flow meter

Test Section

Pressure and differential

pressure transducers

Thermocouples



Test SectionCold Plate

Inlet and outletheaders and channel:

pressure and temperature

measurement

Cold Plate

Cover Plate

InletFlow

OutletFlow

Pressure and temperaturesensors

(along the channels,headersand piping)Cover Plate

Oring

Headers and channel

thermocouples

Headers

Along the channel



Test SectionHeater and TIM

Copper and thermocouples

Cover and Cold Plates assembled


The red highlights mean the correlations used for the comparisons presented in the next slides.

4. Results (Nominal Geometry)

All correlations showed a satisfactory R2.

𝑁𝑁𝑁𝑁𝑤𝑤𝐴𝐴𝑐𝑐𝑐𝑐 =𝑤𝑤𝑤𝐴𝐴𝑐𝑐𝑐𝑐 𝐷𝐷ℎ𝜆𝜆𝑓𝑓𝑐𝑐𝐶𝐶𝑃𝑃𝑤𝑤

𝑁𝑁𝑁𝑁𝑤𝑤𝐴𝐴𝑐𝑐𝑐𝑐 = 𝑎𝑎 𝑅𝑅𝑅𝑅𝑏𝑏𝑃𝑃𝑃𝑃𝑐𝑐

5. Analysis of Results• Sample 1 (manufacturing effect)

• Two “identical” samples (1 and 1extra) were experimentally tested• The two correlations obtained were evaluated for a range of Reynolds

from 100 to 1800 and Prandtl 5 and 11.


05

1015202530354045

0 500 1000 1500 2000

Nus

selt

[-]

Reynolds [-]

Nusselt: Manufacturing Effect

S1 (Pr = 5)

S1 (Pr = 11)

S1extra (Pr = 5)

S1extra (Pr = 11)

Maximum differenceobserved

When Pr = 5 4%

When Pr = 11 12%

5. Analysis of Results• Repeatability: Samples 9 and 11

• Range of Reynolds from 100 to 1800 and Prandtl 5 and 11.



When Pr = 5 4%

When Pr = 11 17%


When Pr = 5 3%

When Pr = 11 7%

02468

10121416

0 500 1000 1500 2000

Nus

selt

[-]

Reynolds [-]

Nusselt: Repeatability Effect (Sample 9)

Original (Pr = 5)

Original (Pr = 11)

Repeated (Pr = 5)

Repeated (Pr = 11)

extrapolation

0

10

20

30

40

50

0 500 1000 1500 2000

Nus

selt

[-]

Reynolds [-]

Nusselt: Repeatability Effect (Sample 11)

Original (Pr = 5)

Original (Pr = 11)

Repeated (Pr = 5)

Repeated (Pr = 11)

5. Analysis of Results• Flow direction effect: Sample 7

• Range of Reynolds from 100 to 1800 and Prandtl 5 and 11.


Potential reason:Pin fins clogging the flow in the outlet of cold plate (it isthe inlet when considering

inverted flow)

High difference when the results were extrapolated

and Pr = 11.About 35%.

0

10

20

30

40

50

60

0 500 1000 1500 2000

Nus

selt

[-]

Reynolds [-]

Nusselt: Flow Direction Effects (Sample 7)

Original (Pr = 5) Original (Pr = 11)Inverted (Pr = 5) Inverted (Pr = 11)

extrapolation

inlet

5. Analysis of Results• Material effect: Straight fin

• Range of Reynolds from 100 to 1800 and Prandtl 5.


Higher fin density results in lower Nusselt(due to the smaller hydraulic diameter). Higher Nusselt for Copper cold plates

5. Analysis of Results• Material effect: In-line pin fin



Higher Nusselt for Copper cold platesHigher fin density results in lower Nusselt(due to the smaller hydraulic diameter).

5. Analysis of Results• Material effect: Staggered pin fin



Higher Nusselt for Copper cold platesHigher fin density results in lower Nusselt(due to the smaller hydraulic diameter).

