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CORRELATING EVAPORATION HEAT TRANSFER COEFFICIENT OF
REFRIGERANT R-134a IN A PLATE HEAT EXCHANGER
Vincent D. Donowski
and
Satish G. Kandlikar
Mechanical Engineering Department
Rochester Institute of Technology
Rochester, NY
ABSTRACT
The present study deals with developing a predictive methodology for evaporation heat
transfer coefficient of refrigerant R-134a flowing in a plate heat exchanger. Correlation schemes
proposed by Yan and Lin (1999b) for modeling the heat transfer coefficient in both a singlephase water-to-water experiment and a two-phase evaporation experiment with refrigerant R134a in a plate heat exchanger are found to result in large discrepancies with their own
experimental data. In the present study Yan and Lin’s plate heat exchanger data is used to
develop improved correlations for single-phase heat transfer coefficient of water as well as twophase evaporation heat transfer coefficients of refrigerant R-134a. Two schemes are presented
for correlating the two-phase data, and they are compared with the correlating schemes available
in literature (Yan and Lin, 1999b; and Kandlikar, 1991). It is found that the new correlation
schemes developed in this work provide an accurate fit to the experimental data, and a final
correlation sche me is proposed for future use in modeling the evaporation heat transfer
coefficient of refrigerant R-134a in a plate heat exchanger configuration.
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NOMENCLATURE
Bo
Co
cp
Dh
Di
f
Ffl
G
hLG
Nu
Pr
q”w
Re
x
Boiling number, eq. (18)
Convective number, eq. (17)
specific heat, J/kgK
hydraulic diameter, m
tube inside diameter, m
friction factor
fluid-dependent parameter
mass flux, kg/m2 s
enthalpy of vaporization, J/kg
Nusselt number, dimensionless, eq. (5)
Prandtl number, dimensionless
imposed wall heat flux, W/m2
Reynolds number, dimensionless
vapor quality
Greek Symbols
α
heat transfer coefficient, W/m2 K
η
viscosity, N s/m2
λ
thermal conductivity, W/m K
ρ
density, kg/m3
Subscripts
eq
G
L
m
r
TP
w
wall
equivalent all- liquid number
vapor phase
liquid phase
average value for the two phase mixture or between the inlet and exit
refrigerant, two-phase
two-phase
water
wall/fluid near the wall
2
1.
INTRODUCTION
Plate heat exchangers have been a popular choice for use in chemical and food processing
applications since the 1930s (Hewitt et al., 1994). Within a compact design, plate heat
exchangers offer low fabrication costs, ease of cleaning, adaptability, and high thermal
efficiency. Introduction of plate heat exchangers as evaporators and condensers in refrigeration
and air conditioning applications has gained most of its interest in the last 20 years (Yan and Lin,
1999b). To date, most studies about plate heat exchanger applications in published literature
focus on the single-phase liquid-to-liquid heat transfer. As a result, limited data resources are
available for plate heat exchangers used as evaporators in two-phase flow boiling applications.
With public awareness of environmental safety concerns in recent years, degradation of
the ozone layer in the atmosphere through the use of CFC refrigerants has been of great concern.
In response to these issues, new HFC refrigerants such as R-134a, R-143a, and R-125 have been
developed as substitute chemicals for use in refrigeration and air conditioning systems. An
excellent example of this conversion to new refrige rants is the introduction of refrigerant R-134a
into automobile air conditioning systems, in place of the traditional CFC refrigerant system. In
order to improve the design of heat exchange systems utilizing these new refrigerants, it is
necessary to first gain an understanding of the fluid heat transfer characteristics through
experimentation and data collection. For these new refrigerants, the majority of published works
have focused on single-phase liquid-to- liquid heat transfer. One recent study (Yan and Lin,
1999b), involves two-phase evaporation heat transfer of the new refrigerant R-134a in a plate
heat exchanger.
The present work analyzes the experimental data of Yan and Lin (1999b) and proposes
two new correlation schemes for the evaporation heat transfer coefficient of refrigerant R-134a
in a plate heat exchanger. These new correlation schemes are compared with the original
experimental data and other correlation schemes available in literature.
2.
REVIEW OF LITERATURE
In this section previously published studies by other investigators are briefly reviewed to
provide relevant information to the present work.
