Formation of the first bubble at nucleation site is an inception of the two phase flow in pool boiling and flow boiling. Bubble dynamics (bubble nucleation, growth, and departure) plays an important role in heat transfer and pressure drop characteristics during two phase flow in microchannels. In this paper, a simplified model has been developed for predicting bubble growth rate at nucleation cavity in microchannel. It is assumed that heat supplied at nucleation site is divided between the liquid phase and the vapor phase as per instantaneous void fraction value. The energy consumed by the vapor phase is utilized in bubble growth and overcoming resistive effects; surface tension, inertia, shear, gravity, and change in momentum due to evaporation. Proposed model shows a good agreement with available experimental works. In addition, the bubble waiting time phenomenon for flow boiling is also addressed using proposed model. Waiting time predicted by the model is also close to that obtained from experimental data.

References

1.
Mudawar
,
I.
,
2001
, “
Assessment of High-Heat-Flux Thermal Management Schemes
,”
IEEE Trans. Compon. Packag. Technol.
,
24
, pp.
122
141
.10.1109/6144.926375
2.
Ali
,
R.
,
2010
, “
Phase Change Phenomena During Fluid Flow in Micro Channels
,” Ph.D. Thesis, Royal Institute of Technology, Stockholm, Sweden.
3.
Lee
,
J.
, and
Mudawar
,
I.
,
2008
, “
Fluid Flow and Heat Transfer Characteristics of Low Temperature Two-Phase Microchannel Heat Sink—Part 1: Experimental Methods and Flow Visualization Results
,”
Int. J. Heat Mass Transfer
,
51
, pp.
4315
4326
.10.1016/j.ijheatmasstransfer.2008.02.012
4.
Phillips
,
R. J.
,
1988
, “
Microchannels Heat Sinks
,”
Lincoln Lab. J.
,
1
, pp.
31
47
. Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.186.2572&rep=rep1&type=pdf
5.
Mudawar
,
I.
,
2011
, “
Two-Phase Microchannels Heat Sink: Theory, Application and Limitation
,”
ASME J. Electron. Packag.
,
133
, pp.
1
31
.10.1115/1.4005300
6.
Tuckerman
,
D. B.
, and
Pease
,
R. F. W.
,
1981
, “
High-Performance Heat Sinking For VLSI
,”
IEEE Electron Device Lett.
2
, pp.
126
129
.10.1109/EDL.1981.25367
7.
Kandlikar
,
S. G.
,
2005
, “
High Flux Heat Removal With Microchannels—A Roadmap of Challenges and Opportunities
,”
Heat Transfer Eng.
,
26
, pp.
5
14
.10.1080/01457630591003655
8.
Kandlikar
,
S. G.
, and
Grande
,
W. J.
,
2002
, “
Evolution of Microchannel Flow Passages––Thermohydraulic Performance and Fabrication Technology
,”
ASME International Mechanical Engineering Congress and Exposition
, Nov. 17–22, New Orleans, LA.
9.
Kosar
,
A.
,
Kuo
,
C. J.
, and
Peles
,
Y.
,
2005
, “
Boiling Heat Transfer in Rectangular Microchannels With Reentrant Cavities
,”
Int. J. Heat Mass Transfer
,
48
, pp.
4867
4886
.10.1016/j.ijheatmasstransfer.2005.06.003
10.
Lu
,
C. T.
, and
Pan
,
C.
,
2011
, “
Convective Boiling in a Parallel Microchannel Heat Sink With a Diverging Cross Section and Artificial Nucleation Sites
,”
Exp. Therm. Fluid Sci.
,
35
, pp.
810
815
.10.1016/j.expthermflusci.2010.08.018
11.
Sui
,
Y.
,
Lee
,
P. S.
, and
Teo
,
C. J.
,
2011
, “
An Experimental Study of Flow Friction and Heat Transfer in Wavy Microchannels With Rectangular Cross Section
,”
Int. J. Therm. Sci.
,
50
, pp.
2473
2482
.10.1016/j.ijthermalsci.2011.06.017
12.
Megahed
,
A.
,
2011
, “
Experimental Investigation Flow Boiling Characteristics in a Cross-Linked Microchannel Heat Sink
,”
Int. J. Multiphase Flow
,
37
, pp.
380
393
.10.1016/j.ijmultiphaseflow.2010.12.002
13.
Balasubramanian
,
K.
,
Lee
,
P. S.
,
Jin
,
L. W.
,
Chou
,
S. K.
,
Teo
,
C. J.
, and
Gao
,
S.
,
2011
, “
Experimental Investigations of Flow Boiling Heat Transfer and Pressure Drop in Straight and Expanding Microchannels—A Comparative Study
,”
Int. J. Therm. Sci.