5. Analysis of Results• Material and fin type effects

• Range of Reynolds from 100 to 1800 and Prandtl 5.• Density of fin: 12 fpi


Higher Nusselt for staggered fin and lower for straight fin


• Range of Reynolds from 100 to 1800 and Prandtl 5.• Density of fin: 25 fpi


Higher Nusselt for staggered fin and lower for straight fin

6. ME Code Validation• Nuexperimental vs NuME_code (Muzychka and Yovanovich)

• Samples 1 and 1e (both copper)• Same geometry (straight fin, 11 channels)


15 20 25 30

15

20

25

30

Nusselt experimental

Nus

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In-house Simulation Code Validation

+20%

-20%

15 20 25 30 35

15

20

25

30

35


Nus

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+20%

-20%

Simulation code underpredicted the results at about 0 to 20 %

Sample 1 Sample 1e


• Sample 1 (Copper), and sample 8 (Aluminum)• Same geometry (straight fin, 11 channels)


15 20 25 30

15

20

25

30


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+20%

-20%

10 15 20 25 3010

15

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25

30


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+20%

-20%

Sample 1 Sample 8

Better prediction for Aluminum cold plate




Sample 2 Sample 9

Still underpredicted for copper cold plate (at about 0 to 10%)

8 10 12 14 16

8

10

12

14

16


Nus

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+20%

-20%

4 5 6 7 8 9 10 114

5

6

7

8

9

10

11


Nus

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+20%

-20%

Overpredicted for Aluminum cold plate


• Sample 9 (Aluminum). Repeatability test• Straight fin, 24 channels


Sample 9Sample 9

(repeated test)

4 5 6 7 8 9 10 114

5

6

7

8

9

10

11


Nus

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+20%

-20%

Results were reproduced.

4 5 6 7 8 9 10 114

5

6

7

8

9

10

11


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+20%

-20%


• Sample 9 (Aluminum). Results from ME code considering the measured geometry• Straight fin, 24 channels


Sample 9

When considering the measured dimensions the numericalresults are much closer of the experimental results

5 7 9 11 13 155

7

9

11

13

15


Nus

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num

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-20%

+20%

3 mm

3 mm1 mm


• Sample 3 (Copper).• Straight fin, 38 channels


Sample 3

For the 3 samples of copper (straight line: 1, 2 and 3) the code is underpredicting at about 0 to 20%.

5 6 7 8 9 10 115

6

7

8

9

10

11


Nus

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num

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+20%

-20%


• Sample 4 (Copper) and sample 11 (Aluminum).• In-line pin fin (samples 4 and 11 respectively considered as 10 and 11 microchannels)


Sample 4

As expected, the code underpredicted the values, since the correlation for straight fin was considered for in-line pin fin (the latter has higher thermal performance).

Sample 11

20 25 30 35 40 45

20

25

30

35

40

45


Nus

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+20%

-20%

15 20 25 30 3515

20

25

30

35


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+20%

-20%


• Sample 11 (Aluminum). Repeatability test• In-line pin fin


Sample 11

Satisfactory repeatability can be observed

Sample 11(repeated test)

15 20 25 30 3515

20

25

30

35


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+20%

-20%

15 20 25 30 35

15

20

25

30

35


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+20% -20%


• Sample 5 (Copper) and sample 12 (Aluminum).• In-line pin fin (samples 5 and 12 considered as 23 microchannels)


Sample 5

Copper cold plate: again, as expected, the results are underpredicted due to the correlation used (developed for straight line fin).

About Aluminum cold plate: see next slide for a general explanation.

Sample 12

10 15 20 2510

15

20

25


Nus

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+20%

-20%

6 8 10 12 14 16

6

8

10

12

14

16


Nus

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+20%

-20%

6. ME Code Validation• Aluminum versus copper behaviors (a general comment about previous results)


Analysing comparatively copper versus aluminum (viz. Slides 20, 21, 25 and 27 / see also miniaturized plots above) it is clear that the predictions for aluminum cold plate always show a «positive shift/bias» when compared with the predictions for copper cold plates and same geometry. Thus, it seems a natural tendency for the

results with aluminum code plate.

