1. CHAPTER4 Nucleate Boiling Heat Transfer
and Forced Convective Evaporation
Topics to be presented in this chapter
Onset of Nucleate Boiling
Subcooled Nucleate Boiling
Saturated Nucleate Boiling and Two-Phase Convective Heat Transfer

2. From: Collier, 1981

3. dz D Z Wf(kg/s) 4.1 Onset of Nucleate Boiling
Review of single-phase heat transfer
Energy balance dz D Z
Wf(kg/s)

4. Length of subcooled region, zsc
Let zsc be the entrance length where , zsc can be
determined by the following equation.

5. Wall temperature distribution in single-phase region
For turbulent flow in a pipe
Dittus-Boeiter correlation
However, it is commonly used in entrance region.

6. Boiling incipience (Onset of subcooled nucleate boiling)
For boiling to occur Tw must be at least ≧Tsat
Non-boiling region

7. Recall that, assuming that a wide range of cavity size available,
for the onset of nucleate boiling.
For water, the correlation of Bergles and Rohsenow’s correlation
maybe used:
For a tube with a constant heat flux, , a mass flux, G, the location
of boiling incipience may be evaluated in the following way:

8. For the criterion for the onset of nucleate boiling,

9. If water is used as the working fluid.

10. Relation between heat flux and wall
superheat at the position incipient
boiling (Form Hino & Ueda, 1985
Int. J. Multiphase Flow vol.11,
No.3, pp )

11. Boiling hysteresis
Partial subcooled nucleate boiling
Fully developed subcooled nucleate boiling
Single-phase liquid
Non-boiling region

12. Boiling curve hysteresis Wall temperature profiles
Form: Hino and Ueda, 1985, “Studies on Heat Transfer and Flow
Characteristics in Subcooled Flow Boiling – Part1, Boling
Characteristics,” Int. J. Multiphase Flow, vol.11, pp

13. Experimental data for the onset of boiling compared with eq.
(Forost and Dzakowic34) Form Collier, 1981

14. 4.2 Heat Transfer in Subcooled Nucleate Boiling
I. Partial subcooled boiling
i. Few nucleation sites
ii. Heat transferred by normal single-phase process
between patches of bubble + boiling
II. Fully developed subcooled boiling
i. Whole surface is covered by bubbles and their influence regions.
ii. Velocity and subcooling has little or no effect on
the surface temperature.

15. Partial subcooled boiling
heat transfer
Single-phase heat transfer

16. Rohsenow correlation

17. Values of Csf in eq. Obtained in the reduction of the forced
(and natural) convection subcooled boiling data of various investigators
(Form Collier, 1981)

18. ●
Wall temp
Full developed
Partial B C E

19. Bergles and Rohsenow correlation
Calculation procedure
Pick Tw
Evaluate and
Determine “C”, ie
form the incipience boiling model
Evaluate from fully-developed
equation but setting

20. Fully developed subcooled boiling
-Surface is covered by bubbles and their influence region

21. H H L L Low subcooling High subcooling H Low G L High G
-Velocity and subcooling has little or no effect on the surface temperature
Low subcooling
High subcooling
H Low G
L High G H H
Fully
developed
boiling L L

22. Correlations for fully developed subcooled boiling
-Jens and Lottes correlation(1951)
-Ranges of data for water only
i.d = 3.63 to 5.74 mm , P = 7 to 172 bar , Tl = 115 to 340℃
G = 11 to 1.05×10-4 kg/m2s , up to 12.5 MW/m2
-Thom et al (1965)
for water only

23. -Jens and Lottes correlation in terms of heat transfer coefficients

24. At P=70bar
At P=150bar

25. It is summarizes the present data of heat transfer of subcooled flow boiling of water in the swirl tube and hypervapotron under one side heating conditions. The data are obtained by experiments in regions fro non-boiling to highly subcooled partial flow boiling under conditions that surface heat fluxes, flow velocities, and local pressure range form 2 to 3 MW/m2, 4 to 16 m/s and 0.5, 1.9 and 1.5 MPa respectively. In the figure, a new heat transfer correlation for such subcooled partial flow boiling under one sides heating conditions on which no literature exists is proposed.
Heat transfer of subcooled water flowing in a swirl tube(Form: S.Toda, ”Advanced Researches of Thermal-Hydraulics under High Heat Load in Fusion Reactor,” Proc. NURETH-8. pp ,1997)

26. -Shah(1977), ASHRAE Trans. Vol.83, Part1, pp.202-217
-Valid for subcooled nucleated boiling of water,
refrigerants and organic fluids, Ref >10000

27. -Correlation of Bjorge, Hall and Rohsenow, 1982
Int. J. Heat Mass Transfer, vol.25, No.6 pp
For subcooled and low quality region
BM Depends upon boiling surface cavity size distribution
and fluids properties For water only, BM=1.89×10-4 in SI units.

