Proceedings of the ASME 2009 7th International Conference on Nanochannels, Microchannels and Minichannels
ICNMM2009
June 22-24, 2009, Pohang, South Korea
Proceedings of the Seventh International ASME Conference on Nanochannels, Microchannels and Minichannels
ICNMM2009
June 22-24, 2009, Pohang, South Korea
ICNMM2009-82249
MEASUREMENT OF HEAT TRANSFER IN THE ENTRANCE REGION OF SMALL DIAMETER
TUBES
Ting-Yu Lin
Thermal Analysis, Microfluidics, and
Fuel Cell Laboratory, Rochester
Institute of Technology, 76 Lomb
Memorial Dr., Rochester, NY 14623
[email protected]
Chien-Yuh Yang
Department of Mechanical Engineering,
National Central University, Chung-Li,
32054, Taiwan
[email protected]
ABSTRACT
Satish G. Kandlikar
Thermal Analysis, Microfluidics, and
Fuel Cell Laboratory, Rochester
Institute of Technology, 76 Lomb
Memorial Dr., Rochester, NY 14623
[email protected]
The study of heat transfer performance in micro channels
has become more important. There have been many
studies, including Wu and Little [1984][1], Wang and
Peng [1994] [2], Yu et al. [1995] [3] and Adam et al.
[1998] [4], dealing with the single-phase forced
convection heat transfer in micro tubes. Most of their
tests results are significantly different from those of
conventional forced convection heat transfer correlations,
which were obtained for larger tubes. Yu et al. [1995] [3]
studied the fluid flow and heat transfer characteristics of
nitrogen gas and water in circular tubes with diameters of
19, 52 and 102 μm and Reynolds numbers ranging from
250 to 20,000. The measured friction factors were
slightly lower than the Moody chart values for both
laminar and turbulent flow regimes. However, the
Nusselt numbers for cooling of water in the turbulent
flow regime were considerably higher than would be
predicted for larger tubes, suggesting that the Reynolds
analogy does not hold for micro channel flow. Adams et
al. [1998] [4] investigated turbulent single-phase forced
convection of water in circular micro channels with
diameters of 0.76 and 1.09 mm. The data suggested that
the enhancement increases as the channel diameter
decreases with increasing Reynolds number. Based on
this data, along with earlier data for small circular
channels by Yu et al. [1995] [3], a correlation was
developed for the Nusselt number for turbulent, singlephase and forced convection in circular micro channels
with diameters ranging from 0.102 to 1.09 mm. Adams et
al. [1999] [4] investigated turbulent single-phase forced
convection of water in non-circular micro channels with
hydraulic diameter of 1.13 mm. The experimental results
predicted by the Gnielinski correlation falls within
± 10%. From the results it was concluded that 1.2 mm
was a lower limit for the applicability of standard
turbulent single-phase correlations for non-circular
Heat transfer coefficient in the entrance region of
water flowing through micro-tubes with diameters of 962
μm and 123 μm was investigated in this study. Two
temperature measurement methods, thermocouple and
liquid crystal thermography (LCT), were used to
measure the tube surface temperature. The experimental
data showed that the Nu in the entrance region can be
predicted well by conventional correlation while using
the LCT to measure the temperature. Using the
temperature measurements from the thermocouples
attached to the surface, the Nu is found to be
significantly higher than the prediction. This was
believed to be due to the error in measurement of
temperature. Simulation results also revealed that the
measured temperature for a small diameter tube can be
significantly decreased with a thermocouple attached to
it. In transition flow, the wall temperature was also found
to have a significantly fluctuation, as large as 2 oC, due
to the unsteady flow conditions, while for fully
established laminar as well as turbulent flow conditions,
the fluctuation was measured to be less than 0.2 oC. The
effect of viscous heating was negligible in the range of
parameters investigated in this study.
Keywords: heat transfer coefficient, micro-tubes,
small diameter tubes, liquid crystal thermography (LCT),
transition flow, transition to turbulent
INTRODUCTION
Owing to the fabrication technology development
during the past decades, the so-called micro tubes with
internal diameters smaller than 1 mm can be easily made
and used to increase the compactness of heat exchangers.