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2.1
Early Correlation Schemes
Many early literature studies focus on the single-phase heat transfer of fluids flowing in a
smooth tube to develop correlation schemes to model the heat transfer coefficients in other
geometries. The most widely used single-phase correlation in a pipe is the well-known DittusBoelter equation (Dittus and Boelter, 1930) and is given by
Nu = 0.023 Re 0.8 Pr 0.4
(1)
where Re represents the fluid Reynolds number, Pr is the Prandtl number, and Nu is the Nusselt
number. Other noteworthy equations are the Sieder-Tate equation (Incropera and Dewitt, 1981),
Nu = 0.023 Re 0.8 Pr1/3 (ηm /ηwall)0.14
(2)
and the Gnielinski correlation (Gnielinski, 1976),
Nu =
( f / 2 )(Re − 1000 )Pr
(
1 + 12.7 f / 2 Pr
2/3
[1 + (D / L) ](Pr/ Pr )
− 1)
2/3
0 .11
i
w
.
(3)
The concept of modeling the two-phase heat transfer coefficient can be traced back to the
1960s. Studies of two-phase phenomenon can likely be traced back earlier; however, Bergles
and Rohsenow (1964) made a significant contribution to this area by suggesting an additive
model for convective and nucleate boiling components. Chen (1966) is also noted for suggesting
an additive model for saturated boiling, using a nucleate boiling term based on a pool boiling
equation by Foster and Zuber (1955), and a convective contribution utilizing the Dittus-Boelter
(1930) equation noted earlier. Both of these models present an ideal that flow boiling can be
separated into a nucleate boiling term as characterized by still fluid being boiled by heat applied
directly at nucleation sights, and a convective boiling term to characterize heat transferred to the
moving fluid. When these terms are brought together in the additive model, the dominant
4
contributing term is decided based on the liquid Reynolds number, a dimensionless number
characterized by liquid mass flow and viscosity.
2.2
Experimentation With Smooth Tubes
Kattan et al. (1998a, 1998b, 1998c) conducted smooth tube experimentation for flow
boiling of several refrigerants, including refrigerant R-134a. Data from Kattan et al.’s work
shows that the heat transfer coefficient will continue to increase with vapor quality, but will
show a sudden drop at a qua lity of approximately 0.85. For very low mass flux the heat transfer
coefficient shows little change as vapor quality increases. Yan and Lin (1998) show similar
results to Kattan et al. (1998b) for the evaporation of refrigerant R-134a in a small pipe. Little
change is seen in the heat transfer coefficient as vapor quality increases for low values of heat
and mass flux. Higher heat transfer values are seen for higher mass flux, or lower saturation
temperature. For higher heat flux, higher values of heat transfer are seen; however, the heat
transfer coefficient decreases as vapor quality increases. Gungor and Winterton (1986) perform
an extensive review of a large flow boiling data base to propose a correlation for two-phase flow
boiling based on the two component model suggested by Chen (1966). The flow boiling
correlation by Kandlikar (1990) was developed with over 10,000 data points and provides an
accurate representation of parametric trends for qualities up to 0.7-0.8. It has been tested with R134a data as well. Since the augmentation techniques employed in tubes, compact evaporators,
and other enhanced geometries delay the transition to dryout beyond a quality of 0.8, the present
work focuses on improving the correlation in this range.
2.3
Augmented Surfaces
Augmented surface tubes are designed to provide better heat transfer than smooth tubes
through the use of enhanced surfaces. Some examples of enhanced surfaces include fins, coil
springs, twisted tape, and helical ribs. These specialized surfaces serve to increase the heat
transfer area in fluid flow, thereby adding significant enhancement to the liquid heat exchange
capabilities, as well as improvements resulting from an increase in the local heat transfer
coefficient.
5
For refrigerant R-134a, Singh et al. (1996) provide an experimental study of the flow
boiling heat transfer coefficient in a microfin tube. Results show that the heat transfer coefficient
is higher for higher heat flux and for higher mass flux. For low mass flux little change is seen in
the heat transfer coefficient as vapor quality increases. Kandlikar (1991) proposes a model for
correlating flow boiling heat transfer in augmented tubes based upon previous work (Kandlikar,
1990) with flow boiling in smooth tubes. Kand likar uses the additive model suggested by
Bergles and Rohsenow (1964) as a basis for developing two-phase correlating schemes.
