On Correlating Experimental Pressure Flow And Heat Transfer

Measurements From Silicon Microchannels With Theoretical

Calculations

Cormac EasonNiall O’Keeffe Ryan Enright Tara Dalton

Stokes Research Institute,University of Limerick,Co. Limerick, Irelandcormac.eason@ul.ie

Causes Of Inconsistencies• Electric double layer

• Loss of the continuum assumption validity due to small length scales

• Fluid property changes along the channel

• Inherent difficulties in taking measurements from flows at microscale

• High uncertainties in results derived from experimental measurements

Micro Scale Friction Factors• Steinke and Kandlikar (2006) compiled 220 sets

of data for single phase flow in microchannels between 1 and 1200 µm in diameter and reported experimental data varying over approximately an order of magnitude around theoretical laminar flow values

• Garimella (2006) also plotted pressure flow data from microchannels from several researchers, showing the same trend of inconsistency in friction factors from paper to paper

Micro Scale Friction Factors

Steinke and KandlikarGarimella

Micro Scale Heat Transfer• Garimella (2006) plots a drastic variation in Reynolds

number Nusselt number correlations measured from microchannels over the past 15 years

• Bavière et al (2006) measured heat transfer from a parallel plate channel, accounting for variation in the channel surface temperature along the channel allowed the measured data to correlate with conventional heat transfer laws in laminar and turbulent regimes

• Numerical simulation of heat transfer has produced good correlation with experimental data in work by Lee and Garimella (2006), and Tiselj et al (2004), indicating that while standard correlations may not work, numerical simulation can correlate well with experimental data for specific test systems

Micro Scale Heat Transfer

Flow Loop Layout

Detail of Manifold Arrangement

Thermocouple Locations in Each Manifold

Experimental Ranges and Uncertainties

Percent Uncertainty

DRIE KOH

23 3.7

0.43 0.15

6.3 3.3

1 0.75

0.98 0.9

0.16 0.15

3.8 2.9

0.61 0.35

Channel Area Measurement

0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450 500 550 600 650x (micron)

y (m

icro

n)

Channel Dimensions

Dh (µm) A (µm)

DRIE 305.28 305.28

KOH 317.35 360.66

Theoretical Pressure Drop

Area Compensation

Eason (2005)

(Darcy’s Equation)

Friction Factors for Rectangular Channels

Rohsenhow (1985)

Trapezoidal Channel Correlation

Rohsenhow (1985)

Rectangular Channel Nu Correlations

These correlations are also used to predict the heat transfer from the inlet and exit manifolds allowing this effect to be subtracted from the experimental data

Schmidt (1985)

Muzychka and Yovanovich Correlation (2004)

Muzychka and Yovanovich Correlation

Manifold Entrance and Exit Losses

• Manifold friction losses are calculated using Darcy’s Equation as described earlier

• AM is the manifold flow area divided by the number of channels (22 for this work)

Rohsenhow (1985)

ResultsfRe Values for DRIE Channel

4

8

12

16

20

24

0 50 100 150 200 250Reynolds Number

fRe

Experimental fRe

Muzychka and Yovanovich fRe

Uncertainty for Muzychka and Yovanovich Data

Fully Developed fRe

ResultsfRe Values for Trapezoidal Channel

4

8

12

16

20

24

0 50 100 150 200 250 300 350Reynolds Number

fRe

Experimental fReMuzychka and Yovanovich fReUncertainty for Muzychka and Yovanovich DataFully Developed fRe

ResultsEffect of Manifold Heating on Data from DRIE Channels

-20

-10

0

10

20

30

40

0 50 100 150 200 250Reynolds Number

Nu

sse

lt N

um

be

r

Raw Nu Nu manifold effect (Muzy)Nu Manifold Effect (Schmidt) Theoretical Nu MuzyNu Schmidt

