S. G. Kandlikar1
Visiting Scientist,
Mechanical Engineering Department and
Plasma Fusion Center,
Massachusetts Institute of Technology,
Cambridge, MA 02139
A Model for Correlating Flow
Boiling Heat Transfer in
Augmented Tubes and Compact
Evaporators
The additive model for the convective and nucleate boiling components originally
suggested by Bergles and Rohsenow (1964) for subcooled and low-quality regions
was employed in the Kandlikar correlation (1990a) for flow boiling in smooth tubes.
It is now extended to augmented tubes and compact evaporators. Two separate
factors are introduced in the convective boiling and the nucleate boiling terms to
account for the augmentation effects due to the respective mechanisms. The fin
efficiency effects in the compact evaporator geometry are included through a reduction in the nucleate boiling component over the fins due to a lower fin surface
temperature. The agreement between the model predictions and the data reported
in the literature is within the uncertainty bounds of the experimental measurements.
Introduction
Augmented tubes and specially designed compact heat exchanger surfaces are being increasingly employed in flow boiling applications. Some of the augmented tube geometries used
in the refrigeration industry include microfin, microgrooved,
low-fin, and inserts such as helical wires and twisted tapes. In
automotive air conditioning evaporators and in many lowtemperature two-phase applications, compact heat exchangers
of plate-fin construction are employed. The compact heat exchangers with low-temperature fluid stream boiling during its
passage are usually called compact evaporators.
The use of augmented surfaces and compact heat exchangers
in refrigeration air conditioning and process industries is justified on the basis of the overall reductions in material cost,
weight, size, and/or pumping power in some instances. In
calculating the potential savings, and also in the actual design,
accurate estimates of the heat transfer coefficients are needed.
A number of investigators have conducted experiments to
determine the flow boiling heat transfer coefficients in a variety
of augmented tube geometries. Their experimental data are
generally reported in a tabular or graphic form. Since there
are no adequate predictive techniques available for these geometries, a designer is usually faced with using the data from
tables and graphs. The resulting loss in accuracy is generally
compensated by the use of generous safety factors.
Some of the recent experimental investigations on compact
evaporators are aimed toward understanding the flow patterns
and heat transfer mechanisms in these highly enhanced geometries. Damainides and Westwater (1988) report the flow
patterns observed in a staggered fin heat exchanger with airwater flow. Cohen and Carey (1990) conducted experiments
with R-113 flowing in single cross-ribbed channels of four
different geometric configurations. The channels were constructed from a copper block, which was heated with electrical
heaters. The top side of the channel was covered with a transparent Lexan cover plate to observe the liquid film behavior.
Revealing information was obtained by Cohen and Carey on
the existence of nucleate boiling in certain preferred locations
'Current address: Professor, Mechanical Engineering Department, Rochester
Institute of Technology, Rochester, NY 14623.
Contributed by the Heat Transfer Division for publication in the JOUSNAI OF
HEAT TRANSFER. Manuscript received by the Heat Transfer Division July 30,
1990; revision received January 8, 1991. Keywords: Augmentation and Enhancement, Boiling, Heat Exchangers.
in the channel. They also obtained local flow boiling data,
which were correlated by modifying the Chen (1966) correlation. The two-phase multiplier F was correlated as a function
of the Martinelli parameter X„ for each geometry tested. A
similar dependence of F on X„ was observed with an earlier
correlating scheme developed by Carey and Mandrusiak (1986)
based on the annular film model.
Robertson and Lovegrove (1983) conducted flow boiling
experiments with R-l 1 in an electrically heated serrated-fin test
section. The local heat transfer coefficients were correlated as
a function of flow rate and quality. The contribution from
nucleate boiling was not included in their correlating scheme.
A recent correlation developed by Kandlikar (1990a) for flow
boiling in smooth circular tubes is able to correlate the data
for refrigerants, cryogens, and water within an average error
ranging from ±10 to ±20 percent. The correlation is based
on an additive model for the convective boiling and the nucleate
boiling contributions represented by the convection number,
Co, and the boiling number, Bo. These dimensionless numbers
were proposed earlier by Shah (1982) in his chart correlation.
In another paper, Kandlikar (1991) presented a flow boiling
map in which the parametric relationships between the heat
transfer coefficient and the major variables were presented in
terms of dimensionless parameters. Specific maps for water,
R-22 and R-l34a were prepared by Kandlikar (1990b) for estimating the heat transfer coefficient under a given set of operating conditions for these fluids.