15 20 25 30

15

20

25

30


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+20%

-20%

10 15 20 25 3010

15

20

25

30


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+20%

-20%

8 10 12 14 16

8

10

12

14

16


Nus

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+20%

-20%

4 5 6 7 8 9 10 114

5

6

7

8

9

10

11


Nus

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+20%

-20%

20 25 30 35 40 45

20

25

30

35

40

45


Nus

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+20%

-20%

15 20 25 30 3515

20

25

30

35


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+20%

-20%

10 15 20 2510

15

20

25


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+20%

-20%

6 8 10 12 14 16

6

8

10

12

14

16


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+20%

-20%

Sample 1

Sample 8

Sample 2

Sample 9

Sample 4

Sample 11

Sample 5

Sample 12


• Sample 6 (Copper) and sample 13 (Aluminum).• Staggered pin fin (samples 6 and 13 considered as 10 microchannels)


Sample 6

As expected, underpredicted results for both cold plates. Also, as explained in the previous slide, aluminum cold plate predictions show a positive shift when

compared with copper cold plate predictions (i.e. closer of the line of -20%).

Sample 13

10 20 30 40 50 6010

20

30

40

50

60


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-20%

20 25 30 35 40 45 50

20

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40

45

50


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+20%

-20%




Sample 7

Same conclusions: i) underpredicted results for both cold plates, and ii) aluminum cold plate predictions show a positive shift when compared with copper cold plate predictions.

Sample 14

10 15 20 25

10

15

20

25


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-20%

+20%

10 15 20 25

10

15

20

25


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+20%

-20%


• Sample 7 (Copper). Flow direction effect.• Staggered pin fin (sample 7 considered as 22 microchannels)


Sample 7

As explained in the slide 11, for inverted flow the pin fins are clogging/obstructing the flow, thus justifying the lower values of Nusselt.

Sample 7 inverted

8 10 12 14 16 18 20

8

10

12

14

16

18

20


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+20% -20%

10 15 20 25

10

15

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-20%

+20%

Local Wall Heat Transfer Coefficient


Data Processing of Single-Phase Tests

7. Local wall HTC results(Samples 1,2,3,4,8,9,11)

• Inlet and outlet Pipes temperatures were used (headers with scattered signals and heat conduction “problems”)• 3 middle base temperatures were used: linearization for the extremes• Heat flux calculated based on the effective heat transferred to the coolant(thus, heat losses were considered)

• 5 inlet temperatures (5, 10, 20, 30, 40 °C) • 8 mass flow rates (30, 40, 50, 60, 70, 80, 90, 100 kg/h)• 7 test sections compared• A total of 5*7*8=280 local wall HTC curves were obtained.

• Comparison performed using the correlation of Muzychka and Yovanovich

• 3 types of graphs are plotted:

- Fixed Section and Temperature, different mass flow rates: 7*5=35 graphs- Fixed Section and Mass flow rate, different temperatures: 7*8=56 graphs- Fixed Mass flow rate and Temperature, different sections: 8*5=40 graphs

• Only a sample of the graphs are shown here

WolverineNovember, 2013 33

7. Local Wall HTC resultsm = 60 kg/h


Copper straight fin12 fpi

Aluminum straight fin12 fpi

7. Local Wall HTC resultsm = 60 kg/h




7. Local Wall HTC results

m = 60 kg/h



7. Local Wall HTC results

m = 60 kg/h


Copper in-line pin fin12 fpi

Aluminum in-line pin fin12 fpi

7. Local wall HTC resultsT = 20 °C






Copper in-line pin fin12 fpi

Aluminum in-line pin fin12 fpi

ALL SECTIONS ALL SECTIONS

ALL SECTIONS ALL SECTIONS


7. Local wall HTC results

7. Local wall HTC resultsOverall conclusions • The data processing to determine the local wall HTC (which considers only three base temperatures

and a linearization model for the extremes of the cold plate) gives satisfactory results in accordance with the mean wall HTC values determined through a 1D conduction scheme (i.e. same tendencies).