28. For rc,min>rmax (the radius of largest cavity, rmax)

29. Comparison of equation with data of Cheng et al.
From: Bjorge, Hall and Rohsenow, 1982

30. 4.3 Saturated Forced Convective Boiling Evaporation
-The associated two-phase flow pattern may be bubby,
slug or annular flow
-Assumption of thermodynamic equilibrium is acceptable
-Heat transfer coefficient may be strongly dependent upon
the heat flux and the mass quality.
Quality change in saturated flow boiling

31. Saturated nucleate boiling Dryout B D 1 Superheated DNB Subcooled
Two-phase
forced-convective heat transfer
Dryout B D 1
Superheated
DNB
Subcooled
From: Collier & Thome, 1994

32. -Saturated nucleate boiling
-Essentially identical to that in the subcooled regions
with zero subcooling.
-Empirical correlation in fully developed subcooled
boiling may be used.
-Suppression of nucleate boiling in two-phase forced convection.
As will be discussed later, in two-phase forced convection
There is a possibility that ΔTsat(=q〞/hTP)
is so low that nucleate boiling will be suppressed.

33. Heat transfer in vertical annular flow
Ref.:Ch6 and 9 in Butterworth & Hewitt.
-When boiling is suppressed, heat transfer in two-phase
forced convection can be in a form of annular flow.
-Triangular Relationship
There are three dependent variables in vertical annular two-phase
flow. Any of them can be calculated from a knowledge of the other
two. The knowledge of these three variables are important for the
determination of heat transfer coefficient.

34. P For example, can be calculated from by the following procedure:
Evaluate the interfacial shear stress, τi
Force balance on the control volume gives ● ● ● ● ● ● ● ● ● ● P
Liquid film
Vapor flow

35. P dz (2) Calculate τ(r) Force balance on the control volume gives,
Vapor flow
Liquid film

36. (3) Calculate the velocity distribution in the film
by integration of the expression
(4) Integrate the velocity profile across the film to give

37. Interfacial waves in annular flow
-A rough rule of thumb:
“If the liquid film occupies 10% by volume of the channel
then the pressure drop increases by a factor of 10 for the same
total gas flow through the channel compared with the smooth
dry pipe. This gross increase is principally caused by the interfacial
waves.”
-Two distinct types of wave:
(1) Ripples-“Acts as a surface roughness and giving rise to an
increased pressure drop.”
-Do not result in droplet entrainment.
(2) Disturbance waves:(most of cases)
-Highly disturbed interface, several times the mean
film thickness in height.
-Entrainment occurs by the tearing away of film, which
beaks up from the surface of the waves.

38. u z y Transport of energy in the liquid film -Energy equation
Assumption
1.Steady state
2.Constant properties
3.Negligible axial conduction
4.Negligible viscous dissipation
5.The flow is one-dimensional
6.Because of the film is quite thin, the film may be treated as a slab. u z y

40. Defining the average bulk temperature as:
Laminar flow solutions
Assume (all the energy is used for evaporation)
and high interfacial shear
High shear stress with phase change is usually associated with
evaporation in up-ward flowing system.

42. The flow field is basically driven by the interfacial shear stress
(gravity is negligibly small)

43. Turbulent flow solutions
-If turbulent eddies are present within the film, the apparent
thermal conductivity and hence the heat transfer coefficient
significantly will be increased for a given film thickness.
-Assumption
(1)
(2) film surface is flat
(3) heat transfer is not affected by the droplets
-Model

44. εH = eddy thermal diffusivity
εM = eddy viscosity
εH ～εM has usually been assumed in theoretical
studies of heat transfer in liquid film.
Assume that εM is related to y in the film in the same way as in single-phase full-pipe flow.
For example
Deissler Model:

45. Von Karman Model:
Define the nondimensional temperature in the following way:

46. Recall that
Thus,

47. To solve T+, u+ needs to be calculated first. u+ depends on the shear
stress and film mass flow rate. Once u+ is determined, T+ can be
evaluated and h can be determined accordingly.
An approximate approach –following Butterwoth & Hewitt
Assume comparing to
as in a full-pipe flow and recall that

48. Assume universal velocity profile, i.e.,
u+=y+, y+ ≦ (viscous sublayer)
u+= ln(y+), 5<y+≦30 (buffer zone)
u+= ln(y+), y+ > (turbulent cure)
a discontinuity at y+ = 30
-Temperature distribution

49. Viscous sublayer 5
Applying the B.C. at y+ = δ+

50. 5 30

51. At y+=5, temperature evaluated from the buffer zone must be equal to
that from the viscous sublayer.
Recall that for the viscous sublayer or

52. For the turbulent core region
Recall that
for the viscous sublayer,
for the butter zone
so, the continuity of temperature at y+ = 5 results in

53. So, for the buffer zone
The continuity of temperature at y+ = 30 results in

54. Viscous sublayer
Buffer zone
Turbulent region

55. This is the Martinelli universal temperature profile.
Note that
U = average liquid flow rate assuming full pipe flow

56. Note that

57. 4.4 Estimation Methods for Forced Convective Boiling
Ref.: Collier & Thom, 1994 ]
The two-phase forced convection is usually associated with annular
flow. Heat is transferred by conduction and convection through the
liquid film and vapor is generated continuously at the interface.
For single-phase turbulent flows
Nu=fn(Re,Pr)
For turbulent flow in an annular flow passage, the same relation will be
still applicable provided the appropriate dimensionless groups are used.
-Re is the same whether the liquid completely fills the tube or
flows as a thin film
for fully occupied case

58. For annular flow with the same mass flow rate,ri R
Annular flow D U
Full-pipe flow
(Same as for fully occupied case)

59. -For both cases, the appropriate physical properties are those of the
liquid, therefore, Pr is the same for both cases.

