Marko Matkovic˘, Padova, I - Eurotherm 2008

5th European Thermal-Sciences Conference, The Netherlands, 2008
HEAT TRANSFER COEFFICIENT DURING
CONDENSATION OF A HIGH PRESSURE REFRIGERANT
INSIDE A CIRCULAR MINICHANNEL
Abstract
M. Matkovič, A. Cavallini, S. Bortolin, D. Del Col, L. Rossetto
Dipartimento di Fisica Tecnica, University of Padova, Padova, Italy
The heat transfer coefficient during condensation of the high pressure refrigerant R32 inside a
circular single minichannel test tube has been measured locally over the entire span of vapor
qualities. A new experimental apparatus has been adopted in order to obtain precise local heat
transfer coefficient measurements in a wide range of test conditions. The facility has been carefully
calibrated and checked for different error issues prior to the condensation tests.
Finally, the experimental results have been checked against some models available in the open
literature. Notably, the experimental HTC can be well predicted by some macro-scale condensation
models available in the open literature.
Nomenclature
c pw specific heat of water [J kg -1 K -1 ]
h LG heat of vaporization [J kg -1 ]
HTC heat transfer coefficient [W m -2 K -1 ]
m mass flow rate [kg s -1 ]
TC, TP thermocouple, thermopile
r, w, c refrigerant, wall, coolant-water
amb, sat ambient, saturation
MS, PS measuring sector, pre-sector
1 Introduction
A significant and still growing part of the engineering research community has been devoted in the
last few decades to scaling down devices, while keeping or even increasing their functionality. The
introduction of minichannels in the field of enhanced heat and mass transfer is surely one of those
attempts. As a result, compact heat exchangers and heat pipes can be found in a wide variety of
applications: from residential air-conditioning to the spacecraft thermal control. Growing interest
for different solutions can be found also in electronic cooling, though these applications are less
interesting from the condensation point of view due to its exothermal nature. Compact elements
work with reduced refrigerant charge and can usually withstand extremely high system pressures.
Small charges can contribute to reduce the direct greenhouse effects of the systems and to promote
the use of flammable or even toxic refrigerants. Furthermore, resistance to high pressures enables to
use natural refrigerants such as carbon dioxide and hence to operate in supercritical region.
Condensation is one of the most widely used phase change phenomena in process engineering. It is
usually associated to the hot part of systems. When applied to minichannels, forced convective
condensation is usually considered. Heat and mass transfer mechanisms seem to be less complicated
in comparison to the flow boiling phenomenon where more parameters have significant effect on
the process. On the contrary, it may be more difficult to perform local heat transfer coefficient
measurements during condensation inside a single minichannel as compared to the flow boiling
case. In this context, a new experimental test apparatus for heat transfer and fluid flow experiments
inside single minichannels has been designed and built. The most important part of the apparatus is
the test section.

5th European Thermal-Sciences Conference, The Netherlands, 2008
2 The Test Section
Figure 1: Design of the experimental test section.
In order to investigate heat transfer and fluid flow within a single minichannel a unique measuring
test section has been designed (Figure 1) and built. Either single-phase tests or experiments during
forced convective condensation and flow boiling phenomenon can be studied with the present
facility. The test section is made of a straight single minichannel with two diabatic and two
adiabatic sectors along its length (Figure 2). The diabatic sectors work as heat exchangers with an
adoption of a secondary fluid; hence experiments are referred to a constant wall temperature
boundary condition. The two sectors are made from 8 mm external diameter cupper bar with 0.96
mm internal bore which is the minichannel itself. The thick-walled tube was machined externally so
as to obtain cooling water channel within the wall thickness. The tortuous path for the secondary
fluid enables a good water mixing properties and thus allows precise local coolant temperature
measurements. In this test section, 15 thermocouples have been inserted into the water channel
along the MS in order to measure the coolant temperature profile. The enhanced coolant heat
transfer surface area moves the thermal resistance toward the internal side and thus reduces the
experimental heat transfer coefficient error due to the refrigerant to wall temperature difference.