2.4
Compact Evaporators and Plate Heat Exchangers
Kandlikar (1991) suggested that heat exchangers, serving as compact evaporators in this
particular study, can be treated similarly to augmented tubes for analysis. From previous work in
correlating heat transfer coefficients in smooth tubes (Kandlikar, 1990), Kandlikar introduced
augmentation factors to account for surface enhancements in augmented tubes and compact
evaporators. Results from the Kandlikar (1991) study show the new model was able to predict
the heat transfer coefficients within 10-15 percent.
For evaporation heat transfer of refrigerant R-134a in a plate heat exchanger, Yan and
Lin (1999b) provide the only detailed published data in a usable form by other researchers. Yan
and Lin first experimented with liquid-only, water-to-water heat transfer to analyze the
uncertainty in experimentation, and to develop a single-phase correlation which can be adapted
to the two-phase situation. The two-phase experiment is then employed for refrigerant R-134a to
investigate the effects of mean vapor quality, mass flux, heat flux, and pressure on the
evaporation heat transfer coefficient. A correlation scheme is introduced by Yan and Lin
(1999b) for modeling the evaporation heat transfer coefficient of refrigerant R-134a in the plate
heat exchanger.
2.5
Summary of Experimental Data and Related Correlation Work
Table 1 presents a brief summary of some of the more relevant studies discussed above.
For the two-phase heat transfer of refrigerant R-134a, published studies have been focused
6
toward smooth and augmented surface tubes. The experimental ranges of the study by Yan and
Lin (1999b) are also presented in this table.
2.6
Objectives of the Present Work
The objectives of the present work are as follows:
1.
Develop a correlation scheme for predicting the evaporation heat transfer coefficient of
refrigerant R-134a in a plate heat exchanger based on experimental data from the literature
and the additive model concept for convective and nucleate boiling contribution terms.
2. Compare the newly developed correlation scheme to other models proposed in the literature
for similar situations.
3. Propose the correlation scheme best suited for use in modeling the evaporation heat transfer
coefficient of refrigerant R-134a in a plate heat exchanger.
3.
DATA ANALYSIS
Yan and Lin (1999b) provide experimental data for evaporation heat transfe r of
refrigerant R-134a in a plate heat exchanger, which serves as the data source for the present
work. Three plates of commercial SS-316 stainless steel formed the plate heat exchanger. Each
plate surface had a corrugated sine shape and 60 degree of chevron angle to the plate vertical
axis. The plates measured 500.0 mm in length by 120.0 mm in width, with corners rounded at a
25.0 mm radius. The thickness of the plates was 0.4 mm, with 3.3 mm pitch between plates and
10.0 mm pitch of the corrugation. Other dimensions show the connection ports to be spaced at
70.0 mm horizontally and 450.0 mm vertically, each port measuring 30.0 mm in diameter. When
the three plates were pressed together, two counter flow channels were formed. Contrary V
shape corrugations on adjoining plates formed a lattice grid which forced flow to move along the
groove. This lattice formation in plate heat exchangers causes a notably high Reynolds number
and turbulent flow, which enhance heat transfer capabilities. For further details, authors are
referred to Yan and Lin (1999b).
4.
RESULTS AND DISCUSSION
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The single-phase data is first compared with the correlation developed by Yan and Lin
(1999b). An improved single-phase correlation, Correlation I, is then developed and compared
against the data. In the two-phase region, the correlation developed by Yan and Lin is first
compared with their own experimental data. The first correlation scheme, Correlation II,
developed here is based on the model by Kandlikar (1991). In the second correlation scheme,
Correlation III, this model is further modified to provide a better fit especially in the higher
quality range.
4.1
Yan and Lin Single-Phase Correlation
Yan and Lin (1999b) proposed the following single-phase correlation us ing water-to
water data from their plate heat exchanger tests:
Nu = 0.2121 Re 0.78 Pr1/3 (ηm /ηwall)0.14
.
(4)
Using the definition of the Nusselt number, Nu, as
Nu = α Dh /λL
,
(5)
equation 4 can be rearranged to provide the following equation for the heat transfer coefficient.