• The wall HTC increases considerably at the inlet of the cold plate when predicted by the correlation of Muzychka and Yovanovich. However, it is only observed in the same intensity with samples 1 and 2 for the current experimental setup and data processing.

• In general the trends are respected, i.e. wall HTC increases with temperature and mass flow rate.

• The comparisons (experimental versus predicted) can be considered satisfactory, with exception for samples 4 and 9. Respectively underpredicted and overpredicted by the correlation of Muzychka and Yovanovich.

• Additionally, even if the mean wall HTC experimentally determined for sample 11 looks satisfactory, the trends are not in accordance, i.e. experimental results show an increase in wall HTC towards the end of the sample for some conditions.

• Finally, in general the correlation of Muzychka and Yovanovich does not show significant effect of the kind of sample on the wall HTC profile (considering the same temperature and mass flow rate, viz. slide 42), which is not the case for the experimental results).


Hydrodynamic Analysis of Experimental Results with 13


November, 2013

Ecole Polytechnique Fédérale de Lausanne / EPFLLaboratoire de Transfert de Chaleur et de Masse / LTCM

Prof. John Richard ThomeDr. Jackson Braz Marcinichen

November, 2013

8. System of Equations• Darcy (Moody) friction factor𝑓𝑓 = 2 𝜌𝜌

𝐺𝐺2𝐷𝐷ℎ𝐿𝐿𝑐𝑐ℎ

∆𝑃𝑃 , it was applied for the 3 types of fin (pin fins were

considered as straight channels and the dimensions were based on the frontal view). 𝐷𝐷ℎ = 4𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴

𝑃𝑃𝐴𝐴𝐴𝐴𝑃𝑃𝑚𝑚𝐴𝐴𝑃𝑃𝐴𝐴𝐴𝐴

• The pressure drop (∆𝑃𝑃) along the microchannel was assumed as a linear extrapolation of the measured value, which was between the position 5 mm and 20 mm from the inlet of microchannels.


Known variables: P1, DP13 and DP34

Via extrapolation DP25 was determined

• Inlet fluid temperature: 5, 10, 20, 30 and 40 oC• Mass flow rate: 30 to 100 kg h-1 (steps of 10 kg h-1)• λCu: 380 W m-1K-1, λAl: 237 W m-1


9. Results (nominal geometry)

𝑓𝑓 = 𝑎𝑎 𝑅𝑅𝑅𝑅𝑏𝑏

10. Analysis of Results

• Coefficient of determination R2


The samples with lower values of R2 (1, 4, 8 and 11) were those with 12 fpi.

It is justified due to the low pressure drop

observed (less restrictedflow samples) and

consequently a nearlyuniform friction factor

with Reynolds. Thus, the results spreaded

specially for low values of Reynolds.

It was less relevant for samples 6 and 13 (both

with 12 fpi and staggered pin fin) since

the level of pressure drop was high.

400 600 800 1000 1200 14000

0.1

0.2

0.3

0.4

Reynolds, []

Fric

tion

fact

or, [

]

Microchannel friction factor (Sample 1)

ExperimentalAdjusted curve

f(x) = a*xb

a = 6.2632b = -0.61957R-squared = 0.86522

+10%

-10%

500 1000 15000.2

0.25

0.3

0.35

0.4

0.45

Reynolds, []

Fric

tion

fact

or, [

]



+10%

-10%

f(x) = a*xb

a = 1.1036b = -0.20617R-squared = 0.89133

500 1000 15000

0.05

0.1

0.15

0.2

0.25

Reynolds, []

Fric

tion

fact

or, [

]



-10%

f(x) = a*xb

a = 1.8183b = -0.46533R-squared = 0.83973

+10%

400 600 800 1000 1200 14000.2

0.25

0.3

0.35

0.4

0.45

Reynolds, []

Fric

tion

fact

or, [

]