In order to measure precise local HTC values 15 thermocouples have been inserted into the wall
thickness, near the minichannel along the measuring sector, without making thermocouple wires
cross the coolant path. Furthermore, two thermocouples and a thermopile are measuring the
refrigerant temperature by measuring external wall surface temperature of the adiabatic sectors –
stainless steel capillary tubes at the two extremes of the measuring sector. When operating in
condensation mode, the first diabatic sector works as a desuperheater. To avoid big temperature
gradients at the inlet of the measuring sector the desuperheater is used to cool down the superheated
refrigerant to the saturation state at the inlet of the measuring sector. Vapor quality is there obtained
from the thermal balance on the coolant side, whereas saturation conditions are checked using the
adiabatic wall temperature and the pressure measurement in the adiabatic sectors.
Thermocouples, thermopile and pressure ports
for fluid temperature and pressure recording
Figure 2: The test section.
30 thermocouples for wall and coolant
temperature measurements

5th European Thermal-Sciences Conference, The Netherlands, 2008
3 The Experimental Technique
3.1 Theory
Condensation heat transfer is performed in the second diabatic sector. It is equipped with 15
thermocouples set in the water channel along the sector, hence the coolant temperature profile is
obtained (Figure 3). The derivative of the temperature profile is proportional to the local heat flux:
1 d Tc
( z)
q'( z)
= m ⋅ c
cpw
π d
⋅ , [W m -2 ] (1)
⋅ dz
i
and it is associated to the local heat transfer coefficient:
HTC ( z)
=
i
q'( z)
( T ( z) −T ( z)
)
sat
w
. [W m -2 K -1 ] (2)
Local saturation temperature (T sat (z)) of the fluid along the sector is calculated from the two
measured values in the adiabatic sectors. The calculation, which considers frictional pressure drop
and pressure recovery due to condensation, is iterative. It is modified so as to take into account local
pressure gradient profile and make the saturation temperature curve converge with the saturation
temperature measurement at the outlet of the measuring sector. On the other hand, the wall
temperature (T wall (z)) is measured locally.
Considering the conservation of energy in the sector, the coolant temperature change is directly
associated to the corresponding enthalpy variation of the refrigerant. Therefore, the local vapor
quality is calculated as follows:
xz ( ) = x −
in
z
π ⋅d ⋅ q'( z)dz
i
m
r
∫
0
⋅h
LG
. [ / ] (3)
45
dT w ( z)
dz
40
T [°C]
35
30
T ( z) −T ( z)
sat
wall
Sat (TC)
Sat (PT)
Wall
Water
TC+TP
TC inox
25
20
z
0 40 80 120 160 200 240
Axial position [mm]
Figure 3: Temperature measurements within the single minichannel test section.

5th European Thermal-Sciences Conference, The Netherlands, 2008
3.2 Improvement of the Measuring Technique
With the purpose of optimum performance of the setup, different experimental uncertainty issues
were studied. It has been shown that there are certain test conditions, which result in the minimum
nominal error for each relative measurement (Cavallini et al., 2005b). Nevertheless, the effects of
heat dissipation, ambient and coolant temperature, viscous heating, wall temperature measurement,
axial heat conduction and coolant mass flow rate were all taken into consideration in the final data
reduction (Matkovič, 2006). Furthermore, precise calibration of the test apparatus has been
performed regularly to maintain the reliability of performed measurements.
As an example of the technique enhancement, the influence of the heat dissipation rate on vapor
quality change is here illustrated. Hereby, the heat exchange in the two sectors was measured at
different boundary conditions. Moreover, coolant to ambient temperature difference was varied
systematically while there was no refrigerant flow in the sectors. In this way the measured heat gain
or heat loss in a wide range of test conditions was used to correct the total heat flow rate. Heat
dissipation in the first heat exchanger results in inlet vapor quality change (Figure 4), whereas
accounting for the heat dissipation in the measuring sector is somewhat more complicated. There
are two major issues for heat dissipation in the sector. The first one refers to a local heat dissipation
rate which directly affects the local measurement of the refrigerant heat flux and hence the local
heat transfer coefficient. In this context, the local specific heat dissipation rate q
diss
was calculated
from the overall measured heat loss in the MS ( Q
MSdiss
), the local and the integral value of coolant
minus ambient temperature difference along the sector (Equation 4).