1
Copyright © 2009 by ASME
channels. Kandlikar et al. [2003] [5] investigated the
pressure drop and heat transfer of laminar flow in smooth
and rough circular tubes with diameters of 1.067 and
0.62 mm. The effect of the changes in the relative
roughness on pressure drop was minimal but the heat
transfer in the entrance region showed a distinct
dependence on roughness.
Some researches revealed the correspondence of
experimental data and conventional correlations. Lelea
etal [2004] [6], Owhaib and Plam [2004] [7], Muwanga
and Hassan [2006] [8], Lin and Yang [2007] [9], Yang
and Lin [2007] [10] indicated that the heat transfer
coefficient can be predicted well by conventional
correlations. Guo and Li [2003] [11] proposed that
measurement accuracy of a tube is one of the most
important factors to cause the discrepancy between
experimental data and conventional correlations.
The non-contact temperature measurement method of
LCT was used to measure the temperature of small scale
in some research. Hohmann and Stephen [2002] [12]
used the non-encapsulated thermochromic liquid crystal
(TLC) to investigate the heat transfer at an evaporating
liquid meniscus. The measured surface area was 640 x
480 μm in a flat plate with a theoretical spatial resolution
of less than 1 μm. The uncertainty of their measured
temperature was 0.51 oC. Muwanga and Hassan [2006]
[8] used non-encapsulated TLC to measure the local heat
transfer coefficient in micro channel with 1.0668 mm
inner diameter and outer diameter of 1.27 mm. The
results indicated that the conventional correlation was
adequate for predicting the heat transfer coefficient. Lin
and Yang [2007] [9] and Yang and Lin [2007] [10]
measured the convective heat transfer performance of
micro-tubes with diameters from 123 to 962μm by LCT.
Their results revealed that the experimental data was in a
very good agreement with conventional correlation.
Since the size of the normal commercial sensor for
measuring micro-tubes surface temperature is
comparable to the size of the micro tubes, it may not be
accurate to measure the surface temperature by attaching
a sensor on micro tube. Furthermore, since the size of the
sensor and tube are extremely small, it is very difficult to
have the sensor firmly contact the tube. In this study, the
non-contact temperature measurement method, is applied
to measure the micro tube surface temperature.
Thermocouples with two attachment methods are
compared to investigate the effect of the contact. This
study is not intended to develop an accurate temperature
measurement by thermocouple, but just to discuss the
temperature
measurement
problems
due
to
thermocouples.
kf
Water conductivity (W/m oC)
L
Tube length (m)
LCT Liquid crystal thermography, dimensionless
•
m Mass flow rate (kg/s)
Nud Nusselt number, dimensionless
q
Heat transfer rate (W)
q” Heat flux (W/m2)
r
Radius (m)
Red Reynolds number, dimensionless
Ti
Inlet water temperature (oC)
Tx Local water temperature (oC)
Twx Local tube inside wall temperature (oC)
Velocity (m/s)
u
TLC Thermochromic liquid crystal, dimensionless
x
Axial position of tubes (m)
μ
Viscosity (N/m2 s)
EXPERIMENTAL SETUP
The schematic diagram of the test facilities is shown in
Figure 1. A pressure vessel connected to high-pressure
nitrogen was used to push the water through the test tube.
The inlet water temperature was measured by a
resistance temperature detector (RTD). DC power was
clapped on both ends of the test tube to offer constant
heat flux to the tube. The flow rate was measured by a
programmable electronic microbalance.
Power
High pressure N2
Water
reservoir
Pressure
vessel
T
P
CCD
Balance
Figure 1. Schematic diagram of test loop
The TLC usually reveals color from red to blue in the
temperature from low to high active range. The
temperature active range of TLC can be from 0.5 to 30
o
C. TLC with lower active range usually has higher
temperature resolution but less temperature detecting
area. To increase the accuracy of temperature
measurement, four TLCs with 5 oC band width from 28
to 33 oC, 33 to 38 oC, 38 to 43 oC and 45 to 50 oC were
used in this study. A black paint was painted under the
TLCs as the background for improving the color
resolution by absorbing un-reflected light.