The basic model developed by Kandlikar (1990a) in arriving
at the smooth tube correlation is now extended to cover augmented tubes and compact evaporator geometries. The details
of the model and the results of a comparison with the available
experimental data are reported in this paper.
Objectives of the Present Work
1 Develop a model for flow boiling heat transfer in augmented tube and compact evaporator geometries based on the
additive concept for the convective and the nucleate boiling
contributions.
2 Provide a quantitative measure for the type of augmentation (convective or nucleate boiling) occurring in a given
geometry.
3 Compare the model predictions with the experimental data
reported in literature.
966 / Vol. 113, NOVEMBER 1991
Transactions of the ASME
Copyright © 1991 by ASME
Downloaded 10 Aug 2009 to 129.21.213.135. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm
Development of the Flow Boiling Model
The correlation developed by Kandlikar (1990a) for smooth
tubes is used as the starting point. The correlation for vertical
tubes, or for horizontal tubes with Froude number, Frto > 0.04,
is given by:
Table 1
relation
Fluid-dependent parameter, F„, in the Kandlikar (1990b) cor-
Smooth tube, Kandlikar correlation:
hTP = larger of
(1)
where the subscripts NBD and CBD refer to the nucleate boiling
dominant and the convective boiling dominant regions, for
which the hTp values are given as:
= 0.6683 a r ° - 2 ( i - x ) ° - X
h7
+1058.0 Bo 0 7 (l - -xf%hl0(2)
and
hTp,CBD= 1.1360 Co-°- 9 (l
-xf%o
+ 667.2 Bo 07 (l -xf%hl0
(3)
The Dittus-Boelter correlation was originally employed by
Kandlikar (1990a) for calculating hi0 in smooth tubes. In a
subsequent paper, Kandlikar (1990b) recommended the
Petukhov-Popov (1963) and the Gnielinkski (1976) correlations, which are able to account for the Prandtl number effect
of different fluids more accurately than the Dittus-Boelter
correlation.
The first terms on the right-hand side of Eqs. (2) and (3)
represent the convective boiling components while the second
terms represent the nucleate boiling components. Fjt is a fluiddependent parameter, which is applied as a multiplier in the
nucleate boiling terms. Table 1 lists the values of Fj-/as reported
by Eckels and Pate (1990) for R-134a, and by Kandlikar (1990a)
for water and other refrigerants. Ffi for nitrogen was also
reported by Kandlikar (1990a), but is likely to undergo further
changes due to a wide scatter in the flow boiling data for
nitrogen available at the present time.
A Model for Augmented
A
Bo
cp
Co
=
=
=
=
D =
ECB
=
E'CB
=
ENB
=
ENB
=
Tubes.
It is postulated that the
area, m2
boiling number, <jr/(Gife)
specific heat, J/kg K
convection number =
(VP/)°- 5 ((I-*)/*) 0 - 8
diameter of a smooth tube,
root diameter of a microfin
tube, or hydraulic diameter
of a compact evaporator
flow channel, m
augmentation factor for
convective boiling contribution
modified augmentation
factor for convective boiling to include the constant
from the unknown singlephase correlation
augmentation factor for
nucleate boiling contribution
modified augmentation
factor for nucleate boiling
to include the constant
from the unknown singlephase correlation
Journal of Heat Transfer
Fluid
Ffl'
Water
R-11
.R-12
1.00
1.30
1.50
R-13B1
R-22
R-113
1.31
2.20
1.30
R-114
R-134a
R-152a
1.24
1.63
1.10
A material dependence of F„ is reported by Kandlikar (1991b). Above
values are applicable to copper tubes only, for stainless steel tubes, use
F,i = 1.0 for all fluids.
effects of x, G, q, and fluid properties on hTP in augmented
tubes and compact evaporators are similar to those in smooth
tubes as represented by Eqs. (l)-(3); one however needs to
take into account the variation of heat flux over the extended
surfaces. The augmentation in hTp is considered to be occurring
due to two separate effects, represented by the augmentation
factors ECB and ENB in the convective and the nucleate boiling
terms, respectively. For augmented tubes with microscale protrusions (fin efficiency close to 100 percent), Eq. (1) is applied
with the following equations for #7-P,NBD and hTPtCvD'Augmented
tubes:
hTp,mD = 0.6683 Co~ 0 2 (l
-xfshloECB
+ 1058.0 Bo 0 7 (l -xfsFf,h,0ENB
(4)
and
Ffi = fluid-dependent parameter
given in Table 1
Fr/0 = Froude number with all
flow as liquid = G2/(pigD)
G = mass flux, kg/m 2 s
K = single-phase heat transfer
coefficient with all flow as
liquid, W/m 2 K
hTP = two-phase heat transfer
coefficient, W/m 2 K
n
= two-phase heat transfer
TP,ti
coefficient in a compact
evaporator, defined by
Eq.(14), W/m 2 K
•ig = latent heat of vaporization,
J/kg
2/3
J = j factor = StPr
k = thermal conductivity, W / m
K
L = fin height, m
m = defined by Eq. (26), n T 1
n = exponent of Re /0 for augmented tubes, Eqs. (18)
and (19)
Pr = Prandtl number = cpjx/k
Q = heat transfer rate, W
^
by Eq.