,
50
, pp.
2413
2421
.10.1016/j.ijthermalsci.2011.07.007
14.
Kandlikar
,
S. G.
,
2002
, “
Fundamental Issues Related to Flow Boiling in Minichannels and Microchannels
,”
Exp. Therm. Fluid Sci.
,
26
, pp.
389
407
.10.1016/S0894-1777(02)00150-4
15.
Kandlikar
,
S. G.
,
2012
, “
History, Advances and Challenges in Liquid Flow and Flow Boiling Heat Transfer in Microchannels: A Critical Review
,”
ASME J. Heat Transfer
,
134
, pp.
1
15
.10.1115/1.4005126
16.
Kandlikar
,
S. G.
,
Colin
,
S.
,
Peles
,
P.
,
Garimella
,
S.
,
Pease
,
R. F.
,
Brandner
,
J. J.
, and
Tuckerman
,
D. B.
,
2012
, “
Heat Transfer in Microchannels—2012 Status and Research Needs
,”
ASME J. Heat Transfer
,
135
, pp.
1
18
.10.1115/1.4024354
17.
Hsu
,
Y. Y.
,
1962
, “
On the Size Range of Active Nucleation Cavities on a Heating Surface
,”
ASME J. Heat Transfer
,
84
, pp.
207
216
.10.1115/1.3684339
18.
Mukherjee
,
A.
,
Kandlikar
,
S. G.
, and
Edel
,
Z. J.
,
2011
, “
Numerical Study of Bubble Growth and Wall Heat Transfer During Flow Boiling in a Microchannels
,”
Int. J. Heat Mass Transfer
,
54
, pp.
3702
3718
.10.1016/j.ijheatmasstransfer.2011.01.030
19.
Davis
,
E. J.
, and
Anderson
,
G. H.
,
1966
, “
The Incipience of Nucleate Boiling in Forced Convection Flow
,”
AIChE J.
,
12
, pp.
774
780
.10.1002/aic.690120426
20.
Kandlikar
,
S. G.
, and
Spiesman
,
P. H.
,
1997
, “
Effect of Surface Characteristics on Flow Boiling Heat Transfer
,”
Paper Presented at the Engineering Foundation Conference on Convective and Pool Boiling
, May 18–25, Irsee, Germany.
21.
Liu
,
D.
,
Lee
,
P. S.
, and
Garimella
,
S. V.
,
2005
, “
Prediction of the Onset of Nucleate Boiling in Microchannels Flow
,”
Int. J. Heat Mass Transfer
,
48
, pp.
5134
5149
.10.1016/j.ijheatmasstransfer.2005.07.021
22.
Basu
,
N.
,
Warrier
,
G. R.
, and
Dhir
,
V. K.
,
2005
, “
Wall Heat Flux Partitioning During Subcooled Flow Boiling: Part I—Model Development
,”
ASME J. Heat Transfer
,
127
, pp.
131
140
.10.1115/1.1842784
23.
Basu
,
N.
,
Warrier
,
G. R.
, and
Dhir
,
V. K.
,
2005
, “
Wall Heat Flux Partitioning During Subcooled Flow Boiling: Part II—Model Validation
,”
ASME J. Heat Transfer
,
127
, pp.
141
148
.10.1115/1.1842785
24.
Yeoh
,
G. H.
,
Cheung
,
S. C. P.
,
Tu
,
J. Y.
, and
Ho
,
M. K. M.
,
2008
, “
Fundamental Consideration of Wall Heat Partition of Vertical Subcooled Boiling Flow
,”
Int. J. Heat Mass Transfer
,
51
, pp.
3840
3853
.10.1016/j.ijheatmasstransfer.2007.11.047
25.
Helden
,
W. G. J. V.
,
Geld
,
C. W. M. V. D.
, and
Boot
,
P. G. M.
,
1995
, “
Forces on Bubbles Growing and Detaching in Flow Along A Vertical Wall
,”
Int. J. Heat Mass Transfer
,
38
, pp.
2075
2088
.10.1016/0017-9310(94)00319-Q
26.
Zeng
,
L. Z.
,
Klausner
,
J. F.
,
Bernhard
,
D. M.
and
Mei
,
R.
,
1993
, “
A Unified Model for the Prediction of Bubble Detachment Diameters in Boiling Systems-II. Flow Boiling
,”
Int. J. Heat Mass Transfer
,
36
, pp.
2271
2279
.10.1016/S0017-9310(05)80112-7
27.
Yeoh
,
G. H.
, and
Tu
,
J. Y.
,
2005
, “
A Unified Model Considering Force Balances for Departing Vapor Bubbles and Population Balance in Subcooled Boiling Flow
,”
Nucl. Eng. Des.