The relation between the hue value and temperature
was calibrated in a thermostat box. It was used to offer
an environment for the calibration of the TLC. The box
is made up of wooden plates having thickness of 10 mm
with a 10 mm heat insulator on it, as shown in Figure 2.
During the calibration process, electrical heating wires
were attached to the inner surfaces of the box to maintain
the entire box space at the designated temperature. The
temperature inside the thermostat box can be adjusted by
setting the input power on the heating wire. T-type
thermocouples were placed on the test tube surface to
measure its temperature distribution. The hue values of
NOMENCLATURE
A
Ac
cp
di
G
Gz
h
Pump
Test tube
Filter
Heat transfer area (m2)
Tube cross section area (m2)
Heat capacity (J/kg K)
Tube inside diameter (m)
Mass velocity (kg/m2 s)
Graetz number, dimensionless
Heat transfer coefficient (W/m2 oC)
2
Copyright © 2009 by ASME
TLC and thermocouple temperature were recorded
simultaneously. The temperature uniformity inside the
box is within ±0.1 oC at different temperature settings.
The thermal shunt problem can be neglected since the
temperature between the test surface and the sensor is the
same.
the heat transfer coefficient h can be derived as:
h=
q
A(Twx − Tx )
(3)
Where A is the heat transfer area, A = πdiL and di is the
tube inside diameter. Twx is the local inside tube surface
temperature, derived from the measured outside surface
temperature. The Reynolds number and Nusselt number
are defined as Re d = Gd i and Nu d = hd i
μ
kf
•
Where G is the water mass flux, G = m /Ac and Ac is
the tube cross-section area.
Figure 2. Thermostat box
A comparison test using a thermocouple to measure
temperature was performed. This test was applied to
qualitatively study the temperature measurement
problem by thermocouple in a small tube. Figure 3
shows the 962 μm tube with a thermocouple attached.
The external diameter of the tube is 1.26mm. Omega
bond was used to cement the thermocouple joint and the
tube surface after they were firmly connected. This
connection method was commonly used to measure the
surface temperature of large tubes.
NUMERICAL SIMULLATION
In this study, a 3D numerical model was formulated to
solve the conduction heat transfer problem. Figure 4(a)
shows the model of a rectangular solid 2 x 2 x 25 mm
stainless steel (SS-304) test section with a thermocouple
attached to it. The material of thermocouple was set as
0.05 x 0.05 x 12 mm copper. The attached location was
in the center of the test section on the surface. The test
section was used as heat source directly under natural
convection situation. The ambient was set to be 25 oC air.
The entire computational grids are 118,245 cells for the
large test section and 1,001,388 cells for the small one.
Figure 4(b) shows the model with dimension of 0.2 x 0.2
x 25 mm, and with the same size thermocouple attached
as the large test section. The commercial software
package Flotherm was used for the computations.
Figure 3. The attachment of thermocouple on 962 μm test
tube
Test section
Thermocouple
DATA REDUCTION
(a)
The heat transfer rate was measured from the DC
power input and is equal to the enthalpy of water flow
increased. Since the electrical power was added
uniformly on the tube surface, the local water
temperature, Tx, at the position x from the heating
entrance, can be estimated by:
•
x
q = m c p (Tx − Ti )
L
Figure 4. Simulation models
RESULTS
To reveal the stability of LCT in this study, hue versus
temperature calibrations were performed for the 962 μm
tube in different date, as shown in figure 5. Plotted data
of “Cal-A # 1” was a calibration performed immediately
after the TLC was sprayed on the tube. “Cal-B # 1, Cal-B
# 2 and Cal-B # 3” were calibrations for another sprayed
TLC. “Cal-B # 1” was also performed immediately after
the TLC was sprayed, while “Cal-B # 2” and “Cal-B # 3”
were performed after 3 days and 7 days, respectively.