+10%

f(x) = a*xb

a = 0.77978b = -0.14625R-squared = 0.86449

-10%



• Samples 6 and 13


500 1000 1500

0.4

0.5

0.6

0.7

Reynolds, []

Fric

tion

fact

or, [

]



f(x) = a*xb

a = 2.4207b = -0.26762R-squared = 0.98596

+10%

-10%

400 600 800 1000 1200 14000.4

0.6

0.8

1

1.2

1.4

Reynolds, []

Fric

tion

fact

or, [

]



-10%

+10%

f(x) = a*xb

a = 3.3126b = -0.22263R-squared = 0.91918

• In general the results of friction factor show lower values when Aluminum cold plates are considered.

• Exception: When comparing Copper with Aluminum cold plates but for staggeredpin fins and 12 fpi opposite effect was observed, i.e. higher friction factor for Aluminum (viz. samples 6 versus 13 ). Reason: Cu staggered pin fins visually

presents thinner pins.

6

6

13

13



• Samples 2, 3, 5, 7, 9, 12 and 14


200 300 400 500 600 7000

0.2

0.4

0.6

0.8

1

Reynolds, []

Fric

tion

fact

or, [

]



-10%

f(x) = a*xb

a = 100.0419b = -1.0343R-squared = 0.99865

+10%

100 200 300 400 5000

0.5

1

1.5

Reynolds, []

Fric

tion

fact

or, [

]Microchannel friction factor (Sample 3)


+10%

-10%

f(x) = a*xb

a = 74.4666b = -0.97889R-squared = 0.99535

200 300 400 500 600 7000.2

0.4

0.6

0.8

1

Reynolds, []

Fric

tion

fact

or, [

]



f(x) = a*xb

a = 7.5394b = -0.47124R-squared = 0.96867

+10%

-10%

200 400 600 8000.2

0.4

0.6

0.8

1

1.2

Reynolds, []

Fric

tion

fact

or, [

]



f(x) = a*xb

a = 7.607b = -0.45648R-squared = 0.95951

+10%

-10%

200 300 400 500 600 7000

0.2

0.4

0.6

0.8

Reynolds, []

Fric

tion

fact

or, [

]



+10%

-10%

f(x) = a*xb

a = 48.0457b = -0.9318R-squared = 0.99221

200 400 600 8000

0.2

0.4

0.6

0.8

Reynolds, []

Fric

tion

fact

or, [

]



+10%

-10%

f(x) = a*xb

a = 8.9191b = -0.60688R-squared = 0.96758

200 400 600 8000.2

0.4

0.6

0.8

1

1.2

Reynolds, []

Fric

tion

fact

or, [

]



+10%

-10%

f(x) = a*xb

a = 7.8398b = -0.43712R-squared = 0.96122

10. Analysis of Results• Material effect: Straight fin

• Range of Reynolds from 100 to 1800.


Higher fin density results in higher Friction Factor for low Reynolds (increase of

pressure drop is more significant than the reduction in channel diameter).

Negligible difference was observed between25 fpi and 40 fpi (potentially the effect of

increase in pressure drop is cancelled by the effect of reduction in channel diameter).

𝑓𝑓 = 2𝜌𝜌

𝑅𝑅𝑅𝑅2𝜇𝜇2𝐿𝐿𝐷𝐷3∆𝑃𝑃

Higher Friction Factor for Copper cold plates

10. Analysis of Results• Material effect: In-line pin fin



For 25 fpi, Aluminum with lowerFriction Factor

Higher fin density results in higher Friction Factor for lowReynolds (it is a dependent result of the competing

effects of hydraulic diameter and pressure drop).

For 12 fpi, Aluminum and Copper cold plates show similar results

(reason: viz. slide 4 samples 4 and 11, Aluminum has less «pseudo-

channels» than copper (10 versus 11)



10. Analysis of Results• Material effect: Staggered pin fin



It justifies the much higher Friction Factor for the Aluminum cold plate

For Copper and low ReynoldsHigher fin density results in higher Friction Factor

Al staggered pin fins are thicker thanCu staggered pin fins for 12 fpi.