60. Lockhart and Martinelli successfully correlated 1-α using Xtt
Xtt = the Lockhart and Martinelli parameter
Chen’s Correlation (1963)
hNCB : Saturate nucleate boiling
hc :Two-phase forced convection

61. -For hNCB Chen used the equation of Zuber and Forster as a beginning
Which is from the instantaneous bubble diameter and growth rate.
However, the actual superheat controlling the bubble growth is not
but , which is smaller
than
In pool boiling, the boundary layer thickness is thick,
therefore,
However, in forced convective boiling, the boundary thickness is thin,
consequently

62. Force convective boiling
ΔTe
Pool boiling
Force convective boiling
ΔTe

63. Therefore, the Zuber and Forster’s equation should be modified as
follows for forced convective boiling
Chen defined a suppression factor S, the ratio of the superheat at
the bubble tip(ΔTe) to the wall superheat ΔTsat

64. Note that from the Clausius-Clapeyron relation
It might be expected that S→1 at low flows, S→0 at high flow.
Therefore, Chen suggested that
ReTP is the two-phase Reynolds number, which will be defined later.

65. -For hC
It is assumed that hC could be represented by a Dittus-Boeltet
type equation.
PrTP ≒Prl , kTP = kl, since heat is transferred to a liquid film
in annular flow regime.
F may be considered as a two-phase convection enhancement factor.

66. Since F is a flow parameter only, it may be expected that F can be
expressed as a function of the Martinelli factor, Xtt
Chen presented F and S graphically as follows.
From Collier, 1981

67. The factors F and S may be fitted as follows:
This fit was presented by Butterworth
From: T.A. Bjornard & P.Griffith, ”PWR Blowdown Heat Transfer”,
Symposium on the Thermal and Hydraulic Aspects of Nuclear Reactor
Safety, vol.1 Light Water Reactors Presented at the Winter Annual
Meeting of the ASME, Atlanta, Geogia, Nov.27-Dec.2
, 1997 Ed. by O.C. Jones Jr. & S.G. Bankoff, NY. NY.

68. Range of conditions for data used in testing Chen’s correlation
Quality
(wt.%)
Heat Flux
ψ(kW/m2)
From: Collier, 1981

69. Comparison of Chen’s correlation with Thom’s and Jens-Lottes’s correlations.
P=10MPa, G=5.4Mgm-2s-1, De =0.3cm.
From: Hewitt, Delhaye & Zuber, Vol.2 ch3.

70. Modification Chen’s correlation
-Hahne, et al.’s correlation, 1989.
Hahne, Shen & Spindles, 1989 Int. J. Heat Mass Transfer
, vol.32, No , 1989

71. --Effect of flow direction is also studied in this paper
--Effect of flow direction is also studied in this paper. There is no clear
effect of flow direction
--Upwards or downwards with a minimum liquid velocity of 0.25 m/s

72. -Gungor-Winterton Correlation
Ref: Gungor. K.E and Winterton, R.H.S(1986),”A general correlation
for flow Boiling in tubes and annuli,” Int. J. Heat Mass Transfer.
Vol.29 pp

73. This correlation for subcooled boiling is with an accuracy of ±25%

74. The Chen correlation compared with our data
Fluid R12 From Hahne et. al. 1989

75. The correlation by Bjorge et al
The correlation by Bjorge et al. compared with the data of Vaihinger and Kaufmann.
The modified Chen correlation compared with our data
Fluid R12 From Hahne et. al. 1989

76. Comparison of flow boiling correlation at 6×105Pa
Comparison of flow boiling correlations at 11×105Pa
Fluid R12 From Hahne et. al. 1989

77. High level interpolation correlations
-Bjorge, Hall and Rohsenow’s correlation (1981)
Ref: Int. J. Heat Mass Transfer, vol.25 No. 6, pp , 1982
In high quality region,
e.g, for annular flow

78. BM=1.89×10-14(in SI unit) for forced convection boiling of water
BM=4.0×10-13 for R12(Hahne, Shen & Spindler)
-Steiner and Taborek’s correlation, 1992

79. hl0= evaluated by Gnielinski correlation, i.e.

80. for 4000<Re<5000000 ; 0.5<Prl<2000/11/10

81. Correlations choosing the maximum of hNCB and hc
-Shah’s correlation