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CH-03-13-1
Predicting Heat Transfer During Flow Boiling
in Minichannels and Microchannels
Satish G. Kandlikar, Ph.D.
Mark E. Steinke
ABSTRACT
Flow boiling in small passages in mini- and microchannels is receiving increased attention due to very high heat
transfer rates possible with such geometries in electronics
cooling, fuel cell, and other emerging applications. These
geometries offer potential for significant enhancements in
refrigerating and air-conditioning systems as well. Since the
effect of surface tension becomes more important at smaller
passage dimensions, the flow boiling correlations developed
for conventional tubes, larger than 3 mm inner diameter, need
to be carefully reviewed. The low flow rate employed in such
geometries, coupled with the small channel hydraulic diameter, often results in a laminar flow with all flow as liquid. In the
present work, a flow boiling correlation for large-diameter
tubes is modified for flow boiling in minichannels by using the
laminar single-phase correlation for the heat transfer coefficient for all liquid flow. The trends in heat transfer coefficient
versus quality are also compared in the laminar region. Excellent agreement is obtained between predicted values and
experimental data. A need for additional experimental data in
the transition region is recognized.
INTRODUCTION
As the channel hydraulic diameter becomes smaller, the
ratio of heat transfer surface area to the fluid flow volume
increases in inverse proportion to the channel hydraulic diameter. For a circular channel, this ratio is given by the following
equation.
π 2
A s ⁄ V = ( πDL ) ⁄  --- D L = 4 ⁄ D
4

(1)
The heat transfer coefficient also increases for lower
channel diameters. For laminar single-phase flow, with a
constant value of Nusselt number, the heat transfer coefficient
dependence on the diameter is seen through the definition of
the Nusselt number.
k
h = Nu ---D
(2)
The heat transfer rate per unit flow volume is given by
q ⁄ V = ( ( hA s ∆T ) ⁄ V ) .
(3)
Combining Equations 1 to 3, we obtain
4k
q ⁄ V = ( hA s ∆T ) ⁄ V = Nu ------2 ∆T .
D
(4)
Assuming a constant value of Nusselt number (such as in
laminar single-phase flow) for a given fluid and a given
temperature difference, the volumetric heat transfer rate thus
depends inversely on the square of the channel diameter. Since
the pressure drop increases significantly as the channel diameter becomes smaller, the flow rates are generally smaller. The
low flow rate combined with a small hydraulic diameter leads
to a low value of Reynolds number, often in the laminar flow
range, making the assumption of constant Nusselt number (for
all liquid flow) quite reasonable in many small heat exchangers employing minichannels or microchannels. A more
detailed parametric analysis is given by Kandlikar (2001b).
For implementing small-diameter channels in evaporators, a thermal equipment designer needs good design tools to
predict the flow boiling heat transfer coefficient. Currently,
there are no specific correlations available for this purpose. In
Satish G. Kandlikar is a professor and Mark E. Steinke is a graduate student in the Mechanical Engineering Department, Rochester Institute
of Technology, Rochester, N.Y.
THIS PREPRINT IS FOR DISCUSSION PURPOSES ONLY, FOR INCLUSION IN ASHRAE TRANSACTIONS 2003, V. 109, Pt. 1. Not to be reprinted in whole or in
part without written permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1791 Tullie Circle, NE, Atlanta, GA 30329.
Opinions, findings, conclusions, or recommendations expressed in this paper are those of the author(s) and do not necessarily reflect the views of ASHRAE. Written
questions and comments regarding this paper should be received at ASHRAE no later than February 7, 2003.
FLOW BOILING CORRELATIONS
FOR MINICHANNELS
Literature Review
Figure 1 Flow boiling map in the saturated region
depicting the trends in flow boiling heat transfer
coefficient with quality, Kandlikar (1991a).
his earlier work, Kandlikar (2002a, 2002b) observed that the
Kandlikar (1990, 1991b) flow boiling correlation is able to
predict flow boiling heat transfer in large diameter tubes quite
well at high flow rates, but significant overprediction was seen
at lower flow rates in minichannels. He identified the presence
of laminar flow conditions as the main reason for the overprediction. In the present work, the low flow rate data are further
analyzed, and the range of applicability of the Kandlikar
correlation is extended to cover the laminar and laminar-turbulent transition.