,
235
, pp.
1251
1265
.10.1016/j.nucengdes.2005.02.015
28.
Qu
,
W.
, and
Mudawar
,
I.
,
2002
, “
Prediction and Measurement of Incipient Boiling Heat Flux in Micro-Channel Heat Sinks
,”
Int. J. Heat Mass Transfer
,
45
, pp.
3933
3945
.10.1016/S0017-9310(02)00106-0
29.
Kandlikar
,
S. G.
,
2001
, “
A Theoretical Model to Predict Pool Boiling CHF Incorporating Effects of Contact Angle and Orientation
,”
ASME J. Heat Transfer
,
123
, pp.
1071
1079
.10.1115/1.1409265
30.
Kandlikar
,
S. G.
,
2004
, “
Heat Transfer Mechanisms During Flow Boiling in Microchannels
,”
ASME J. Heat Transfer
,
126
, pp.
8
16
.10.1115/1.1643090
31.
Kandlikar
,
S. G.
,
2010
, “
Scale Effects on Flow Boiling Heat Transfer in Microchannels: A Fundamental Perspective
,”
Int. J. Therm. Sci.
,
49
, pp.
1073
1085
.10.1016/j.ijthermalsci.2009.12.016
32.
Kandlikar
,
S. G.
,
2010
, “
A Scale Analysis Based Theoretical Force Balance Model for Critical Heat Flux (CHF) During Saturated Flow Boiling in Microchannels and Minichannels
,”
ASME J. Heat Transfer
,
132
, pp.
1
13
.10.1115/1.4001124
33.
Mukherjee
,
A.
, and
Kandlikar
,
S. G.
,
2005
, “
Numerical Simulation of Growth of a Vapor Bubble During Flow Boiling of Water in a Microchannels
,”
Microfluid. Nanofluid.
,
1
, pp.
137
145
.10.1007/s10404-004-0021-8
34.
Thome
,
J. R.
,
Dupont
,
V.
, and
Jacobi
,
A. M.
,
2004
, “
Heat Transfer Model for Evaporation in Microchannels. Part I: Presentation of the Model
,”
Int. J. Heat Mass Transfer
,
47
, pp.
3375
3385
.10.1016/j.ijheatmasstransfer.2004.01.006
35.
Zhuan
,
R.
, and
Wang
,
W.
,
2010
, “
Simulation on Nucleate Boiling in Microchannel
,”
Int. J. Heat Mass Transfer
,
53
, pp.
502
512
.10.1016/j.ijheatmasstransfer.2009.08.019
36.
Wang
,
E. N.
,
Devasenathipathy
,
S.
,
Lin
,
H.
,
Hidrovo
,
C. H.
,
Santiago
,
J. G.
,
Goodson
,
K. E.
, and
Kenny
,
T. W.
,
2006
, “
A Hybrid Method for Bubble Geometry Reconstruction in Two-Phase Microchannels
,”
Exp. Fluids
,
40
, pp.
847
858
.10.1007/s00348-006-0123-z
37.
Gedupudi
,
S.
,
Zu
,
Y. Q.
,
Karayiannis
,
T. G.
,
Kenning
,
D. B. R.
, and
Yan
,
Y. Y.
,
2011
, “
Confined Bubble Growth During Flow Boiling in a Mini/Micro-Channel of Rectangular Cross-Section Part I: Experimental and 1-D Modeling
,”
Int. J. Therm. Sci.
,
50
, pp.
250
266
.10.1016/j.ijthermalsci.2010.09.001
38.
Plesset
,
M. S.
, and
Zwick
,
S. A.
,
1954
, “
Growth of Vapor Bubbles in Superheated Liquids
,”
Appl. Phys.
,
25
, pp.
493
500
.10.1063/1.1721668
39.
Forster
,
H. K.
, and
Zuber
,
N.
,
1954
, “
Growth of a Vapor Bubbles in Superheated Liquid
,”
Appl. Phys.
,
25
, pp.
474
478
.10.1063/1.1721664
40.
Plesset
,
M. S.
, and
Prosperetti
,
A.
,
1977
, “
Bubble Dynamics and Cavitation
,”
Ann. Rev. Fluid Mech.
,
9
, pp.
145
185
.10.1146/annurev.fl.09.010177.001045
41.
Fu
,
B. R.
, and
Pan
,
C.
,
2009
, “
Bubble Growth With Chemical Reactions in Microchannels
,”
Int. J. Heat Mass Transfer
,
52
, pp.
767
776
.10.1016/j.ijheatmasstransfer.2008.07.018
42.