Q
MSdiss
q diss
( z) = ⋅[ Tc ( z)
−T
Z
amb ]
[W m -2 ] (4)
π ⋅d ⋅ T z −T ⋅dz
∫[ ( ) ]
i c amb
0
The second one, instead, refers to the cumulative value of the heat dissipation rate along the MS,
which leads to the required correction for the local vapor quality calculation (Figure 4). Similarly,
all the other different effects mentioned above have been studied with the motivation of
experimental precision enhancement.
1,5
1,5
Dissipated Heat Flow Rate [W]
1,0
0,5
0,0
-0,5
-1,0
-1,5
Pre-sector
Measuring sector
-10 -5 0 5 10
Water to Ambient Temperature Difference [°C]
Dissipated Heat Flow Rate [ W ]
1,0
0,5
0,0
-0,5
G100
G200
G400
-1,0
G600
G1000
G1600
-1,5
-0,10 -0,05 0,00 0,05 0,10
dx [ / ]
Figure 4: (left) Heat dissipation measurement for the two sectors versus water to ambient temperature
difference. Tests were performed at water mass flow rates around 10 kg/h; (right) Calculated effect of the
dissipated heat on vapor quality change for different mass velocities of R32.

5th European Thermal-Sciences Conference, The Netherlands, 2008
3.3 Experimental Uncertainty
Nominal uncertainty of the local heat transfer coefficient during condensation of R32 within a
single minichannel test tube has been calculated from equation 5. The first term is associated to the
coolant mass flow rate uncertainty; the second term refers to the coolant temperature gradient; the
third one to the saturation to wall temperature difference and the last one to the uncertainty of the
internal diameter dimension. Nominal error for the coolant temperature gradient was assumed to be
equal to 0.2 K over the length of the measuring sector, 0.15 K for the saturation to the wall
temperature difference and 0.02 mm for the minichannel diameter. On the other hand, the coolant
mass flow meter nominal error was defined from the calibration curve given by manufacturer.
2 2 2 2
⎛ ∂HTC(z) ⎞ ⎛ ∂HTC(z) ⎞ ⎛ ∂HTC(z) ⎞ ⎛ ∂HTC(z)
⎞
δ
HTC(z)
= ⎜ ⋅δ
m
( m
)
c c ⎟ + ⎜ ⋅δ
Tc′ ⎟ + ⎜ ⋅δ
ΔTr−
w
⎟ + ⎜ ⋅δdh
⎟
⎝ ∂m
c ⎠ ⎝ ∂T ′
c(z) ⎠ ⎝ ∂ΔT r−
w(z) ⎠ ⎝ ∂dh
⎠
(5)
Bars of the experimental uncertainty calculated from the equation above are plotted in Figure 7 for
all referenced heat transfer coefficients.
4 Experimental Results
The local heat transfer coefficient has been measured during condensation of the high pressure
refrigerant R32 inside a horizontal single circular 0.96 mm diameter minichannel. The experiments
have been performed over the entire range of vapor quality at 40°C saturation temperature and mass
velocity ranging from 100 kg m -2 s -1 up to 1200 kg m -2 s -1 . In the present technique, the dominant
thermal resistance during the condensing process is on the refrigerant side, as can be seen from
Figure 3. This is favorable to the reduction of the experimental uncertainty associated to the
determination of the heat transfer coefficient. Since the purpose of the present apparatus is to
accurately measure the local heat transfer coefficient, several tests have been performed to verify
that the heat transfer coefficient does not depend on the conditions of the secondary fluid.
Besides, Figure 5 shows the experimental heat transfer coefficient measured at 600 kg m -2 s -1 by
imposing different inlet conditions to the refrigerant entering the test section. In the test runs, the
refrigerant has been first sent as superheated vapor to the measuring sector, and then at lower and
HTC [kW m -2 K -1 ]
25
20
15
10
G600 sup.