The classification of small diameter channels is being
actively addressed in the literature. According to a new classification proposed by Kandlikar and Grande (2002), the
following ranges are employed:
Conventional channels
Dh > 3 mm
Minichannels
200 µm ≤ Dh < 3 mm
Microchannels
10 µm ≤ Dh < 200 µm
Transitional Channels
10 µm > Dh > 0.1 µm
(100 nanometer, nm,
or1000 Å)
Molecular Nanochannels
Transitional
Microchannels
10 µm ≥ Dh > 1 µm
Transitional
Nanochannels
1 µm ≥ Dh > 0.1 µm
Flow Conditions Covered by Conventional
Channel Flow Boiling Correlation
Flow boiling heat transfer correlations, such as those of
Kandlikar (1990, 1991b), utilize the single-phase, all-liquid
heat transfer coefficient in predicting the nucleate boiling and
convective boiling components as given by the following
equations.
 h TP, NBD
h TP = l arg er o f 
 h TP, CBD
h TP, NBD = 0.6683Co
– 0.2
+ 1058.0Bo
0.1 µm ≥ Dh
The classification is based on the mean free path of molecules in the single-phase flow and surface tension effects and
flow patterns in the two-phase flow applications.
2
There are a number of correlations available in the literature for predicting flow boiling heat transfer coefficient
inside a channel. The correlations by Chen (1966), Shah
(1982), Gungor and Winterton (1987), and Kandlikar (1990,
1991b) are among the widely used ones. An important feature
that is often overlooked in comparing the correlations is the
trends predicted by these correlations for heat transfer coefficient variation with quality.
Kandlikar (1998) developed a flow boiling map, shown in
Figure 1, to depict the variation of heat transfer coefficient, h,
with quality, x. The liquid to vapor density ratio and the boiling
number are used as parameters. For a high density ratio (ρL/
ρG), the convective effects dominate as quality increases and
lead to an increasing trend in h with increasing x. On the other
hand, a high boiling number results in a higher nucleate boiling contribution, which tends to lower h as the vapor fraction
increases, resulting in a decreasing trend in h with increasing
x. For example, the high-pressure water data exhibit a decreasing trend in h vs. x, while the low-pressure water data display
the familiar increasing h vs. x trend. Refrigerants such as R113, R-114, R-11 (with a low value of liquid to vapor density
ratio at normal refrigeration operating conditions) exhibit a
decreasing trend of heat transfer coefficient with quality. The
heat transfer coefficient thus exhibits all three trends depending on the values of density ratio and boiling number. This map
is based on the trends seen in conventional channels. In the
present work, the correlation and trends are verified for
minichannels.
h TP, CBD = 1.136Co
– 0.9
+ 667.2Bo
(1 – x)
0.7
(1 – x)
(1 – x)
0.7
0.8
0.8
(1 – x)
f 2 ( Fr LO )h LO
0.8
(5b)
F Fl h LO
f 2 ( Fr LO )h LO
0.8
(5a)
(5c)
F Fl h LO
The single-phase, all-liquid-flow heat transfer coefficient
hLO is given by the following correlations by Petukhov and
Popov (1963) and Gnielinski (1976), respectively.
CH-03-13-1
TABLE 1
Table of Recommended FFl (Fluid Surface Parameter)
Values in Flow Boiling Correlation
by Kandlikar (1990, 1991b)
Fluid
FFl
Water
1.00
R-11
1.30
R-12
1.50
R-13B1
1.31
R-22
2.20
R-113
1.30
R-114
1.24
R-134a
1.63
R-152a
1.10
R-32/R-132
3.30
R-141b
1.80
R-124
1.00
Kerosene
0.488
Re LO Pr L ( f ⁄ 2 ) ( k L ⁄ D )
h LO = ------------------------------------------------------------------2⁄3
0.5
1 + 12.7 ( Pr L – 1 ) ( f ⁄ 2 )
f 2 ( Fr LO ) = 1.0 .