Lee
,
J. Y.
,
Kim
M. H.
,
Kaviany
,
M.
, and
Son
,
S. Y.
,
2011
, “
Bubble Nucleation in Microchannels Flow Boiling Using Single Artificial Cavity
,”
Int. J. Heat Mass Transfer
,
54
, pp.
5139
5148
.10.1016/j.ijheatmasstransfer.2011.08.042
43.
Lee
,
P. C.
,
Tseng
,
F. G.
, and
Pan
,
C.
,
2004
, “
Bubble Dynamics in Microchannels. Part I: Single Microchannel
,”
Int. J. Heat Mass Transfer
,
47
, pp.
5575
5589
.10.1016/j.ijheatmasstransfer.2004.02.031
44.
Thome
,
J. R.
,
2004
,
Engineering Data Book III
,
Wolverine Tube, Inc.
,
Lausanne, Switzerland
.
45.
Hewitt
,
G. F.
,
1982
,
Measurement of Void Fraction-Handbook of Multiphase Systems
,
McGraw-Hill
,
New York
.
46.
Fletcher
,
N. H.
,
1959
, “
On Ice-Crystal Production by Aerosol Particles
,”
J. Meteorol.
,
16
, pp.
173
180
.10.1175/1520-0469(1959)016<0173:OICPBA>2.0.CO;2
48.
Kaun
,
W. K.
, and
Kandlikar
,
S. G.
,
2008
, “
Experimental Study and Model on Critical Heat Flux of Refrigerant-123 and Water in Microchannels
,”
ASME J. Heat Transfer
,
130
, pp.
1
5
.10.1115/1.2804936
49.
Xavier
,
C.
,
1993
,
Fortran 77 and Numerical Methods
,
New Age
,
New Delhi, India
.
50.
Shakir
,
S.
, and
Thome
,
J. R.
,
1986
, “
Boiling Nucleation of Mixtures on Smooth and Enhanced Surfaces
,”
8th International Heat Transfer Conference
, San Francisco, CA, Vol.
4
, pp.
2081
2086
.
51.
Jensen
,
M. J.
,
2002
, “
Bubbles in Microchannels
,” M.Sc. thesis, Technical University of Denmark, Kongens Lyngby, Denmark.
52.
Li
,
H. Y.
,
Tseng
,
F. G.
, and
Pan
,
C.
,
2004
, “
Bubble Dynamics in Microchannels. Part II: Two Parallel Microchannels
,”
Int. J. Heat Mass Transfer
,
47
, pp.
5591
5601
.10.1016/j.ijheatmasstransfer.2004.02.032
53.
Meder
,
S.
,
2007
, “
Study on Bubble Growth Rate in a Single Microchannel Heat Exchanger With High-Speed CMOS-Camera
,” M.S. thesis, Swiss Federal Institute of Technology Zurich and Stanford University, Stanford, CA.
54.
Griffith
,
P.
,
Clark
,
J. A.
, and
Rohsenow
,
W. M.
,
1958
, “
Void Volumes in Subcooled Boiling System
,” Technical Report No. 12, Massachusetts Institute of Technology, Cambridge, MA.
55.
Ahmadi
,
R.
,
Ueno
,
T.
, and
Okawa
,
T.
,
2012
, “
Bubble Dynamics at Boiling Incipience in Subcooled Upward Flow Boiling
,”
Int. J. Heat Mass Transfer
,
55
, pp.
488
497
.10.1016/j.ijheatmasstransfer.2011.09.050
56.
Fazel
,
S. A. A.
, and
Shafaee
,
S. B.
,
2010
, “
Bubble Dynamics for Nucleate Pool Boiling of Electrolyte Solutions
,”
ASME J. Heat Transfer
,
132
, pp.
1
7
.10.1115/1.4001315
57.
Li
,
J.
, and
Cheng
,
P.
,
2004
, “
Bubble Cavitation in a Microchannels
,”
Int. J. Heat Mass Transfer
,
47
, pp.
2689
2698
.10.1016/j.ijheatmasstransfer.2003.11.020
58.
Kandlikar
,
S. G.
,
2006
, “
Nucleation Characteristics and Stability Considerations During Flow Boiling in Microchannels
,”
Exp. Therm. Fluid Sci.
,
30
, pp.
441
447
.10.1016/j.expthermflusci.2005.10.001
59.
Kandlikar
,
S. G.
,
Garimella
,
S.
,
Li
,
D.
,
Colin
,
S.
, and
King
,
M. R.
,
2006
,
Heat Transfer and Fluid Flow in Minichannels and Microchannels
,
Elsevier
,
Oxford, UK
.
You do not currently have access to this content.