From “Cal-A # 1” and “Cal-B # 1” it is observed that
(1)
•
Where m is the water flow rate, L is the tube length
and Ti is the water inlet temperature. From the Newton’s
Law of cooling,
q" =
q
= h (Twx − Tx )
A
(b)
(2)
3
Copyright © 2009 by ASME
lower than that measured by TLC. The difference is more
than 1 oC, which is significantly higher than the
experimental uncertainty. The lower temperature
measured by thermocouple is due to the attachment,
which is not a perfect match (3M tape), or the thermal
shunt problem (Omega bond). In this case the
temperature error caused by Omega bond is slightly
higher than that of 3M tape.
calibration curves for new TLC had no significantly
difference. From “Cal-B # 1” and “Cal-B # 2” it is
observed that the calibrated correlation after 3 days is
still the same. At 45.8 oC the TLC started to appear clear
in color and the hue value was about 60. After 7 days,
“Cal-B # 2” showed the active temperature of TLC was
about 46.4 oC with the hue value about 90. There was no
detectable color which appeared with a temperature
lower than 46.4 oC and hue value under 90. It was also
observed that hue value in the lower temperature region
was slightly lower than the other calibration. This
situation means that the TLC started to decay. In this
work, all the experiments were performed within 2 days.
The temperature measurement error caused by the
calibration correlation changes can be neglected in this
study. In figure 5 it is also observed that the slope is
higher in the higher hue value region. This means the
resolution to temperature is lower and the uncertainty to
measure temperature is higher in the higher hue value
region.
Figure 6. Color of TLC on a 250 μm external diameter tube
with a thermocouple attached on it
50
52
TLC
TC (3M Tape)
TC (Omega bond)
49
Di=962μm Cal-A # 1
Di=962μm Cal-B # 1
Temperature (oC)
51
Di=962μm Cal-B # 2
Temperature (oC)
50
Di=962μm Cal-B # 3
49
48
47
46
48
47
45
46
44
44
45
40
45
46
47
48
49
50
o
TLC temperature ( C)
60
80
100
120
140
160
Figure 7. Comparison of temperature measured by TLC
and the thermocouple
Hue
Figure 5. Calibration of hue values versus temperature with
962 μm tube, performed on different dates
The experimental values of the local Nu in the
entrance region are compared with the correlation of
Shan and Bhatti [1987] [13], as shown in Figure 8. Eight
thermocouples were attached to the test tube to measure
the temperature in equivalent distances from the entrance
region to the fully developed region. The conventional
correlation shows that the local Nusselt number
decreases along the flow direction and asymptotically
approaches the value of theoretical constant heat flux
fully developed heat transfer coefficient, 4.36. Graetz
number (Gz), which is defined as [(x/d)/RePr], was used
to define the flow development situation. The lower Gz
means the flow length is shorter or the Re is larger.
Gz=0.05 was used to define the thermal developing
situation.
Gz higher than this value was considered to
be fully developed. From Figure 8, it is observed that the
data obtained from TLC can be well predicted by
conventional correlation, while for the data from the
thermocouples is significantly higher than the prediction.
The departure increases with the increasing of Gz. This is
because the thermocouple under estimates the wall
Figure 6 shows the TLC color of the 123 μm tube. A
thermocouple was attached to it by Omega bond. The
external diameter of the tube was 250 μm and spread
with 45 to 50 oC TLC. The tube was offered with
uniform heat flux. It is observed that at the two ends of
the tube the color is blue, which means the temperature is
in higher temperature region. Near the bond the color is
red, which means the temperature is in the lower
temperature region of active range. The color showed of
Omega bond was black, which means that the
temperature is under than the active range. Figure 6
clearly reveals that the temperature was cooled down by
the Omega bond and thermocouple.
Figure 7 shows the comparison temperature
measurements on 962μm tube, made by TLC and
thermocouple. 3M tape and Omega bond were used to
maintain the attachment between thermocouple sensor
joint and test tube surface. It is observed that the
temperature measured by thermocouple is significantly
4
Copyright © 2009 by ASME
rate was steady state. Hence, for each test the heat flux
and fluid temperature were steady. From equation 2 it
can be observed that the wall temperature Twx changes
while the heat transfer coefficient change. Agostini et al.
[2004][14] investigated the convective heat transfer
characteristics of R134a in multi-port extruded tubes.