q = heat flux defined
(15), W/m 2
Re = Reynolds number = GD/p,
St = Stanton number = h/(Gcp)
/ = fin thickness
difference between the
•* p - sat
prime and saturation temperatures, K
X = quality
•n = fin efficiency
p = viscosity, kg/m s
3
p = density, kg/m
=
Subscripts
CBD = convective boiling dominant region
F = fin
g = vapor
/ = liquid
Ig = latent
lo = with all flow as liquid
NBD = nucleate boiling dominant
region
P = prime surface
NOVEMBER 1991, Vol. 113/967
Downloaded 10 Aug 2009 to 129.21.213.135. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm
hrp,cBD= 1-1360 Co "•\\-xrhl0ECB
+ 667.2 Bo 07 (l -xf%hi0ENB
(5)
The enhancement factors ECB and ENB are assumed to be
characteristics of the augmented tube geometry, and independent of the operating parameters. The numerical constants
appearing in Eqs. (4) and (5) are the same as those in the
Kandlikar correlation for smooth tubes.
The heat transfer coefficient hh in Eqs. (4) and (5) is obtained
from the single-phase correlation for the augmented geometry
with total flow as liquid. One of the essential requirements for
the single-phase correlation is to provide the correct Reynolds
number relationship applicable to the augmented tube. In situations where a reliable single-phase correlation is not available, the Reynolds number exponent n in a Dittus-Boelter type
correlation is treated as a third constant along with ECB and
ENB, and their values are determined from the experimental
flow boiling data.
A Model for Compact Evaporators. The flow boiling heat
transfer in compact evaporators differs from that in smooth
tubes in two ways. Firstly, the geometries employed in compact
evaporators are highly augmented with the use of cross ribs,
interrupted plate fins, or other similar flow channels. Secondly,
the nucleate boiling contribution varies considerably over the
channel surfaces due to nonuniform fin surface temperature.
The model presented here utilizes the single-phase heat transfer correlation for compact evaporators to describe the dependence of the heat transfer coefficient on Re and Pr. The
presence of fins is assumed to affect the nucleate boiling component as it is dependent on the local fin temperature, while
the convective boiling component is assumed to be uniform
over the entire fin and the prime surfaces at a given section.
The resulting equations are given as follows:
For prime surface:
'77>,P,NBD
hrp,p = larger of
(6)
'77>,P,CBD
where
/*r/>,p,NBD = 0.6683 C o " 0 ^ !
-xf*hloECB
+ 1058.0 Bo£ 7 (l -xf8Fflhl0ENB
(7)
and
hTP,P,cm= 1.1360 Co~ a 9 (l
-xf%0ECB
+ 667.2 Bo?,-7(l -XfAFflhl0ENB
(8)
For fin surface:
hrp.F—larger of
(9)
where
hTp,F,NBD = 0.6683 C o - 0 2 ( l
-xf\0ECB
+ 1058.0 Bo£ 7 (l ~x)0-8FfihioENB
(10)
and
hTp,F,cED= 1.1360 C o - ° ' ' ( l - x ) c \ £ c i !
+ 667.2 Bo£ 7 (l -x)Ffih,0ENB
(11)
In Eqs. (6)-(ll), h/0 is the single-phase heat transfer coefficient in the compact evaporator with all flow as liquid. The
values of Ffl and the numerical constants are the same as those
in the Kandlikar correlation for smooth tubes. The boiling
numbers on the prime surface, Bo/>, and on the fins, Bo/r, are
different due to the differences in the respective heat fluxes,
qP and qF (average heat flux over the fins). ECB and ENB are
the augmentation factors for the convective boiling and the
nucleate boiling terms, respectively, and are assumed to be
characteristics of the compact evaporator geometry.