For AluminumHigher fin density results in lower Friction Factor (effect of increase pressure drop higher than the

effect in reduction of hydraulic diameter)



competing effects of hydraulic diameter and

pressure drop.


• Range of Reynolds from 100 to 1800.• Density of fin: 12 fpi.


As expected, higher Friction Factor for staggered fin and

lower for straight fin.

Aluminum staggered fin shows higher Friction Factor than Copper staggered fin for 12 fpi due to differences in manufacture

(thicker pin fin)


• Range of Reynolds from 100 to 1800.• Density of fin: 25 fpi


As expected, higher Friction Factor for staggeredfin and lower for straight fin.

11. ME Code Validation• ∆Pexperimental versus ∆PME_code (Muzychka and Yovanovich) versus ∆Padjusted_correlation



ME code overpredicts the results of pressure drop

Sample 1 Sample 8

100 200 300 400 500 600

100

200

300

400

500

600

DP experimental [Pa]

DP

num

eric

al [P

a]

Pressure drop numerical versus experimental

ME codeAdjusted Correlation

+20%

-20%

100 200 300 400 500 600

100

200

300

400

500

600


DP

num

eric

al [P

a]



+20%

-20%

Higher range of pressure drop for Sample 1 (Copper)




ME code with results around the line of equalpressure drop (variation higher than ± 20%)

Sample 2 Sample 9

Similar range of pressure drop for both samples

200 400 600 800 1000200

400

600

800

1000


DP

num

eric

al [P

a]



+20%-20%

200 400 600 800 1000

200

400

600

800

1000


DP

num

eric

al [P

a]



-20%

+20%


• Sample 3 (Copper).• Straight fin, 38 channels


ME code underpredicts the results of pressure drop

Sample 3

500 1000 1500 2000

500

1000

1500

2000


DP

num

eric

al [P

a]Pressure drop numerical versus experimental


+20%

-20%


• Sample 4 (Copper) and sample 11 (Aluminum).• In-line pin fin (samples 4 and 11 respectively considered as 10 and 11 microchannels)


Sample 4 Sample 11

200 400 600

200

400

600


DP

num

eric

al [P

a]



-20%

+20%

100 200 300 400 500 600100

200

300

400

500

600


DP

num

eric

al [P

a]



+20%

-20%

ME code underpredicts the results of pressure drop(specially for pressure drop values higher than 400 Pa)

ME code correlation was not developed for in-line pin fins


• Sample 5 (Copper) and sample 12 (Aluminum).• In-line pin fin (samples 5 and 12 considered as 23 microchannels)


Sample 5 Sample 12

ME code underpredicts the results of pressure drop for sample 5

500 1000 1500 2000

500

1000

1500

2000


DP

num

eric

al [P

a]



+20%

-20%

200 400 600 800 1000200

400

600

800

1000


DP

num

eric

al [P

a]



+20%

-20%

ME code correlation was not developed for in-line pin fins




Sample 6 Sample 13

As expected, ME code underpredicts the results of pressure drop. Correlation wasdeveloped for noncircular straight channel, i.e. it was not for in-line or staggered pin fins

200 400 600 800

200

400

600

800


DP

num

eric

al [P

a]



+20%-20%

500 1000 1500

500

1000

1500


DP

num

eric

al [P

a]



+20%

-20%




Sample 7 Sample 14

Again, as expected, ME code underpredicts the results of pressure drop for cold plates with staggered pin fins

500 1000 1500 2000

500

1000

1500

2000


DP

num

eric

al [P

a]



+20% -20%

500 1000 1500 2000

500

1000

1500

2000


DP

num

eric

al [P

a]



+20% -20%

11. ME Code Validation

In summary:

1. ME code correlation (Muzychka and Yovanovich) underpredicted the results forsamples with in-line pin fin and staggered pin fin (as expected). Exception was sample12 (Aluminum in-line pin fin), which shows results between ± 20%.