Tube wall temperature was measured by 0.5mm E-type
thermocouple. Their experimental data reveal that in
transition flow the tube wall temperature fluctuation is
about 0.2 oC, which was three times higher than that of
laminar or turbulent flow. From this study it was found
that the fluctuation could be much higher than 0.2 oC.
The response time of TLC is about 36 to 450
milliseconds, proposed by Hoffs [1992][15]. The
transient temperature change was able to be observed
clearly. The results indicated that the TLC can be further
used to measure the transient temperature due to the
shorter response time.
temperature, as shown in the results in Figure 7. For the
same Red, the lower Gz data means the temperature was
measured in the entrance region. For constant heat flux
heating, the fluid and wall temperature increases with the
heating length. In the small Gz region (upstream entrance
region of the tube) the wall temperature was lower. The
temperature of tube wall and ambient were small, the
under estimation of temperature was not significant.
However, in the higher Gz region (downstream fully
developed region of the tube) the wall temperature was
high and the temperature difference between wall and
ambient was much higher. The under estimate was
significant. From equation (2) it can be observed that the
underestimation of the wall temperature will cause the
heat transfer coefficient to be higher. The higher
underestimation in the fully developed region caused the
Nu to be higher than that in the entrance region.
25
Shah and Bhatti [1987]
Red=570-LCT
20
Red=620-LCT
0.00s
0.03
s
0.07s
0.10s
0.13s
0.17s
0.20
s
0.23s
0.27s
0.30s
Red=590-thermocouples
Red=640-thermocouples
Nud
15
10
(a) Re=12078 (turbulent flow)
5
0
2
4
6
Gz
X
0
8
10
12
14
0.53s
0.57
s
0.60s
0.63s
0.67s
0.70s
0.73
s
0.77s
0.80s
0.83s
100
Figure 8. Heat transfer coefficient in the entrance region by
different measurement
Transition flow
(b) Re=2674 (transition flow)
Figure 9. Frames of external diameter 1.26 mm tube with
TLC at different time
Figure 9 (a) shows 10 continuous pictures taken in 0.3
seconds of the tube of external diameter 1.26 mm. The
tube has TLC on it, and has Reynolds number of 12,078.
Images were taken 30 frames per second. There is no
significantly color difference over time. However, in
transition flow, Figure 9 (b) shows the tube color was
changed significantly, especially for the pictures at 0.63
and 0.67s. After converting the color to temperature, the
temperature fluctuation (difference between instant
temperature Tinst and average temperature Tavg) with time
was found to be high as shown in Figure 10. The
fluctuation can be higher than 2 oC. In calibration,
laminar and turbulent flow, the fluctuation was observed
to be less than 0.2 oC. The higher temperature fluctuation
in transition flow is due to the changing flow regimes.
The heat transfer coefficient is low in laminar flow and is
high in turbulent. In transition flow, the flow regime
transits from laminar to turbulent and back to laminar
continuously due to unsteadiness. Hence, the heat
transfer coefficient changed continuously. In this study,
uniform heat flux was applied for heating and the flow
o
Tinst-Tavg ( C)
2
Calibration
Re=1884 (Laminar)
Re=12078 (Turbulent)
Re=2674 (Transition)
1
0
-1
0.0
0.2
0.4
0.6
0.8
1.0
Time (s)
Figure 10. Transient tube surface temperature fluctuation
5
Copyright © 2009 by ASME
on the test section was not significantly influenced by the
thermocouple. The thermocouple temperature was higher
near the test section and decreased with the distance. The
temperature in the attachment of test surface was 60.4 oC
which was slightly decreased by the attached
thermocouple. For the 0.2 x 0.2 x 25mm test section the
decrease was significant. The temperature distribution
without attaching a thermocouple is shown in Figure 14.
The input heat was set to be 0.037 W. The maximum
temperature was 45.3 oC which was in the center of test
section. By attaching the same size thermocouple the
temperature was significantly decreased, as shown in
Figure 15. The temperature in the attachment was 40.7 oC.
The decrease was as high as 4.6 oC. The detailed
simulation results are shown in Table 1.