α w = 0.2121 Re 0.78Pr1/3 (ηm /ηwall)0.14λL/Dh
.
(6)
It should be noted that the single-phase correlation proposed by Yan and Lin (1999b) shows
striking similarity to the Sieder-Tate equation (Incropera and Dewitt, 1981) provided in eq. 2,
which is known to provide reliable results in modeling single-phase liquid heat transfer in
smooth tubes. Here the single-phase model is applied to the plate heat exchanger, with an
increased multiplier to account for surface enhancement through the use of corrugated plates.
Two assumptions must be made in plotting the proposed correlation. Firstly, it is assumed that
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the bulk fluid temperatures are 95 °C for the hot side inlet and 15 °C for the cold side inlet.
Second, it is assumed that the viscosity ratio raised to such a low power can be taken as 1.0.
When Yan and Lin’s correlation is plotted on the same plot with the experimental data, as
shown in Fig. 1, large deviations are noted. This was extensively investigated by contacting the
authors, but the error could not be resolved. Their correlation seems to be off from the data by a
fixed multiplier. To correct this situation, an improved correlation is developed in the present
work as described in the following section.
4.2
Correlation Scheme I – Improved Single-Phase Correlation
Noting the similarity between the Yan and Lin (1999b) proposed correlation and the
Sieder-Tate equation, it seems logical to begin the development of a new correlation using
smooth tube equations as the basis. Starting with the well-known Dittus-Boelter (eq. 1) and
Sieder-Tate (eq. 2) equations, the improved correlation begins to take the form
α w = E1 ReE2 PrE3 λL/Dh
(7)
Here the variables E1 , E2 , and E3 can be varied to fit the data. According to the Dittus-Boelter
and Sieder-Tate equations, and eq. (6), the variable E2 becomes 0.78 or 0.8, and the variable E3
takes on the value of 1/3 or 0.4. Combinations of these variables are used, and the multiplier E1
varied using a spreadsheet solver to develop an improved correlation to best fit the data. The
new Correlation Scheme I results in
α w = 0.2875 Re 0.78 Pr1/3 λL/Dh
(8)
A comparison of the single-phase Correlation I (eq. 8) to the Yan and Lin’s correlation (eq. 6)
and the experimental data is provided in Fig. 1. As seen from this figure, the improved
correlation provides an excellent fit to the experimental data for the single-phase water-to-water
heat transfer in the plate heat exchanger. This equation will be used in the next phase of the
present work for developing an improved two-phase correlation scheme.
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4.3
Yan and Lin’s Two-Phase Correlation Scheme
Yan and Lin (1999b) proposed the following correlation in modeling their own two-phase
data for evaporation heat transfer of refrigerant R-134a,
α r = 1.926 Re eq Pr1/3 Re-0.5 Boeq λL / Dh
(9)
Reeq = Geq Dh / ηL
(10)
Boeq = q”w / (Geq hLG)
(11)
Geq = G [(1 – xm) + xm (ρL / ρG)0.5 ] .
(12)
where,
The terms Re eq and Bo eq are, respectively, the equivalent Reynolds number and equivalent
Boiling number as proposed by Akers (1958). The Reynolds number, Re, and Prandtl number,
Pr, are defined for all liquid flow:
Re = G Dh / ηL
(13)
Pr = ηL cp / λL.
(14)
Fluid properties used in testing the correlation are taken from the REFPROP (NIST, 1999)
refrigerant property computer program. Results of using the Yan and Lin correlation vs.
experimental data can be found in Fig. 2 through Fig. 11. Again for the two-phase scenario,
significant discrepancy is found between the Yan and Lin’s correlation and their experimental
data. Extensive checks were performed to resolve the discrepancy but it was clear that there is a
major error in their correlation as published in the literature. For purposes of the present work it
is desirable to accept that a discrepancy exists in their correlation, and to develop an improved
model to fit the experimental data set.
4.4
Other Two-Phase Correlation Schemes
10
Two-phase correlation schemes were proposed in the works of Kattan et. al. (1998c),
Gungor and Winterton (1986), and Kandlikar (1991). A brief review of these works was
presented in section 2 of this paper, and in Table 1. Here the importance of these studies to the
present work is evaluated for development of an improved model.