ResultsEffect of Manifold Heating on Data from DRIE Channels

0

1

2

3

4

5

6

0 50 100 150 200 250Reynolds Number

Nu

sse

lt N

um

be

r

Raw NuNu manifold effect (Muzy)Nu Manifold Effect (Schmidt)Theoretical Nu MuzyNu Schmidt

ResultsEffect of Manifold Heating on Data from Trapezoidal Channels

-60

-40

-20

0

20

40

60

0 50 100 150 200 250 300 350Reynolds Number

Nu

sse

lt N

um

be

r

Raw Nu Nu-Manifold (Muzy)

Nu-Manifold (Rohsenow) Theoretical Nu (Muzy)Theoretical Nu (Rohsenow)

ResultsEffect of Manifold Heating on Data from Trapezoidal Channels

0

2

4

6

8

10

0 50 100 150 200 250 300 350Reynolds Number

Nu

sse

lt N

um

be

r

Raw Nu Nu-Manifold (Muzy)

Nu-Manifold (Rohsenow) Theoretical Nu (Muzy)Theoretical Nu (Rohsenow)

ResultsCurve Fits For Data from Trapezoidal Channels

y = 0.0289x1.0009

R2 = 0.9997

0

2

4

6

8

10

0 50 100 150 200 250 300 350Reynolds Number

Nu

sse

lt N

um

be

r

Nu-Manifold (Muzy)Nu-Manifold (Rohsenow)Linear (Nu-Manifold (Rohsenow))Linear (Nu-Manifold (Muzy))Power (Nu-Manifold (Muzy))

y=0.0315x

R2=0.9976

y=0.029x

R2=0.9998

Suitable Correlations?

ResultsCorrelations for Experimental Data for Trapezoidal Channels

0

2

4

6

8

10

0 50 100 150 200 250 300 350Reynolds Number

Nu

sse

lt N

um

be

r

Nu - Manifold (Muzy) Nu - Manifold (Rohsenow)Theoretical Nu (Muzy) Theoretical Nu (Rohsenow)Seider and Tate ColburnChoi

ResultsCorrelations for Experimental Data for DRIE Channels

0

1

2

3

4

5

6

0 50 100 150 200 250Reynolds Number

Nus

selt

Num

ber

Nu - Manifold (Muzy) Nu - Manifold (Schmidt)

Theoretical Nu (Muzy) Theoretical Nu (Schmidt)

Seider and Tate Colburn

Choi

Conclusions• The fRe values from the system are less than predicted by both

developing and fully developed theory. Though the DRIE channel data does not show an experimentally significant deviation from theory, this deviation is still unexpected as previous pressure flow work on similar channels correlated extremely well with theory

• The limited depth of field of the optical microscope used in measuring the channels may have caused unforseen errors in measuring the channels compared to previous SEM measurements

• Accounting for the effect of manifold heating on the heat transfer from the channel is essential to the correct interpretation of the data from the system

• The Nusselt number measured for this work shows a strong linear dependence on the Reynolds number but is not matched very closely by available correlations

• Numerical simulation of the test system will be performed in order to conclude as to the validity of the Nusselt number data

Questions?

References• Bavière, Roland, Michel Favre-Marinet, Stéphane Le Person, 2006, “Bias effects on heat transfer measurements in

microchannel flows”, International Journal of Heat and Mass Transfer, 2006, Article in Press.• Bejan, A., 2000, Shape and Structure, From Engineering to Nature, Cambridge University Press, Cambridge, UK.• Çengel, Yunus A., 1998, Heat Transfer A Practical Approach, International Edition, WCB McGraw-Hill.• Choi, S.B.; R.F. Barron, R.O. Warrington, 1991, “Fluid flow and heat transfer in microtubes”, Micromech. Sensors Actuat.

Syst. ASME DSC 32 (1991) 123–134.• Eason, C., T. Dalton, C. O'Mathúna, O. Slattery, M. Davies, 2005. “Direct Comparison Between Five Different

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