Viscous heating
When compare to the flow in large tubes, the flow
velocity in micro-tubes is relatively higher. Due to the
high flow velocity, an evaluation of viscous heating in
the fluid is necessary. In steady state, the energy balance
for channel flow is generalized as follows:
ρuπR 2 c p (Tx − Ti ) = ∫
L
0
∫
R
0
∂u
) 2πrdrdx
∂r
2
u(
(4)
with the assumptions of: circular cross-section, fully
developed laminar (Poiseuille) velocity profile and
constant fluid properties along the tube length. The fluid
temperature difference between measuring position Tx
and inlet position T i is as follows:
Tx − Ti =
32μuL
2
ρd i c p
Gnielinski
Nu = 4.364
(4.2)
d
100
(5)
Nud
From this equation it is observed that the temperature
difference increases with the decreasing tube diameter.
Considering the viscous heating the fluid temperature
will be increased. The Nusselt number increases due to
the fluid temperature increase. From equation (5) it is
also observed that the fluid temperature increases with
velocity and tube length. Figure 11 shows the effect of
viscous heating on heat transfer coefficient for the 123
μm tube. Long length and high fluid velocity cases were
plotted to clarify the effect of viscous heating. Both of
the two cases show that there was no significant effect of
viscous heating in this diameter. Considering the viscous
heating, the Nu was increased with the increase of Red
from 2.4 to 3.7% for 145 mm length tube. For the 29 mm
length tube the increase was from 0.1 to 0.3%. Viscous
heating was considered to be negligible in this research
due to the high cp of water. It was also found that the Nu
of 29 mm length tube was significantly higher than 4.364
and is a function of Red with Red higher than 1,000. It
was because of the measuring length was too short for
the flow to be fully developed. The flow was still in
developing region hence the Nud was higher. For the 145
mm length tube the Nud corresponded to 4.364 and did
not change with Red, since the tube length was long
enough for the flow to be fully developed, even at high
Red.
Figure 12 shows the temperature distribution of the 2 x
2 x 25mm test section without a thermocouple attached
to it. The input heat was set to be 0.12 W with uniform
heating to the test section. The temperature distribution
was uniform, and the minimum to maximum values
ranged from 61.6 to 62.2 oC. In the edge region the
temperature is lower due to more heat transfer area under
natural convection. The maximum temperature 62.2 oC
appeared in the center of the test section surface. Figure
13 shows the temperature distribution of the test section
with a thermocouple on it. The temperature distribution
Lm=29mm
withount viscous heating
Lm=29mm
with viscous heating
Lm=145mm
withount viscous heating
Lm=145mm
with viscous heating
10
1000
10000
Red
Figure 11. The effects of viscous heating in 123μm tube
o
C
62.2
61.9
61.6
Figure 12. temperature distribution of 2 x 2 x 25mm
without thermocouple
6
Copyright © 2009 by ASME
o
heating were discussed. Based on the present study the
following conclusions are drawn:
1. In a small tube the temperature can be significantly
decreased by attaching a thermocouple on it.
2. Temperature measured by TLC revealed that Nu can
be predicted well by conventional correlations, while
for thermocouple measurements it was significantly
higher.
3. Transient temperature phenomenon can be clearly
observed by LCT. In transition flow the temperature
was found to have high fluctuation larger than 2 oC.
4. Viscous heating effect was not significant in this
study.
C
61.5
50.9
35.0
Figure 13. temperature distribution of 2 x 2 x 25mm with
thermocouple
o
C
45.3
44.4
43.0
Figure 14. temperature distribution of 0.2 x 0.2 x 25mm
without thermocouple
o
C
44.6
42.6
39.7
Figure 15. temperature distribution of 0.2 x 0.2 x 25mm
with thermocouple
Table 1. Temperature in the center of test section surface
Test section
(mm)
Input heat
(W)
Without TC
(oC)
With TC
(oC)
ΔT
(oC)
2 x 2 x 25
0.2 x 0.2 x 25
0.12
0.037
62.2
45.3
60.4
40.7
1.8
4.6
Conclusions
This study investigated the heat transfer in micro tubes.
Temperature measurement, transient flow and viscous
ACKNOWLEDGMENTS
The work was conducted at National Central University,
Chung-Li, Taiwan, and Rochester Institute of Technology,
Rochester, NY, USA.
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