2. For straight fins, copper and aluminum cold plates showed satisfactory results whenconsidering a fin density of 25 fpi and 40 fpi (samples 2,3 and 9). For a fin density of12 fpi (samples 1 and 8) the ME code correlation overpredicted the results.


12. Water versus EG-Water (50%)

• Range of Prandtl and Reynolds• Sample 1• Temperatures: 5, 10, 20, 30, and 40 oC• Mass flow rates: 30 to 100 kgh-1 with steps of 10 kgh-1


About 3.7 times higher when consideringwater as working fluid

About 4.6 times higher when consideringEG-Water (50%) as working fluid

12. Water versus EG-Water (50%)

• Overall impact on Nusselt and Friction Factor when considering the averagemultiplier for Reynolds and Prandtl (respectively 3.7-1 and 4.6) and theexperimentally adjusted correlations for Nusselt and Prandtl


As expected, lower values of Nusselt and higher values of friction factor when considering EG-Water (50%)

13. Extrapolation/Generalizationof Adjusted Correlations


Nusselt correlationsThe cold plates were separated in 6 groups which consider the same material and type of fin.

A general correlation was adjusted for each group considering an extra adimensional term thatrepresents the ratio between hydraulic diameter (Dh) and cold plate length (L)

(mathematical expression usually found in the literature).

𝑁𝑁𝑁𝑁𝑤𝑤𝐴𝐴𝑐𝑐𝑐𝑐 = 𝑎𝑎 𝑅𝑅𝑅𝑅𝑏𝑏𝑃𝑃𝑃𝑃𝑐𝑐𝐷𝐷ℎ𝐿𝐿

𝑤𝑤Correlation and coefficients to beimplemented in the simulation code

Correlations can be usedfor different channelheight and length (of

course, since a reasonableengineering coherence is

respected).



Height effect on NusseltSample 1 considering different heights (1000 mm to 6000mm steps of 1000mm)

Nucorrelation_Sample1 versus Nucorrelation_Group1 versus NuME_code (Muzychka and Yovanovich)

General inputs for simulations• Temperatura of 20 oC• Mass flow rate of 50 kgh-1

• Fluid: water• Heat flux of 30 Wcm-2

For extrapolations, it seems better to consider the correlationadjusted for the group of samples (here, it is the group 1).



Friction Factor correlation• An overall unified correlation was also developed considering the same extra adimensional

term considered for the Nusselt correlations, i.e. the ratio between hydraulic diameter (Dh) and cold plate length (L)

(mathematical expression usually found in the literature)

𝑓𝑓𝑐𝑐ℎ = 𝑎𝑎 𝑅𝑅𝑅𝑅𝑏𝑏𝐷𝐷ℎ𝐿𝐿

𝑐𝑐



Height effect on Pressure DropSample 2 considering different heights (1000 mm to 6000mm steps of 1000mm)

DPcorrelation_Sample2 versus DPcorrelation_overall versus DPME_code (Muzychka and Yovanovich)

General inputs for simulations• Temperature of 20 oC• Mass flow rate of 50 kgh-1

• Fluid: water• Heat flux of 30 Wcm-2

It seems that the overall adjusted correlation is able to follow quite well the behaviordepicted by the MEcode for about ±2 mm around the 4 mm fin heigth of sample 2.

14. Nusselt versus Pressure Drop


General inputs for simulations• Temperature of 20 oC• Reynolds range: 100 to 1800• Prandtl: 5

12 fpi 25 fpi

It is clear that staggered and in-line pin fin show the highestNusselt; however the highest pressure drop

15. Ongoing Activities and Final Remarks

• Implement correlations in the ME code.

• The nominal values of dimensions of the cold plates were used for allanalyzes, since it was judged that in a real application and manufacturingline, these values will be considered for the end users (it takes into accountpotential problems of manufacturability, as observed in the present work,viz. Slide 4).


thermal and hydrodynamic analysis of the … and hydrodynamic analysis of the experimental results...

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