The overall heat transfer coefficient hTP<n is defined in terms
968 / Vol. 113, NOVEMBER 1991
of the total heat transfer rate dQ in an element and the temperature difference A7>„ sat between the prime surface and the
saturation temperature
dQ = hTP^dAP
+ dAF)ATPJSM
(12)
+ hTP,FdAFriF)ATP-s:it
(13)
Also,
dQ=(hTPtPdAP
where -qF is the fin efficiency.
From Eqs. (12) and (13), hTp,r, may be expressed as
hTp,n = lhTp,p+ hTP!F(AF/AP)riFy(l
+AF/AP)
(14)
The average heat flux q may be expressed as
q = dQ/(dAP + dAF) = hTP,,ATP.sat
(15)
The heat fluxes qP and qF on the prime and fin surfaces,
respectively, are given by
qP= hTPiPATP_sal = q(hTPiP/hTP^
(16)
and
qF= hTP,FATP_sMriF= q(hTPiF/hTP^f\F
(17)
The values of Bop and Bo f in Eqs. (6)-(ll) are not known
initially, and an iterative scheme with Eqs. (16) and (17) is
needed when the average heat flux q is specified. The predicted
value of hTPitl is then obtained from Eq. (14).
It may be noted that all heat transfer coefficient and heat
flux values are local at any given section in the compact evaporator.
Comparison With Experimental Data
The flow boiling models presented earlier are compared here
with the experimental data. For this purpose, three experimental investigations have been selected from the literature
based on the completeness of the reported results and accuracy
of measurements. Table 2 lists the details of the experimental
conditions and an estimate of the errors involved in various
measurements.
Results With Augmented Tube Data. The augmented tube
correlation is checked with the data obtained by Khanpara et
al. (1987). They report the flow boiling data in a microfin tube
with two refrigerants, R-113 and R-22. The microfin tube
dimensions and other experimental details are given in Table
2.
In the correlation developed here, the root diameter is used
as the characteristic dimension for calculating Re and Nu, while
the heat transfer coefficients hTP and hh are based on the actual
inside surface area of the microfin tube.
Equations (1), (4), and (5) require information on the singlephase heat transfer coefficient with liquid flow for augmented
tubes. The experimental results reported by Khanpara (1986)
on the single-phase heat transfer coefficient with R-113 in the
microfin tube indicate that Nu/Pr 0 4 is proportional to Re 1,7
in the Re range from 6000 to 10,000, while the data for R-22
in the range 12,000 to 15,000 are well below the extension of
the R-113 line. Also, the R-22 data are scattered by as much
as a factor of 2 for a given Re. The scatter is believed to be
due to wall temperature fluctuations caused by swirling/vortex
shedding near the wall of the micro-fin tube. The two-phase
data however do not exhibit such a scatter. For these reasons,
the single-phase data could not be correlated with any reasonable accuracy. To overcome this problem, the Reynolds
number exponent n is introduced as an additional constant in
the Dittus-Boelter type single-phase correlation. The augmentation factors ECB and ENB in Eqs. (4) and (5) were modified
to ECB and E^B to include the unknown leading constant (in
place of 0.023) from the single phase correlation. The resulting
equations take the following form:
Transactions of the ASME
Downloaded 10 Aug 2009 to 129.21.213.135. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm
Table 2 Details of experiments conducted by previous investigators
for generating data on a microfin tube and compact evaporators employed in testing the proposed model
Investigator
Tube or evaporator Geometry
Geometry
Microfin tube, copper, ID-8.75mm,
electrically heated, Fin height0.22 mm, Fin pitch-0.455mm,
Aaug/Asmooth=l-54, Fin geometryrounded tip-and flat valley
(width 0.203mm)
Khanpara,
Pate and
Bergles,
(1987) V\_/A / \ /"V.
Robertson
Lovegrove, ^Sr^|JsL5iiTJM
Cohen and
Carey
(1990);
Geomerty 1
N^S^VVDohen and
~arey
(1990);
Geometry 3
xxxxxxx
R--11; x: 0.01-0.8,
Serrated aluminum fin compact
evaporator, single channel heated
P: 304-720 kPa,
2
electrically from top and bottom,
G: 34.4-159 kg/m s
2
Fin thickness - 0.2mm, Fin heightq: 1.3-3.0 kW/m
6.15 mm, DH=2.65mm, AF/AF=4.06
Horizontal flow;
Measurement accuracy:
T- ±0.2 K, Heat leak5%; Rotameter- <1%,
h TP : 10-15%
Cross-ribbed copper plate fin
R- 113 ; x: 0.02-0.75,
compact evaporator, single channel
P: 101 kPa
2
electrically heated from one side,
G: 111.3 kg/m s,
2
rib angle-30°, rib pitch-28.6mm,
q: 56-133 kW/m
rib height-3.2mm, rib thickness
1.6mm, DH=6.78mm, AF/AP=0.56
Vertical up flow,
electrically heated
copper block;
Measurement accuracy:
Q- ±6%, T- ±0.06 K,
h TP - ±11%
R- 113 : x: 0.06-0.75,
Cross-ribbed copper plate fin
compact evaporator, single channel
P: 101 kPa,
2
electrically heated from one side,
G: 110.7 kg/m s,
2
rib angle-60°, rib pitch-17.1mm,
47-159
kW/m
q:
rib height-3.2mm, rib thickness1.6mm, DH=6.83mm, AF/AP=0.54
Table 3 Comparison between the experimental data and model predictions
Investigators
Khanpara et al.