(6)
(7)
for 3000 ≤ ReLO ≤ 104, where f = [1.58ln(ReLO)-3.28]-2, is the
friction factor, and FFl is a fluid-surface parameter. FFl for
various liquid-surface combinations is given in Table 1.
The correlation given by Equations 5a to 5c considers the
flow conditions existing in the evaporator. It is applicable to
the wetted wall region of the evaporator tube, starting from the
saturated flow boiling at near-zero quality to the location of the
dryout. The separated flow in conventional tubes causes the
liquid to flow along the bottom of a horizontal tube evaporator,
while the vapor flows in the upper portion of the tube, separated by a thin liquid film from the wall. The Froude number
correction factor (f2 = 25FrLO, with a maximum value limited
to f2 = 1.0) predicts the net effect of this flow structure on the
flow boiling heat transfer in horizontal tubes. It should not be
treated as the identifier for the separated flow regime but
should be considered as the multiplier that includes the effect
of the separated flow structure on heat transfer. It should be
noted that this multiplier is able to predict the heat transfer data
in the separated flow regime extremely well; for example,
Kandlikar (1990) showed that the data of Chawla (1967) for R11 is predicted accurately, within 10% or less, by the above
correlation in various tubes ranging from 3 to 25 mm diameter.
CH-03-13-1
(8)
Flow Boiling Correlation in
Minichannels and Microchannels
for 104 ≤ ReLO ≤ 5 × 106, and
( Re LO – 1000 ) Pr L ( f ⁄ 2 ) ( k L ⁄ D )
h LO = -----------------------------------------------------------------------------2⁄3
0.5
1 + 12.7 ( Pr L – 1 ) ( f ⁄ 2 )
In minichannels and microchannels, the flow pattern
observations made by Kandlikar (2001a) showed that a separated flow pattern does not exist in small diameter channels
due to a strong surface tension effect, which draws liquid all
around the circumference of the tube. Therefore, the Froude
number correction factor, FrLO in Equations 5b and 5c, is taken
as 1 for minichannels and microchannels.
Froude number correction factor for flow boiling in horizontal minichannels and microchannels, in Equations 5b and
5c, in the entire range of Froude numbers is given by
The flow boiling correlation for minichannels is given by
Equations 5a through 5c and Equation 8. The single-phase allliquid-flow correlations given by Equations 6 and 7 are
replaced by appropriate laminar single-phase all-liquid-flow
correlations as described below.
The Reynolds number for all-liquid flow in minichannels
and microchannels generally falls in the laminar flow region
due to (1) the small hydraulic diameter and (2) lower mass
fluxes employed to limit the pressure drop in the flow channel.
The single-phase flow heat transfer coefficient in the correlation given by Equations 5a to 5c, therefore, needs to be appropriately adjusted to reflect the laminar flow conditions.
For a circular channel, the Nusselt numbers for fully
developed flow under constant heat flux and constant temperature boundary conditions are given by the following equations:
NuH = 4.36
(9)
for constant heat flux boundary condition in circular tubes,
NuT = 3.66
(10)
for constant temperature boundary condition in circular tube.
For a square cross section, the above numbers are NuH =
3.61 and NuT = 2.98. A detailed listing for other geometries is
found in Kakac et al. (1987).
The laminar to turbulent transition takes place over a
range of Reynolds numbers from 1900 to 3500, depending on
the flow configuration and inlet conditions. A recent study by
Kandlikar and Campbell (2002) confirms this range for the
flow of oil in a 25.4 mm inner diameter tube. It was seen that
depending on the inlet condition, the flow may exhibit turbulent behavior for Reynolds numbers as low as 1900. Such a
study is not available for flow in minichannels and microchannels.
The flow boiling correlation given by Equations 5a to 5c
is thus modified to include the laminar, single-phase, all-liquid
heat transfer coefficient given by Equations 9 and 10 for circular tubes. However, the presence of the two-phase flow is
believed to further influence the transition to turbulent flow.
