On Correlating Experimental Pressure
Flow And Heat Transfer Measurements
From Silicon Microchannels With
Theoretical Calculations
Cormac Eason Niall O’Keeffe Ryan Enright
Stokes Research Institute,
University of Limerick,
Co. Limerick, Ireland
cormac.eason@ul.ie
Tara Dalton
Causes Of Inconsistencies
•
•
Electric double layer
•
•
Fluid property changes along the channel
•
High uncertainties in results derived from
experimental measurements
Loss of the continuum assumption validity
due to small length scales
Inherent difficulties in taking
measurements from flows at microscale
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
Garimella
Steinke and Kandlikar
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
450
400
350
y (micron)
300
250
200
150
100
50
0
0
50
100 150 200 250 300 350 400 450 500 550 600 650
x (micron)
Channel Dimensions
DRIE
KOH
Dh (µm)
305.28
317.35
A (µm)
305.28
360.66
Theoretical Pressure Drop
(Darcy’s Equation)
Area Compensation
Eason (2005)
Friction Factors for Rectangular
Channels
Rohsenhow (1985)
Trapezoidal Channel
Correlation
Rohsenhow (1985)
Rectangular Channel Nu
Correlations
Schmidt (1985)
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
Muzychka and Yovanovich
Correlation (2004)
Muzychka and Yovanovich
Correlation
Manifold Entrance and Exit Losses
Rohsenhow (1985)
• 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)
Results
fRe Values for DRIE Channel
24
Experimental fRe
Muzychka and Yovanovich fRe
20
Uncertainty for Muzychka and Yovanovich Data
Fully Developed fRe
fRe
16
12
8
4
0
50
100
150
Reynolds Number
200
250
Results
fRe Values for Trapezoidal Channel
24
Experimental fRe
Muzychka and Yovanovich fRe
Uncertainty for Muzychka and Yovanovich Data
Fully Developed fRe
20
fRe
16
12
8
4
0
50
100
150
200
Reynolds Number
250
300
350
Results
Effect of Manifold Heating on Data from DRIE Channels
40
Raw Nu
Nu Manifold Effect (Schmidt)
Nu Schmidt
Nu manifold effect (Muzy)
Theoretical Nu Muzy
Nusselt Number
30
20
10
0
-10
-20
0
50
100
150
Reynolds Number
200
250
Results
Effect of Manifold Heating on Data from DRIE Channels
6
Nusselt Number
5
4
3
2
Raw Nu
Nu manifold effect (Muzy)
Nu Manifold Effect (Schmidt)
Theoretical Nu Muzy
Nu Schmidt
1
0
0
50
100
150
Reynolds Number
200
250
Results
Effect of Manifold Heating on Data from Trapezoidal Channels
60
Raw Nu
Nu-Manifold (Rohsenow)
Theoretical Nu (Rohsenow)
Nusselt Number
40
Nu-Manifold (Muzy)
Theoretical Nu (Muzy)
20
0
-20
-40
-60
0
50
100
150
200
Reynolds Number
250
300
350
Results
Effect of Manifold Heating on Data from Trapezoidal Channels
Raw Nu
Nu-Manifold (Rohsenow)
Theoretical Nu (Rohsenow)
Nusselt Number
10
Nu-Manifold (Muzy)
Theoretical Nu (Muzy)
8
6
4
2
0
0
50
100
150
200
Reynolds Number
250
300
350
Results
Curve Fits For Data from Trapezoidal Channels
Nu-Manifold (Muzy)
Nu-Manifold (Rohsenow)
Linear (Nu-Manifold (Rohsenow))
Linear (Nu-Manifold (Muzy))
Power (Nu-Manifold (Muzy))
Nusselt Number
10
8
y=0.0315x
R2=0.9976
y=0.029x
R2=0.9998
6
1.0009
y = 0.0289x
2
R = 0.9997
4
2
0
0
50
100
150
200
Reynolds Number
250
300
350
Suitable Correlations?
Results
Correlations for Experimental Data for Trapezoidal Channels
Nu - Manifold (Muzy)
Theoretical Nu (Muzy)
Seider and Tate
Choi
10
Nu - Manifold (Rohsenow)
Theoretical Nu (Rohsenow)
Colburn
Nusselt Number
8
6
4
2
0
0
50
100
150
200
Reynolds Number
250
300
350
Results
Correlations for Experimental Data for DRIE Channels
6
5
Nu - Manifold (Muzy)
Nu - Manifold (Schmidt)
Theoretical Nu (Muzy)
Theoretical Nu (Schmidt)
Seider and Tate
Colburn
Choi
Nusselt Number
4
3
2
1
0
0
50
100
150
Reynolds Number
200
250
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?
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References
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