(1987), Micro-fin Tube;
n=0.4, E' CB =82.0,
E'N8=72.0
Robertson and
Lovegrove, (1983)
Compact Evaporator,
Serrated fin;
E CB =1.20, ENB=0.77
Cohen and Carey,
(1990),
Compact Evaporator,
Cross-ribs, Geometry i;
E CB =2.45, E NB =0.63
Cohen and Carey,
(1990),
Compact Evaporator,
Cross-ribs, Geometry 3;
E CB =3.00, E NB =0.30
% E r r o r = 100
RMS
Mean
%
%
10.8
8.3
Abs
same as above
1E4
Mean
Microfin tube
n = 0.4, E' CQ = 82, E' NB = 72
8000
+1 8
t
^
5.4
7.4
-4 3
i
6000
4000
i
O
A
2000
8.2
6.1
R-113 data
R-22 data
+0 2
0
2000
4000
6000
8000
10,000
hn,, Experimental, W/irfK
3.6
2.9
-0 2
(Experimental-Predicted)/Experimental
Augmented tube:
hTp,Nm = 0.6683 Co- 02 (l -jf)°-8Re£Pr?-4i%B
+ 1058.0 Bo07(l -xf*F/,Re'l0PrrEhB (18)
and
U8
AT/>.CBD= 1-1360 a m i -x) Re? 0 Prr^ B
+ 667.2 Boa7(l - xf'FflRelPr^EhB (19)
A total of 26 data points were reported by Khanpara (1986)
for R-113 and 34 data points for R-22 for the microfin geometry
listed in Table 2. These data points were used in determining
Journal of Heat Transfer
Test Fluid and
Details of Experimental
Parameter Ranees
Set up
R -113 ; x: 0.025-0.74,
Horizontal flow;
P: 324-343 kPa
Measurement accuracy:
2
G: 248-600 kg/m s
q- ±4%, h TP - ±15%;
2
Radial guard heater
q: 8.1-39.7 kW/m
R--22; x: 0.020-0.78,
P: 84-8-969 kPa,
2
G: 280-533, q: 7.1 -12.8 kW/m
Fig. 1 Comparison between the model predictions and experimental
data by Khanpara et ai. (1987) for flow boiling of R-22 and R-113 inside
a microfin tube
the constants n, E'CB, and E'NB in Eqs. (18) and (19). The
combination of the three constants yielding the lowest rms
error for both refrigerant data sets was selected.
, The values of the constants for the microfin tube determined
from the data are n = 0.4, EQB = 82.0, and E^B = 72.0. These
values are specific to the microfin geometry listed in Table 2.
The rms, mean, and absolute mean differences between the
experimental and the predicted values for R-113 and R-22 are
given in Table 3. Figure 1 shows a plot of the predicted versus
experimental values of hrp for the microfin tube. The limits
of the reported experimental uncertainty of ±15 percent are
also shown on the plot. Out of a total of 60 data points, 75
percent of the points are correlated to within ± 10 percent, 90
NOVEMBER 1991, Vol. 1137 969
Downloaded 10 Aug 2009 to 129.21.213.135. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm
4000
8000
R-11
Serrated Plate fin evaporator
R-113
Cross-ribbed plate fin evaporator
Geometry 1
E C B = 1.20, E N B = 0.77
A A
i4 6000
1000
2000
3000
hrp, Experimental, W/irfK
10,000
|j
4000
i
2000
«*>
2000
4000
6000
10,000
b,,,, Experimental, W/nfK
Fig. 2 Comparison between the model predictions and experimental
data by Lovegrove and Robertson (1983) for flow boiling of R-11 inside
a serrated fin compact evaporator
Fig. 3 Comparison between the model predictions and experimental
data by Cohen and Carey (1990) for flow boiling of R-113 inside a crossribbed compact evaporator (geometry 1)
percent within ±15 percent, and only one data point lies beyond ±18 percent. Considering the experimental uncertainty
and the scatter in the experimental data sets, the agreement is
seen to be very good.