The results of comparison with the available experimental data
are discussed in the following sections.
3
TABLE 2
Selected Flow Boiling Heat Transfer Studies for Minichannels
Fluid/Heating
Method
x
Comments
1,933 2,013
8.8 -90.75
0 - 0.9
Heat transfer identified with
various flow patterns, h
decreases with increasing x
35 -300
mL/min
217- 626
50 - 600
0.01-0.65 Average h over the test section
decreases with increasing outlet x
50 -200
372- 2,030
5 - 20
Avg., 0.1 - H decreases with increasing x
0.9
for all G except G=200; data
compares well with previous
large dia. data
G, kg/m2s
Re
Round, D=2.92 mm
50 -300
54 rectangular parallel
microchannels, 1mm deep,
0.27 mm wide, 20.52 mm
long
R-134a, Resistance Round, D=2 mm, 28 parallel
heaters in the contubes
tacting copper
plates
Wambsganss, France, R-113, direct elecJendrzejczyk, Tran,
tric heating of tube
1993
Ravigururajan, Cuta,
McDonald, and
Drost, 1996
Yan and Lin, 1998
q
kW/m2
Channel Specifications
Author/Year
R-124, electric
heater
Lin, Kew, and Corn- R-141b, direct elecwell, 1999
tric heating of tube
Round, D=1 mm
510
1,591
18 - 72
0-1
h increases with x at lower q
and decreases with x at higher
q
Kamidis and RaviguR-113, electric
rurajan, 1999
heating of the base
block
Round, copper – 2.78 mm,
3.97 mm, 4.62 mm, Al. –
1.97 mm
Re = 1901250
190-1250
30 - 100
-
Quality not reported
R-11, electrically
heated
Rectangular,
1×20×357 mm
G = 60 4586
-
-
Subcooled
and low x
Saturated data well represented by Kandlikar (1990,
1991b) correlation
Bao, Fletcher,
Haynes, 2000
R-11 and R-123,
wrapped band heaters
Copper tube, D=1.95 mm
50 -1800
-
5 - 200
0 - 0.9
Nucleate boiling dominant in
the entire range
Kim and Bang, 2001
R-22, electrical
Round and square, Dh=1.66
wire heating around
mm
test section
384 -570
2,8495,873
2 - 10
0 - 0.8
h increases with increasing x
Warrier, Pan, and
Dhir, 2001
FC-84/water heated
557 -1600
-
0 - 59.9
0 - 0.55
h decreases with increasing x
93 - 570
536- 2,955
18 - 72
-0.02 - 1.0
h increases with x at lower q
and decreases with x at higher
q
Lakshmi-narasimhan
et al., 2000
Rectangular, Dh=0.75 mm
Lin, Kew, and Corn- R-141b, direct elec- Round, D=1.1 mm, 1.8 mm,
well, 2001
tric heating of tube
2 mm × 2 mm
TABLE 3
Absolute Mean Deviation (AMD) with Predicted Values
for Reported Data Sets in Selected Papers
Selected Paper
Bao et al. (2000)
Absolute Mean Deviation (percent),
Single-Phase Correlation Used
16.0, transition and turbulent flow
Kamidis and Ravigururajan 21.1, all turbulent flow
(1999)
Kim and Bang (2001)
27.9, all transition flow
Lin et al. (1999)
12.3, laminar and transition flow
Lin et al. (2001)
21.9, laminar and turbulent flow
Ravigururajan et al. (1996) 16.3, all laminar flow
Wambsganss et al. (1993)
19.7,* all turbulent flow
Yan and Lin (1998)
15.5, laminar and turbulent flow
*
as calculated by Wambsganss et al. (1993) with original correlation by Kandlikar (1990, 1991b)
4
Details of the Experimental Data Analyzed
The refrigerants used in the present study include R-11,
R-12, R-113, R-123, R-124, R-134a, and R-141b. The mass
flux range is between 50 and 1600 kg/m2s, and the heat flux
range is between 5 and 600 kW/m2. Only those channel
hydraulic diameters falling within the minichannel diameter
range were investigated; the actual range of hydraulic diameters considered is from 400 µm to 2.97 mm. Currently there are
no complete sets of reported experimental data available for
microchannels. In the present work, only those sets that
reported complete data needed for analysis are included. Table
2 shows the details of the data sets considered.