Kattan et al. (1998c) developed a two-phase model for various refrigerants based on data
from previous works (Kattan et al., 1998a; and Kattan et al., 1998b). The proposed correlation
scheme utilizes the study of boiling flow pattern as a basis for the proposed model. While the
Kattan flow pattern model provides excellent results in the referenced work, the proposed model
is complex and limited at this point to flow in horizontal tubes.
Based on an early general correlation proposed by Chen (1966), Gungor and Winterton
(1986) developed an additive model for two-phase boiling in tubes and annuli. This model takes
into account the contributions of pool boiling and convective boiling, which are brought together
in determining the heat transfer coefficient. The results provided in the literature for the Gungor
and Winterton model show an uncertainty of +40 %, which is larger than desired for this study.
An additive model was also suggested by Kandlikar (1991) for flow boiling applications.
The Kandlikar work is based on an additive model suggested by Bergles and Rohsenow (1964),
consisting of convective and nucleate boiling components. Kandlikar takes a previous model
(Kandlikar, 1990) for flow boiling in smooth tubes and extends it to augmented tubes and
compact evaporators. Results in the Kandlikar (1991) study show the Kandlikar correlation
scheme to provide a reliable fit to data, with an uncertainty of +15 %.
4.5
Kandlikar Two -Phase Correlation Scheme
For the present work, it is desirable to find a best- fit correlation for the evaporation heat
transfer coefficient of refrigerant R-134a. The Kandlikar (1991) correlation noted above has
been shown in the literature to be adaptable to augmented surface systems while maintaining
reasonable accuracy in results. Kandlikar suggests the following correlation scheme to model
flow boiling for augmented tubes:
α TP,NBD = 0.6683 Co-0.2 (1 – x)0.8 α L ECB
+ 1058.0 Bo 0.7 (1 – x)0.8 Ffl α L ENB
11
(15)
and
α TP,CBD = 1.1360 Co-0.9 (1 – x)0.8 α L ECB
+ 667.2 Bo 0.7 (1 – x)0.8 Ffl α L ENB .
(16)
Equations 15 and 16 solve for the heat transfer coefficient for the nucleate boiling dominant, and
convective boiling dominant cases, respectively. The actual heat transfer coefficient is the larger
of the two values. The factors ECB and ENB are the enhancement factors to be applied to the
convective boiling contribution and nucleate boiling contribution, respectively. The convective
number, Co, and the boiling number, Bo, are defined as
Co = (ρG / ρL)0.5 ((1 – x) / x)0.8
(17)
Bo = q” / (G hLG)
(18)
A fluid-dependent parameter, Ffl, is used in the correlation to account for varying fluid
characteristics. For stainless steel surfaces, Kandlikar (1991) suggests that this fluid-dependent
parameter is equal to 1 for all fluids. The term α L is the all- liquid heat transfer coefficient for the
single-phase situation. Correlation I (eq. 8) was introduced earlier as an improved fit to the
single-phase experimental data, and can be employed here as the all- liquid heat transfer
coefficient for refrigerant R-134a. For the plate heat exchanger, fluid flow is turbulent even at
very low Reynolds numbers. As a result, it is assumed that the heat transfer will rely dominantly
on the convective boiling contribution. Hence, eq. 16 will be used for comparison with the
experimental data.
Fluid properties are again taken from the REFPROP program. Employment of the
Kandlikar correlation here predicts the data with an uncertainty of +20 % for mean vapor quality
between 0.2 and 0.8. Fitting the Kandlikar correlation to the data to minimize absolute error
results in the correlation values ECB = 0.659 and ENB = 0.006 for the augmentation effects of the
heat exchanger, giving the final equation as
α TP,CBD = 1.1360 Co-0.9 (1 – x)0.8 α L ECB
+ 667.2 Bo 0.7 (1 – x)0.8 Ffl α L ENB ,
where,
12
(19)
ECB = 0.659
ENB = 0.006 .
Although the above scheme based on the Kandlikar correlation provides a reasonable fit
to the data, this scheme results in a curve that does not match the shape of the data, especially in
the high quality region as seen in Fig. 2 through Fig. 11 for various mass flux, heat flux and,
pressure conditions. Therefore a new model development is undertaken to match the
experimental data and the trends of heat transfer coefficient in the plate heat exchanger.