It may be noted that the same values of the augmentation
factors E'CB and EhB were able to correlate both R-113 and R22 data sets obtained with the same microfin tube. These factors therefore are believed to be characteristic of the microfin
tube in the range of parameters tested. Since the constant from
the single-phase correlation is absorbed in these factors, only
the ratio of the convective to the nucleate boiling augmentation
can be obtained as E'CB/E^B = 82/72 = 1.14. This indicates
that in the microfin tube tested, the convective augmentation
is slightly higher than the nucleate boiling augmentation. Such
information could be used in developing augmentation techniques suitable for specific applications. Incorporating smallscale surface changes on the tube surface such as re-entrant
cavities and narrow grooves will enhance nucleate boiling and
Ef/B will increase, while the convective component and E'CB will
increase if the tube surface offers large-scale disturbances due
to fins, wires, ridges, and grooves.
Cross-ribbed geometry, No. 3, Cohen and Carey (1990):
Results With Compact Evaporator Data. The flow boiling
model given by Eqs. (6)-(ll), (14), (16), and (17) was tested
with the data reported by Robertson and Lovegrove (1983) for
R-11 in a serrated plate fin evaporator, and by Cohen and
Carey (1990) for two rib geometries of cross-ribbed channels.
Some of the details of the experimental setup and measurement
accuracy of the two investigations are given in Table 2.
In the correlations presented for compact evaporators, Nu
and Re are based on the hydraulic diameter of the flow channel,
and the heat transfer coefficients hTPj1j hTp,p and hTPiF are
defined by Eqs. (12), (16), and (17), respectively.
The single-phase heat transfer coefficients for the evaporators are obtained from Eqs. (20)-(23), which are derived
from the experimental ./-Re plots.
Serrated fin geometry, Robertson and Lovegrove
StPr
2/3
= 0.2106 Re"
038
(1983):
(20)
Cross-ribbed geometry, No. 1, Cohen and Carey (1990):
StPr 2/3 = 0.418Re"°"
970 / Vol. 113, NOVEMBER 1991
(21)
StPr 2/3 = 0.341Re-°-30
(22)
hi0 is then obtained from the corresponding St/0 with all liquid
flow as:
h,0 = St,0Gcp
(23)
The fin efficiency expressions are as follows:
Serrated fin geometry, Robertson and Lovegrove
T]F=tanh(mL)/mL
(1983):
(24)
Cross-ribbed fin geometry, Cohen and Carey (1990):
rip = (tanh (mL) + hTP,F/(kFm)} / {m(L +1/2)
[1 + tanh(mL)hTP,F/(kFm)
]
(25)
where m in Eqs. (24) and (25) is given by
m = [2hTP/(kFt)]°
(26)
A procedure similar to that explained for the augmented
tubes was followed in obtaining the constants ECB and ENB
from the experimental data. A total of 22 data points reported
by Robertson and Lovegrove (1983) were utilized for the serrated plate fin evaporator, and 18 data points for geometry 1
and 14 data points for geometry 3 reported by Cohen and
Carey (1990) were employed for the cross-rib geometry. The
experimental data were first reduced to yield the value of hTPtn
as defined by Eq. (14).
The rms, mean and absolute mean differences between the
experimental and the predicted values are given in Table 3.
Also, the values of the constants obtained from the data analysis are included.
Comparisons of the experimental and predicted values of
the heat transfer coefficients for each data set are presented
in Figs. 2, 3, and 4. Two lines indicating the approximate
accuracy limits of the experimental data are also drawn in Figs.
2-4. It can be seen that the model predictions are in excellent
agreement with the experimental data.
The values of the convective boiling and the nucleate boiling
augmentation factors are given in Figs. 2-4 as well as in Table
3 for each geometry investigated. It can be seen that the convective boiling augmentation ECB in compact evaporators is
quite large compared to the nucleate boiling augmentation ENB.