RESULTS AND DISCUSSION
Eight data sets from available literature are used in the
present analysis since the detailed data tabulations for all sets
reported in Table 2 were not available. The results of comparison with the present correlations given by Equations 5a-5c
and Equations 9 are shown in Table 3. In the following paraCH-03-13-1
Figure 2 Wambsganss et al. (1993) R-113 data (points)
compared to the present correlation (lines) using
turbulent
(Dittus-Boelter)
single-phase
correlation. Psat = 150 kPa; Re = 1,995, 2,013,
and 1,934.
Figure 3 Revigururajan et al. (1996) R-124 data (points)
compared to the present correlation using
laminar single-phase equation in rectangular
channels. q” = 50-600 W/m2; Re = 217-626.
graphs, only a few representative plots are displayed due to
space constraints.
Figure 2 shows a comparison of Wambsganss et al. (1993)
data with the present correlation. The tube diameter is 2.92
mm with R-113 as the working fluid. Since the Reynolds
number is around 2000, the use of Gnielinski or Dittus-Boelter
correlations is not appropriate. Although not applicable, they
are used to represent the turbulent behavior in the single-phase
region. The Wambsganss et al. (1993) data falls close to the
predictions using the Dittus-Boelter single-phase correlation,
while using laminar flow equation results in significant underprediction. The flow structure is thus seen to be turbulent in
character with Re around 2000. Although the use of the DittusBoelter correlation results in a very good agreement, its use is
not justified as the Reynolds number of 2000 is well below the
range of applicability of the Dittus-Boelter correlation.
Figure 3 shows a comparison of the present correlation
with Ravigururajan et al. (1996) data for R-124 in parallel
rectanuglar channels with a hydraulic diameter of 0.425 mm.
The Reynolds number range is between 217 and 626. The
present correlation scheme results in a mean absolute deviation of 16.3% using the single-phase laminar flow correlation.
Another data set by Yan and Lin (1998) is shown in Figure
4 for a Reynolds number of 525. Here the agreement for R134a in a 2-mm-diameter tube with the Kandlikar correlation
using the laminar all-liquid-flow single-phase correlation is
seen to be very good.
An exhaustive data set obtained by Lin et al. (2001) covers
a Reynolds number range of 535-2955 for R-141b. The low
Reynolds number data are well represented by the laminar
flow equation, while the higher Reynolds number data fall in
the transition region. Details of the comparison with the
CH-03-13-1
Figure 4 Yan and Lin (1996) data (points) for R-134a
compared to the correlation by Kandlikar (1990,
1991b) using laminar single-phase equation. G
= 50kg/m2s, Re = 506.
present correlation are shown in Figures 5 to 11 and discussed
in the following paragraphs.
Figure 5 shows a comparison of a series of data sets
obtained by Lin et al. (2001) at a constant mass flux corresponding to Re = 1160. Using the laminar flow equation for
fully developed flow, the Kandlikar correlation is seen to accurately predict the heat transfer coefficient as well the trends
over the entire range of heat fluxes. Use of the turbulent flow
correlation (Dittus-Boelter) results in a significant overprediction, although, as explained earlier, the Dittus-Boelter correlation is used simply to capture the turbulent flow
characteristics.
5
Figure 5 Flow boiling data of Lin et al. (2001), Figure 3a,
compared to the correlation by Kandlikar (1990,
1991b) using laminar single-phase correlation.
Fluid = R-141b, dc = 1.1 mm, Ffl = 1.8, q” = 11.3
- 53.3 kW/m2; ReLo = 1,156.
