In this paper, a fractal model for nucleate pool boiling heat transfer is developed based on the fractal distribution of sites (areas) of nucleation sites on boiling surfaces. Algebraic expressions for the fractal dimension and area fraction of nucleation sites are derived, which are shown to be a strong function of wall superheat. The predicted fractal dimension is shown in good agreement with those determined by the box-counting method. The fractal model for nucleate boiling heat transfer is found to be a function of wall superheat, the contact angle of the fluid and the heater material, and physical properties of the fluid with a minimum number of empirical constants. The predicted total heat flux from a boiling surface based on the present fractal model is compared with existing experimental data. An excellent agreement between the model predictions and experimental data is found, which verifies the validity of the present fractal model.

Issue Section:
Evaporation, Boiling, and Condensation
Keywords:
fractals, boiling, heat transfer, contact angle, Boiling, Heat Transfer, Phase Change
Topics:
Boiling, Fractals, Heat flux, Heat transfer, Nucleate pool boiling, Nucleation (Physics), Dimensions, Cavities
1.
Dhir
,
V. K.
,
1991
, “
Review, Nucleate and Transition Boiling Heat Transfer Under Pool and External Flow Conditions
,”
Int. J. Heat Fluid Flow
,
12
(
4
), pp
290
–
313
.
2.
Mikic
,
B. B.
, and
Rohsenow
,
W. M.
,
1969
, “
A New Correlation of Pool Boiling Data Including the Effect of Heating Surface Characteristics
,”
J. Heat Transfer
,
91
, pp.
245
–
250
.
3.
Judd
,
R. L.
, and
Hwang
,
K. S.
,
1976
, “
A Comprehensive Model for Nucleate Pool Boiling Heat Transfer Including Microlayer Evaporation
,”
Int. J. Heat Mass Transf.
,
98
, pp.
623
–
629
.
4.
Ivery
,
H. J.
,
1967
, “
Relationship Between Bubble Frequency, Departure Diameter, and Rise Velocity in Nucleate Boiling
,”
Int. J. Heat Mass Transf.
,
10
, pp.
1023
–
1040
.
5.
Han
,
C. Y.
, and
Griffith
,
P.
,
1965
, “
The Mechanism of Heat Transfer in Nucleate Pool Boiling—Part I and II
,”
Int. J. Heat Mass Transf.
,
8
, pp.
887
–
913
.
6.
Benjamin
,
R.
, and
Balakrishnan
,
A. R.
,
1996
, “
Nucleate Pool Boiling Heat Transfer of Pure Liquids at Low to Moderate Heat Fluxes
,”
Int. J. Heat Mass Transf.
,
39
, pp.
2495
–
2504
.
7.
Torikai, K., Hori, M., Akiyama, M., Kobori, T., and Adachi, H., 1964, “Boiling Heat Transfer and Burn Out Mechanism in Boiling Water Cooled Reactor,” Third United Nations International Conference on the Peaceful Uses of Atomic Energy,” Paper No. 28/P580.
8.
Wang
,
C. H.
, and
Dhir
,
V. K.
,
1993
, “
Effect of Surface Wettability on Active Nucleation Site Density During Pool Boiling of Saturation Water
,”
J. Heat Transfer
,
115
, pp.
659
–
669
.
9.
Yu
,
B. M.
, and
Cheng
,
P.
,
2002
, “
Fractal Models for the Effective Thermal Conductivity of Bidispersed Porous Media
,”
AIAA J. Thermophysics and Heat Transfer
,
16
(
1
), pp.
22
–
29
.
10.
Mandelbrot, B. B., 1982, The Fractal Geometry of Nature, W. H. Freeman, New York.
11.
Feder, J., 1988, Fractals, Plenum Press, New York.
12.
Majumdar
,
A. A.
, and
Bhushan
,
B.
,
1990
, “
Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces
,”
ASME J. Tribol.
,
112
, pp.
205
–
216
.
13.
Majumdar
,
A.
,
1992
, “
Role of Fractal Geometry in the Study of Thermal Phenomena
,”
Annu. Rev. Heat Transfer
,
IV
, pp.
51
–
110
.
14.
Hsu
,
Y. Y.
,
1962
, “
On the Size Range of Active Nucleation Cavities on a Heating Surface
,”
J. Heat Transfer
,
84
, pp.
207
–
215
.
15.
Bankoff
,
S. B.
,
1958
, “
Entrapment of Gas in the Spreading of a Liquid over a Rough Surface
,”
AIChE J.
,
4
, pp.
24
–
26
.
16.
Van Stralen
,
S. J. D.
,
Sohal
,
M. S.
,
Cole
,
R.
, and
Sluyter
,
W. M.
,
1975
, “
Bubble Growth Rates in Pure and Binary Systems: Combined Effect of Relaxation and Evaporation Microlayers
,”
Int. J. Heat Mass Transf.
,
18
, pp.
453
–
467
.
17.
Yu
,
B. M.
, and
Li
,
J. H.
,
2001
, “
Some Fractal Characters of Porous Media
,”
Fractals
,
9
(
3
), pp.
365
–
372
.
18.
Paul
,
D. D.
, and
Abdel-Khalik
,
S. I,.
,
1983
, “
A Statistical Analysis of Saturated Nucleate Boiling Along a Heater Wire
,”
Int. J. Heat Mass Transf.
,
26
, pp.
509
–
519
.
Copyright © 2002
 by ASME
You do not currently have access to this content.