Transactions of the AS ME
Downloaded 10 Aug 2009 to 129.21.213.135. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm
1 E4 |
1
1
r-i
j3<
E C B = 3.00, E N B = 0.30
^
/
/
/
@
@ ®
•
/
/f
*6000 •$
&/•
*V m
5
/®@
A general comment seems appropriate here regarding the
way in which the experimental heat transfer data are reported
by the investigators of compact evaporators. They generally
plot their hTP versus x data on a log-log scale. A linear scale
for x however seems more appropriate since the changes in x
are linearly related to the enthalpy changes (under constant
system pressure assumption) along the evaporator. Further,
the quality range from 0.01-0.1 is greatly expanded on a loglog plot, occupying almost half the width, while the range from
0.5 onward is compressed. The low-quality range is not used
in the refrigeration evaporator, whereas the heat transfer and
dryout considerations are of major importance in the highquality region of an evaporator. It is therefore recommended
that a linear scale be used for x. The log scale for hTP may be
justified when the post-dryout data, which are usually an order
of magnitude lower than the wet surface data, are also shown
on the same plot.
1—7—
R-113
Cross-ribbed plate fin evaporator
8000 - Geometry 3
/
/
/
/
/Ao
i
2000
0
J£
0
1
1
1
1
2000
4000
6000
8000
hjp, Experimental, W/irfK
1
10/300
Fig. 4 Comparison between the model predictions and experimental
data by Cohen and Carey (1990) for flow boiling of R-113 inside a crossribbed compact evaporator (geometry 3)
This is to be expected since the geometries considered do not
have any special surface structure to enhance the nucleate
boiling, whereas the complex flow passages provide a high
degree of convective augmentation. In fact, the nucleate boiling
is significantly suppressed (ENB< 1) in these geometries due to
the presence of a high wall shear stress. Additional discussion
on the suppression effects due to wall shear stress is presented
by Kandlikar (1990c).
Further comparison can be made between the two geometries
tested by Cohen and Carey. The nucleate boiling enhancement
factor for geometry 1 (ENB = 0.63) is higher than that for
geometry 3 (Em = 0.30). This is in agreement with the visual
observations made by Cohen and Carey (1990) through the
top transparent cover on the flow channels. They observed a
number of nucleation sites in the channel with geometry 1,
while there were only a few small bubbles seen in the corner
regions in geometry 3. On the other hand, the convective enhancement factor ECB for geometry 1 (ECB = 2.43) is lower
than that for geometry 3 (ECB = 3.0). A closer look at the
two geometries described in Table 2 and the single-phase correlations given by Eqs. (21)and (22) reveals that the flow passages for geometry 3 are more tortuous and yield a higher heat
transfer coefficient than that for geometry 1. From the above
discussion, it can be seen that the model developed here is able
to provide important clues regarding the mechanisms during
flow boiling inside augmented tubes and compact evaporators.
Additional Remarks
The results presented in this paper indicate that it is possible
to extend the additive model employed in the Kandlikar (1990a)
correlation for different geometries by critically evaluating the
additional effects. Another area where these concepts could
be employed is the flow boiling of multicomponent mixtures
in smooth and enhanced tubes, and in compact evaporator
geometries. Because of the additional complexity introduced
due to mass transfer effects, the problem is unquestionably
more challenging. The two aspects where attention should be
focused are: (0 changes in properties with concentration and
its effect on the convective and the nucleate boiling components, and (if) the complex effect of heat flux on the nucleate
boiling component due to diffusion of one or more volatile
components through the mixture. Results based on this approach are presented by Kandlikar (1991) for binary refrigerant
systems.
Journal of Heat Transfer
Conclusions
The additive model employed in the Kandlikar (1990) correlation is extended to cover the flow boiling heat transfer in
augmented tubes and compact evaporators. Two separate augmentation factors are introduced in the convective and the
nucleate boiling terms. In the case of compact evaporators,
effects due to fin efficiency are included by using appropriate
heat fluxes over the prime and the fin surfaces. Experimental
data obtained by Khanpara et al. (1987) for R-22 and R-113
boiling in a microfin tube have been correlated with an average
deviation of 8.3 percent. The augmentation factors have been
found to be specific to the tube geometry and independent of
the refrigerant or operating conditions over the range of parameters investigated. The compact evaporator data obtained
by Robertson and Lovegrove (1983) for flow boiling of R-ll
in a serrated plate-fin geometry, and by Cohen and Carey
(1990) for flow boiling of R-113 in two cross-rib geometries
were correlated with average deviations of 7.4, 6.1, and 2.9
percent respectively. The enhancement factors ECB and ENB in
case of augmented tubes, and ECB and Em in case of compact
evaporators, were able to provide important clues regarding
the type of enhancement (convective or nucleate boiling) occurring in the channel during flow boiling.
References
Bergles, A. E., and Rohsenow, W. M., 1964, "The Determination of Forced
Convection, Surface Boiling Heat Transfer," ASME JOURNAL OF HEAT TRANSFER, Vol. 86, pp. 365-372.