Figure 6 Flow boiling data of Lin et al. (2001), Figure 4a,
compared to the correlation by Kandlikar (1990,
1991b) using laminar and turbulent single-phase
correlations; dc = 1.8 mm, q” = 53.3 kW/m2,
ReLO = 1089.
Figures 6 to 8 show comparisons of specific data sets by
Lin et al. (2001) with the present correlation using laminar and
turbulent flow single-phase correlations. Effect of a systematic increase in Reynolds number on the correlation comparison is illustrated in these figures.
Figure 6 shows the data for Re = 1089 for R-141b using
the laminar (solid line) and turbulent (dashed line) correlations. The experimental data fall close to the prediction using
the laminar single-phase correlation. The predicted trend in h
vs. x also closely matches with the data. Figure 7 shows similar
results for Re =1156.
Figures 8, 9, and 10 show comparisons similar to those in
Figures 6 and 7 but at increasing Re of 1600, 1970, and 2955,
respectively. As Reynolds number increases, the agreement of
data shifts from predictions using the laminar single-phase
correlation toward the ones using the turbulent single-phase
correlation. Although the Dittus-Boelter and Gnielinski correlations are employed here at such low values of Re, their use
is intended to indicate the trends with the turbulent flow correlation. One could surmise from Figures 8 to 10 that the flow
enters the transition region for Re above 1600.
Figure 11 shows a plot for the same conditions as those in
Figure 10 but for a higher value of heat flux. It is seen that the
higher value of heat flux causes a shift toward the turbulent
region. This indicates that the increased bubble nucleation,
caused by higher heat flux, causes a shift toward the turbulent
region.
The transition in the single-phase all-liquid-flow correlation from laminar to turbulent is seen to depend on the channel
hydraulic diameter and Reynolds number. A secondary effect
due to heat flux is seen through Figures 10 and 11; however,
further experimental data are needed to validate this effect.
Figure 12 is a plot depicting the correlation—laminar,
Dittus-Boelter, or Gnielinski for hLO—that results in the best
agreement with the flow boiling data. For this plot, all data sets
Figure 7 Flow boiling data of Lin et al. (2001), Figure 3a,
compared to the correlation by Kandlikar (1990,
1991b) using laminar and turbulent single-phase
correlations; dc = 1.1 mm, q” = 34.6 kW/m2, ReLO
= 1156.
6
listed in Table 3 are included. It is seen that for ReLO below
1600, the use of the laminar flow correlation for hLO in Equations 5a to 5c predicts the data well in all cases except for one.
For ReLO > 3000, the use of Gnielinski correlation provides the
best results. In the intermediate region, between 1600 and
3000, the picture is not clear.
Providing more accurate transition criteria is not possible
at this stage since, in general, the transition region is very difficult to model. The additional complexity introduced by nucleation and two-phase flow makes it even more difficult to
develop predictive techniques for flow boiling in the transition
region of Re from about 1600 to 3000. The particular flow
geometry leading to the test section, such as location of a bend,
CH-03-13-1
Figure 8 Flow boiling data of Lin et al. (2001), Figure 3b,
compared to the correlation by Kandlikar (1990,
1991b) using laminar and turbulent single-phase
correlations: dc = 1.1 mm, q” = 36.2 kW/m2,
ReLO = 1600.
Figure 9 Flow boiling data of Lin et al. (2001), Figure 7b,
compared to the correlation by Kandlikar (1990,
1991b) using laminar and turbulent single-phase
correlations: dc = 2 mm, q” = 40.2 kW/m2, ReLO
= 1970.
projections, or distributors, etc., also influences the transition
from laminar to turbulent flow. As a recommendation, for
ReLO > 3000, use of Gnielinski correlation is suggested, while
the laminar single-phase correlation is recommended for ReLO
< 1600. Further work is being done by the authors for developing an appropriate interpolation scheme in the region of
1600 < ReLO < 3000.
CONCLUSIONS
1.
2.
3.
The single-phase all-liquid flow in minichannels and
microchannels is generally in the laminar region. The
present work extends the range of the correlation by Kandlikar (1990, 1991b) by introducing the use of fully developed laminar flow equations, such as Equation 8, for the allliquid-flow heat transfer coefficient in Equations 5a
through 5c.