G600 x=0.95
G600 x=0.95r
G600 x=0.91
G600 x=0.87
G600 x=0.82
G600 x=0.78
HTC [kW m -2 K -1 ]
10
8
6
4
G200 t=19°C
G200 t=22°C
G200 t=25°C
G200 t=26°C
G200 t=29°C
5
2
0
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
VAPOUR QUALITY [/]
Figure 5: Experimental local heat transfer coefficient
versus vapour quality at different inlet vapour
conditions ranging from superheating to 0.78 quality.
0
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
VAPOUR QUALITY [/]
Figure 6: Experimental local heat transfer coefficient
versus vapour quality at different inlet inlet coolant
temperatures ranging from 19 °C to 29 °C.

5th European Thermal-Sciences Conference, The Netherlands, 2008
HTC [kW m -2 K -1 ]
26
24
22
20
18
16
14
12
10
8
G1200
G1000
G800
G600
G400
G200
G100
6
4
2
0
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
x [ / ]
Figure 7: Experimental local heat transfer coefficient during condensation of R32 inside single minichannel
versus vapour quality at different mass velocities ranging from 100 kg m -2 s -1 to 1200 kg m -2 s -1 .
lower values of vapor quality, down to 78% quality. The local heat transfer coefficient determined
in the different test runs perfectly overlap, as it can be seen in Figure 5. That is, the present test
apparatus provides exactly the same value of the heat transfer coefficient at the same refrigerant
conditions, no matter which location this coefficient is measured along the channel. Beside mass
velocity and vapor quality, the effect of the saturation to wall temperature difference can be
investigated by varying the inlet temperature of the coolant. Such a study has been conducted at 200
kg m -2 s -1 with coolant temperature ranging between 19 and 29 °C, at constant refrigerant saturation
temperature. Because of the peculiar design of the coolant channel, as previously mentioned, the
dominant thermal resistance is on the refrigerant side and therefore these variations of the coolant
temperature imply a consequent significant change in the wall temperature and thus in the saturation
to wall temperature difference. The results are plotted in Figure 6, showing no effect of the
temperature difference in the heat transfer coefficient at 200 kg m -2 s -1 . These results confirm that
the effect of gravity in around 1 mm diameter channel is not significant in comparison with the
other forces influencing the condensation heat transfer at 200 kg m -2 s -1 mass velocity.
The complete set of the experimental heat transfer coefficients is plotted in Figure 7 versus vapor
quality. As expected for forced convective condensation inside conventional pipes, the experimental
heat transfer coefficients measured at 100 kg m -2 s -1 and those at 200 kg m -2 s -1 are very close to each
other, showing little effect of mass velocity. It is worth reminding that the lower the mass velocity
the higher the experimental uncertainty of the heat transfer coefficient, due to the low local heat
fluxes. Nevertheless, this overlapping of the HTCs at the lower tested values of mass velocity was
not found with the refrigerant R134a and may be explained with the flow pattern and the properties
of R32.
4.1 Comparison against Models
Experimental results have been compared against six different models available in the open
literature. Akers et al. (1959), Cavallini et al. (2002) and Cavallini et al. (2006) were all developed
for HTC predictions inside macro-scale tubes. Moreover, Wang et al. (2002), Cavallini et al.
(2005a) and Moser et al. (1998) are here adopted. The model by Moser et al. (1998) was initially
developed for conventional pipes and later on modified by using the Zhang and Webb (2001) for
pressure drop calculation inside small-diameter tubes. The model by Cavallini et al. (2005a) has
been built on a database of HTC measurements for three different fluids during condensation inside
multi-port extruded aluminium tube with smooth square minichannels. The graphs show the good

5th European Thermal-Sciences Conference, The Netherlands, 2008
Figure 8: Comparison of the experimental heat transfer coefficients versus prediction models. Akers et al.