Carey, V. P., and Mandrusiak, G. D., 1986, "Annular Film-Flow Boiling of
Liquids in a Partially Heated Vertical Channel With Offset Strip Fins," International Journal of Heat and Mass Transfer, Vol. 29, pp. 927-939.
Chen, J. C , 1966, " A Correlation for Boiling Heat Transfer to Saturated
Fluids in Convective Flow," Industrial and Engineering Chemistry, Process
Design and Development, Vol. 5, pp. 322-329.
Cohen, M., and Carey, V. P., 1990, " A Comparison of the Flow Boiling
Performance Characteristics of Partially-Heated Cross-Ribbed Channels With
Different Rib Geometries," International Journal of Heat and Mass Transfer,
in press.
Damainides, C. A., and Westwater, J. W., 1988, "Two-Phase Flow Patterns
in a Compact Heat Exchanger and in Small Tubes," Proceedings of the Second
UK National Conference on Heat Transfer, Vol. II, pp. 1257-1268.
Eckels, S. J., and Pate, M. B., 1990, "An Experimental Comparison of
Evaporation and Condensation Heat Transfer Coefficients for HFC-134a and
CFC-12," International Journal of Refrigeration, Nov., pp. xx-oo.
Gnielinski, V., 1976, "New Equations for Heat and Mass Transfer in Turbulent Pipe and Channel Flow," International Chemical Engineer, Vol. 16, pp.
359-368.
Kandlikar, S. G., 1989, "Development of a Flow Boiling Map for Subcooled
and Saturated Boiling of Different Fluids Inside Circular Tubes," in: Heat
Transfer With Phase Change, X. X. Habib et al., eds., Vol. 114, pp. 51-62;
also accepted for publication in the ASME JOURNAL OF HEAT TRANSFER.
Kandlikar, S. G., 1990a, " A General Correlation for Saturated Two-Phase
Flow Boiling Heat Transfer Inside Horizontal and Vertical Tubes," ASME
JOURNAL OF HEAT TRANSFER, Vol.
112, pp. 219-228.
Kandlikar, S. G., 1990b, "Flow Boiling Maps for Water, R-22 and R-134a
in the Saturated Region," presented at the 9th International Heat Transfer
Conference, Jerusalem, Aug.
NOVEMBER 1991, Vol. 113 / 971
Downloaded 10 Aug 2009 to 129.21.213.135. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm
Kandlikar, S. G., 1990c, " A Mechanistic Model for Saturated Flow Boiling
Heat Transfer," Single and Multiphase Conveclive Heat Transfer, M. A. Ebadian, K. Vafai, and A. Lavine, eds., ASME HTD-Vol. 145, pp. 61-69.
Kandlikar, S. G., 1991, "Correlating Flow Boiling Heat Transfer Data in
Binary Systems," Phase Change Heat Transfer, E. Hensel et al., eds., ASME
HTD-Vol. 159.
Khanpara, J. C , 1986, "Augmentation of In-Tube Evaporation and Condensation With Micro-Fin Tubes," Ph.D. Dissertation, Iowa State University,
Ames, IA.
Khanpara, J. C , Pate, M. B., and Bergles, A. E., 1987, "Local Evaporation
Heat Transfer in a Smooth Tube and a Micro-fin Tube Using Refrigerants 22
972 / Vol. 113, NOVEMBER 1991
and 113," in: Boiling and Condensation in Heat Transfer Equipment, E. G.
Ragi et al., eds., ASME HTD-Vol. 85, pp. 31-40.
Petukhov, B. S., and Popov, V. N., 1963, "Theoretical Calculation of Heat
Exchange and Frictional Resistance in Turbulent Flow in Tubes of an Incompressible Fluid With Variable Physical Properties," Teplofiz. Vysok. Temperatur (High Temperature Heat Physics), Vol. 1, No. 1.
Robertson, J. M., and Lovegrove, P. C , 1983, "Boiling Heat Transfer With
Freon 11 (Rl 1) in Brazed Aluminum Plate-Fin Heat Exchangers," ASME JOURNAL OF HEAT TRANSFER, Vol.
105, pp. 605-610.
Shah, M. M., 1982, "Chart Correlation for Saturated Boiling Heat Transfer:
Equations and Further Study," American Society of Heating, Refrigerating and
Air Conditioning Engineers Transactions, Vol. 88, Part I, pp. 185-196.
Transactions of the ASME
Downloaded 10 Aug 2009 to 129.21.213.135. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm