on correlating experimental pressure flow and heat transfer measurements from silicon microchannels...
TRANSCRIPT
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, [email protected]
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
Microchannels, Part 1: Channel Manufacture and Measurement”, Heat Transfer Engineering, 26(3):79-88, Taylor and Francis Inc.
• Eason, C., T. Dalton, C. O'Mathúna, O. Slattery, M. Davies, 2005. “Direct Comparison Between Five Different Microchannels, Part 2: Experimental Description and Flow Friction Measurement”, Heat Transfer Engineering, 26(3):89-98, Taylor and Francis Inc.
• Eason, Cormac, 2005, “Measurement of Pressure Drop and Heat Transfer Analysis of Microchannels”, PhD Thesis, University of Limerick, Ireland.
• Garimella, Suresh V., 2006, “Advances in mesoscale thermal management technologies for microelectronics”, Microelectronics Journal 37 (2006) 1165-1185
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• Muzychka, Y. S. and M. M. Yovanovich, 2004. “Laminar Forced Convection Heat Transfer in the Combined Entry Region of Non-Circular Ducts”, Journal of Heat Transfer, Transactions of the ASME, February 2004, Vol. 126, pp. 54-61.
• Rohsenow, W.M., J.P. Hartnett, E.N. Ganić, (ed.), 1985, Handbook of Heat Transfer Fundamentals, 2nd Edition, McGraw-Hill Book Company.
• Schmidt, F. W., presented in Shah, R. K. and A. L. London, 1978, “Laminar Flow Forced Convection in Ducts”, Academic, New York, 1978.
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• Tiselj, I; G. Hetsroni, B. Mavko, A. Mosyak, E. Pogrebnyak, Z. Segal, 2004, “Effect of axial conduction on the heat transfer in micro-channels”, International Journal of Heat and Mass Transfer 47 (2004) 2551-2565.