(1959), Cavallini et al. (2002) and Cavallini et al. (2006) were developed for macro scale tubes, whereas
Moser et al. (1998) modified by Zhang and Webb (2001), Wang et al. (2002) and Cavallini et al. (2005a)
are used for HTC prediction during condensation inside minichannels.

5th European Thermal-Sciences Conference, The Netherlands, 2008
performance of models developed for macro-scale condensation such as the ones by Cavallini et al.
(2002, 2006). Good agreement with experimental data is also shown by Moser et al. (1998) (Figure
8). None of the correlations is able to satisfactory predict the heat transfer coefficient measurements
taken at 100 kg m -2 s -1 . Akers et al. (1959) and Wang et al. (2002) systematically under predict heat
transfer coefficients whereas Cavallini et al. (2005a) model overestimates HTCs. Similar agreement
between macro-scale models and experimental results was also found with the lower pressure
refrigerant R134a (Cavallini et al. 2007).
5 Concluding Remarks
Heat transfer coefficients during condensation of R32 inside a horizontal circular single
minichannel have been measured for a wide range of test conditions. The high pressure fluid has
been tested at 40 °C saturation temperature over the entire span of vapor qualities and mass
velocities ranging from 100 to 1200 kg m -2 s -1 . HTCs have been obtained from just above 1000 W
m -2 K -1 to 24 kW m -2 K -1 . The novel test facility and the experimental technique have been shown to
work efficiently in a wide range of test conditions. Improvement of the measuring technique prior to
the test runs as well as validation of measurements in post processing have turned out to be crucial
for the assessment of precise heat transfer coefficients. Finally, overall good predictive capability of
applied correlations over the entire range of test conditions, but the lowest mass velocity, has been
shown in the paper. Macro-scale models for condensation heat transfer coefficient have been found
efficient in HTC prediction during condensation of R32 inside minichannels.
6 References
Akers, W.W., Deans, H.A., Crosser, O.K., 1959, Condensing heat transfer within horizontal tubes,
Chem. Eng.Prog. Symp. Series, vol. 55, pp. 171-176.
Cavallini A., Del Col D., Doretti L., Matkovic M., Rossetto L., Zilio C., 2005a, A model for
condensation inside minichannels. HT05 National Heat Transfer Conference. July 17-22, San
Francisco, CA, USA. Paper No. HT2005-72528.
Cavallini A., Del Col D., Matkovic M., Rossetto L., 2005b, Measurement of the heat transfer
coefficient during condensation in a circular minichannel. IIR International Conference
Thermophysical Properties and Transfer Processes of Refrigerants. 31 Aug-2 Sept, Vicenza, Italy.
pp. 103-110, ISSN 0151-1637, ISBN 2-913149-43-X.
Cavallini A., Censi G., Del Col D., Doretti L., Matkovic M., Rossetto L. and Zilio C., 2006,
Condensation in Horizontal Smooth Tubes: A New Heat Transfer Model for Heat Exchanger
Design. Heat Transfer Engineering. Vol. 27 no.8, pp. 31-38, ISSN: 0145-7632.
Cavallini A., Del Col D., Matkovic M., Rossetto L., 2007, Local Heat Transfer Coefficient During
Condensation inside a Single Minichannel, Sixth International Conference on Enhanced, Compact
and Ultra-Compact Heat Exchangers: Science, Engineering and Technology, September 16-21,
Potsdam, Germany.
Matkovič M., 2006, Experimental Condensation inside Minichannels, Ph.D. Thesis, Università di
Padova, 209 p.
Moser K. W., Webb R. L., Na B., 1998, A new equivalent Reynolds number model for
condensation in smooth tubes, J. of Heat Transfer, 120: 410-417.
Wang Wei-Wen W., Radcliff T.D., Christensen R.N., 2002, A condensation heat transfer
correlation for millimetre-scale tubing with flow regime transition, Experimental Thermal and Fluid
Science, vol. 26, pp. 473-485.
Zhang M., Webb R.L., 2001, Correlation of two-phase friction for refrigerants in small-diameter
tubes, Experimental Thermal and Fluid Science, vol. 25, pp. 131-139.