4.6
Improved Correlation II – Two -Phase With Augmentation Factors
With reasonable accuracy achieved by eq. (19) above, it is logical to develop an
improved correlation scheme based on the same additive model. Using the same exact form as
the Kandlikar (1991) correlation, the model is represented by
α r = [y1 Coy2 ECB + y3 Boy4 Ffl ENB] (1 – x)y5 αLy6 .
(20)
Variables y1 through y6 , and the augmentation factors, ECB and ENB, are solved for in fitting the
correlation to the experimental data. The fluid-dependent parameter, Ffl, is again taken to be 1.0
for the stainless steel plates. In fitting the proposed correlation to the heat exchanger data using a
spreadsheet solver, the following values are obtained for the constants in eq. (20):
y1 = 2.312,
y2 = -0.3,
y3 = 667.3,
y4 = 2.8,
y5 = 0.003,
y6 = 1,
ECB = 0.512, and ENB = 0.338 .
The final equation for the Correlation Scheme II is given by
α r = [2.312 Co-0.3 ECB + 667.3 Bo 2.8 Ffl ENB] (1 – x)0.003 α L
where
ECB = 0.512,
13
(21)
ENB = 0.338.
Figures 2 through 11 show that Correlation II (eq. 21) provides a better fit than the original
Kandlikar (1991) correlation, with a maximum deviatio n of 17 % for all data points. It can be
seen that the experimental data trend is well matched by Correlation II in the entire range of
quality.
4.7
Improved Correlation III – Two-Phase Without Augmentation Factors
A second improved correlation has been developed in the present work by leaving out the
augmentation factors and the fluid-dependent parameter. This correlation then takes on the form
α r = [z1 Coz2 + z3 Boz4] x mz5 αLz6 z7 .
(22)
A multiplier z7 has been added to the correlation scheme. Here only the variables z1 through z7
need to solved for in fitting the correlation to the experimental data. For the best fit curve for
evaporation of refrigerant R-134a in the plate heat exchanger, the resultant values are
z1 = 1.056,
z2 = -0.4,
z3 = 1.02,
z4 = 0.9
z5 = -0.12,
z6 = 0.98, and z7 = 1.055 .
With these constants, Correlation III takes the following form.
α r = 1.055 [1.056 Co-0.4 + 1.02 Bo 0.9 ] xm-0.12 αL0.98
.
(23)
Correlation III as suggested here provides an excellent fit with a maximum deviation of 16 %, as
seen in Fig. 2 through Fig. 11. As can be seen, the data is well represented in the entire range of
quality.
4.7
Discussion of Results
14
Figures 2 through 11 show the results of the two-phase correlation schemes discussed in
this study. Alternate figures show the predicted heat transfer coefficient plotted against the
experimental heat transfer coefficient with 20% error bounds. It is easily seen from the figures
that the Yan and Lin correlation (eq. 9) yields a large discrepancy, and the Kandlikar correlation
(eq. 16) yields a different curve form the experimental data. The newly developed correlations,
Correlation II (eq. 21) and Correlation III (eq. 23) both provide an excellent fit to the data set.
Correlation III however is developed specifically for the present data set. It lacks the
theoretical basis, and the improvement over Correlation II is quite small, about 1 percent.
Therefore Correlation II represented by eq. (21) is recommended as the final correlation in the
present work.
5.
CONCLUSIONS
The experimental data for evaporation of refrigerant R-134a in a plate heat exchanger
obtained by Yan and Lin (1999b) is used in developing two-phase flow boiling correlation in this
study. As a result of the present work, the following observations can be made:
•
A single-phase correlation, Correlation I (eq. 8), is developed for the single-phase heat
transfer in the 60 degree chevron plate heat exchanger with Dh =6.6 mm. This correlation is
able to represent the experimental single-phase data to within 3 percent.
•
The Kandlikar (1991) scheme for augmented tubes and compact evaporators resulted in a
reasonable overall accuracy, but the trend in the high quality region was not correctly
represented. The original correlation was intended for qualities below 0.8.
•
Two modified correlaions, Correlations II and III were developed to represent the two-phase
data for R-134a in plate heat exchanger obtained by Yan and Lin (1999b). In Correlation II,
the basic form of the Kandlikar (1991) correlation is retained, but the exponents for Bo, Co,
and (1-x), and the constants in the correlation are re-evaluated from the best fit to the
experimental data. Correlation II is able to correlate the data within 17 percent mean error.