Figure 10 Flow boiling data of Lin et al. (2001), Figure 4b,
compared to the correlation by Kandlikar (1990,
1991b) using laminar and turbulent single-phase
correlations: dc = 1.8 mm, q” = 36.2 kW/m2,
ReLO = 2995.
The transition between the laminar and turbulent flow, as
seen through the single-phase all-liquid-flow correlation is
not well defined. In general, the flow with ReLO < 1600 may
be treated as fully developed laminar flow, while the flow
may be considered in the transition region for 1600 < ReLO
< 3000. The Gnielinski correlation is applicable for ReLO >
3000. An appropriate interpolation scheme needs to be
developed in the region of 1600 < ReLO < 3000. The singlephase correlations are used in conjunction with the flow
boiling correlation by Kandlikar (1990, 1991b) given by
Equations 5a to 5c.
4.
The laminar to turbulent transition in the flow boiling
depends on the all-liquid-flow Reynolds number, the channel hydraulic diameter, and, to a lesser extent, on the heat
flux. Presence of two-phase flow and the nucleating
bubbles appear to introduce additional complexity in the
transition conditions.
Based on the data analyzed in this work, it is seen that the
trends in h versus x exhibited in minichannels are similar to
those observed in conventional channels. The use of the
laminar flow equation results in excellent agreement of the
available experimental data with a correlation by Kandlikar
(1990, 1991b). More accurate predictive methodology
needs to be developed for predicting hLO in the transition
region.
5.
Additional systematic experiments are recommended in the
transition region before any refinements in the correlation
can be made at this stage.
CH-03-13-1
7
Figure 11 Flow boiling data of Lin et al. (2001), Figure 4b,
compared to the correlation by Kandlikar (1990,
1991b) using laminar and turbulent single-phase
correlations: dc = 1.8 mm, q” = 72.6 kW/m2,
ReLO = 2995.
6.
It is expected that additional changes may have to be incorporated in the correlation for very low Reynolds number
flow in smaller diameter channels as the data become available in literature.
NOMENCLATURE
As
Bo
Co
D
dc
f
FFl
=
=
=
=
=
=
=
Fr
hLO
=
=
hTP
iLG
kL
L
Nu
NuH
=
=
=
=
=
=
NuT
=
q, q”
ReLO
=
=
8
heat transfer surface area, m2
boiling number, = q/(GiLG)
convection number, = (ρG/ρL)0.5((1-x)/x)0.8
tube diameter, m
channel hydraulic diameter, m
friction factor
fluid-surface parameter recommended by Kandlikar
(1990, 1991a)
Froude number
all-liquid-flow single-phase heat transfer
coefficient, W/m2 °C
two-phase heat transfer coefficient, W/m2 °C
latent heat of vaporization, J/kg
thermal conductivity of liquid, W/m°C
length of tube, m
Nusselt number
Nusselt number for constant heat flux boundary
condition
Nusselt number for constant temperature boundary
condition
heat flux, W/m2
all liquid flow Reynolds number
Figure 12 Flow boiling correlation map. Plot of hydraulic
diameter versus Reynolds number showing which
Nusselt Number correlation is used to predict
hLO.
T
x
V
= temperature, °C
= quality
= flow volume, m3
Greek letters
µ
ρ
= viscosity, kg/m-s
= density, kg/m3
REFERENCES
Bao, Z.Y., et al. 2000. Flow boiling heat transfer of Freon R11 and HCFC123 in narrow passages. International
Journal of Heat and Mass Transfer 43: 3347-3358.
Chawla, J.M. 1967. Warmeubergang und Druckabfall in
waagrechten Rohren bei der Stromung von verdampfenden Kaltemitteln. VDI-Forschungsheft, No. 523.
Chen, J.C. 1966. A correlation for boiling heat transfer to
saturated fluids in convective flow, industrial and engineering chemistry. Process Design and Development
5(3): 322-329.
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