It is also able to represent the variation of heat transfer coefficient with quality accurately in
the entire range of quality for all mass flux, heat flux and pressure conditions.
15
•
Correlation III is developed as a simplified form as given by eq. (23). It is obtained as the
best fit to the data, resulting in a mean error of 16 percent. However, since the correlation
lacks a theoretical basis, and the improvement over Correlation II is not significant, it is not
recommended.
•
Correlation II, given by eq. (21) , is recommended for correlating the flow boiling heat
transfer coefficient for R-134a in the 60 degree chevron plate heat exchanger investigated by
Yan and Lin (1999b).
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Transfer, Vol.120, pp. 156-165.
Singh, A., Ohadi, M. M., and Dessiatoun, S., 1996, “Flow Boiling Heat Transfer
Coefficients of R-134a in a Microfin Tube,” Journal of Heat Transfer, Vol. 118, pp. 497-499.
Yan, Y.-Y., and Lin, T.-F., 1998, “Evaporation Heat Transfer and Pressure Drop of
Refrigerant R-134a in a Small Pipe,” International Journal of Heat and Mass Transfer, Vol. 41,
pp. 4183-4194.
Yan, Y.-Y., and Lin, T.-F., 1999a, “Condensation Heat Transfer and Pressure Drop of
Refrigerant R-134a in a Small Pipe,” International Journal of Heat and Mass Transfer, Vol. 42,
pp. 697-708.
Yan, Y.-Y., and Lin, T.-F., 1999b, “Evaporation Heat Transfer and Pressure Drop of
Refrigerant R-134a in a Plate Heat Exchanger,” ASME Journal of Heat Transfer, Vol. 121, pp.
118-127.
17
Table I - Summary of the Experimental Data and Rele vant Correlations
Investigator Experimental
Test Fluid/
Experimental
System
Parameters
Uncertainties
Gungor and Vertical and
Data taken from
Used +40 % for
Winterton,
horizontal tubes 28 authors for 7
experimental
(1986)
and annuli
fluids for saturated uncertainty
and subcooled
boiling
Kandlikar
Augmented
Data taken from
+15 % used for
(1991)
tubes and
literature for
experimental
compact
refrigerants R-11,
uncertainty
evaporators
R-22, R-113
Kattan,
Thome, and
Favrat
(1998c)
Horizontal tubes,
Smooth surface,
Copper,
Di : 10.92 –
12.00 mm
Yan and
Lin, (1998)
Small pipe,
Smooth surface,
Di = 2.0 mm
Yan and
Lin, (1999b)
Plate heat
exchanger,
60 deg chevron,
Dh = 6.6 mm,
Single pass,
Three plates,
Stainless steel
R-134a, R-123,
Accuracy;
R-402A, R-404A,
T: +0.10 o C
R-502;
G: +0.2 %
G: 100 –
P: +0.5 %
2
500 kg/s m
h: +7.2 %
Tsat : -1.3 – 10.3 o C
X: 0.04 – 1.0
q”: 0.44 –
36.54 kW/m2
R-134a;
Uncertainties;
o
Tsat : 5 – 31 C
A: +1 %
q”: 5 – 20 kW/m2
T: +1 o C
G: 50 –
P: +0.001 MPa
2
200 kg/s m
G: +2 %
X: ~0.05 – 0.95
q: +0.5 %
X: +0.03
hr : +6 %
R-134a;
X: 0.1 – 0.9
P: 0.675 –
0.8 MPa
q”: 11 –
15 kW/m2
G: 55 –
70 kg/s m2
Tsat : 25.5 – 31 o C
18
Accuracy;
A: +7e-05 m2
T: +0.2 K
P: +0.002 MPa
G: +2 %
X: +0.03
hr : +15 %
Results
Developed an
additive
model based
on Chen
(1966)
Developed an
additive
model to
account for
surface
enhancements
Developed
two-phase
model based
on flow
pattern
Developed a
two-phase
additive heat
transfer
model, similar
to that
proposed by
Kandlikar
(1990)
Developed a
correlation to
model twophase
evaporation
heat transfer
coefficient of
refrigerant
R-134a