Proceedings of the ASME 2011 9th International Conference on
Nanochannels, Microchannels, and Minichannels
ICNMM2011
June 19-22, 2011, Edmonton, Alberta, CANADA
ICNMM2011-58102
AN EXPERIMENTAL INVESTIGATION ON HEAT TRANSFER CHARACTERISTICS
OF AIR AND CO2 IN MICROTUBES
Chia-Wei Chen
National Central University
Chung-Li, Taoyuan, Taiwan
Ting-Yu Lin
Rochester Institute of Technology
Rochester, New York, USA
Chien-Yuh Yang
National Central University
Chung-Li, Taoyuan, Taiwan
Satish G. Kandlikar
Rochester Institute of Technology
Rochester, New York, USA
ABSTRACT
Several researches dealing with the single-phase forced
convection heat transfer inside micro channels have been
published in the past decades. The performance of liquid flow
has been proved that agree with the conventional correlations
very well (Yang and Lin [2007]). However, owing to the low
heat transfer coefficient of gaseous flow, it is more difficult to
eliminate the effects of thermal shunt and heat loss than water
flow while measuring its heat transfer performance. This study
provides an experimental investigation on forced convective
heat transfer performance of air and gaseous carbon dioxide
flowing through two microtube with inner diameter of 920 µm.
A non-contacted liquid crystal thermography (LCT)
temperature measurement method that proposed by Lin and
Yang [2007] was used in this study to measure the surface
temperature of microtube. The test results show that the
conventional heat transfer correlations for laminar and
turbulent flow can be well applied for predicting the fully
developed heat transfer performance in microtubes while taking
account of the compressibility effect of high pressure gaseous
flow in micro tubes. There is no significant difference between
CO2 and air in both heat transfer and friction.
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 for
increasing the compactness of heat exchangers. These kinds of
heat exchangers are able to attain extremely high heat transfer
surface area per unit volume, high heat transfer coefficient and
low thermal resistance. The study on heat transfer performance
in micro tubes has become more important due to the rapid
growth of the application for high heat flux electronic devices
cooling. However, the conventional forced convection heat
transfer correlations were derived from tubes with diameter
much larger than those used in micro-channels. They have not
been verified to work well for predicting the heat transfer
coefficient inside small diameter tubes.
Several researches dealing with the single-phase forced
convection heat transfer in micro tubes have been published in
the past decades. Yu et al. [1995] 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 near 20,000. The
measured friction factors were slightly lower than the Moody
chart values for both laminar and turbulent regimes. However,
the Nusselt numbers for cooling of water in the turbulent
regime were considerably higher than those would be predicted
for larger tubes, suggesting that the Reynolds analogy does not
hold for micro-channel flow. Adams et al. [1998] investigated
turbulent single-phase forced convection of water in circular
micro-channels with diameters of 0.76 and 1.09 mm. Their data
suggested that the extent of enhancement increases as the
channel diameter decreases and Reynolds number increases.
Based on the data they obtained, along with earlier data for
small circular channels by Yu et al. [1995], they developed a
correlation for the Nusselt number for turbulent, single-phase,
forced convection in circular micro-channels with diameters
range from 0.102 mm to 1.09 mm. Mala and Li [1999]
investigated water flow through micro tubes with diameters
ranging from 50 to 254 µm. The experimental results indicate
that at high Reynolds number laminar flow condition, the
friction factor is higher than that given by the conventional
Poiseuille flow theory.
Celata et al. [2002] reported the results of refrigerant R114 flowing in capillary tubes with a diameter of 130 µm. They
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found that the friction factor was in good agreement with the
Poiseuille theory for Reynolds number below 600 but higher
than that for higher Reynolds number. Li et al. [2003] tested
the frictional characteristic of water flowing in glass, silicon
and stainless steel micro tubes with diameters ranging from
79.9 to 205.3 µm. They concluded that for smooth tubes, the
friction factor is consistent with the results in macro tubes,
while the value of fRed in rough tubes is 15 ~ 37% higher than
64. Yang et al. [2003] provided a systematic test of friction
characteristic for air, water, and liquid refrigerant R-134a in 10
tubes with inside diameters from 0.173 to 4.01 mm including
the laminar and turbulent flow regime. The test results show
that the conventional correlations for large tubes may be
adequately used to estimate the friction factors for water,
refrigerant, and laminar air flow in microtubes. For turbulent
airflow, however, the flow Mach number is too high to be
treated as incompressible flow. Yen et al. [2003] measured heat
transfer performance of laminar refrigerant R-123 flow in 0.3
mm diameter tube by direct attaching K-type thermocouple on
the tube wall. The results are in reasonable agreement with the
analytical laminar constant heat flux value (Nud = 4.36).
However, the data have a very high Nusselt number scattering
distribution from around 2 to 5. Lelea et al. [2004] investigated
developing and laminar distilled water flow in micro tubes with
diameter 0.1, 0.3 and 0.5 mm. The experimental results confirm
that, including the entrance effects, the conventional or
classical theories are applicable for water flow through micro
tubes of the sizes tested.
Celata et al. [2009] presented the work deals with the
compressible flow of nitrogen gas inside microtubes ranging
from 30 to 500 µm and with different values of the surface
roughness (<1%), for different flow regimes. Their results
showed that classic correlations can predict friction factor in
laminar flow without revealing any evident influence of the
surface roughness. The laminar-to- turbulent transition starts
for Reynolds number not lower than 2000 for smooth pipes,
while tending to larger values (3200–4500) for rough pipes. In
the fully developed turbulent regime, obtained for both smooth
and rough pipes, an agreement between experimental data and
the Blasius correlation has been verified for smooth pipes,
while for rough pipes the agreement with predictions given by
the Colebrook equation is rather modest.
In summarizing the above literature review, friction factors
for both liquid and gas in micro tubes can be adequately
predicted by the conventional correlations. The heat transfer
test results for liquid can also be well predicted by the
traditional forced convection heat transfer correlations. But
very few test results for gaseous flow in microtubes have been
published. For heat transfer test, the measurement accuracy of
micro tube wall temperature may be the most important factor
that causes this discrepancy. Since the diameter of the sensors
for measuring micro-tube surface temperature is comparable to
the size of the micro-tube itself, the tube surface temperature
cannot be accurately measured due to the effect of sensor wire
thermal shunt. Furthermore, since the size of thermocouple is
extremely small, it is very difficult to have it firmly contacted
on the tube wall. Lin and Yang [2007] proposed a noncontacted Liquid Crystal Thermography (LCT) method to
measure the surface temperature of micro tubes. It is
successfully avoid the thermal shunt and contact problem
caused by using thermocouple.
This study provides an experimental investigation on
laminar and turbulent forced convective heat transfer
characteristics of air and CO2 flowing through micro stainless
steel tube with inside diameter of 920 µm. Thermocouple and
the LCT method proposed by Lin and Yang [2007] were used
in this study to measure the surface temperature of micro tube.
EXPERIMENTAL METHOD
Tubes Size Measurement and Experiment System Setup
A steel tube with inside diameter of 920 µm was tested in
the present study. The tubes inside diameters were measured
from the enlarged photographs taken by Optical Microscope
(OM). Figure 1 shows the sample enlarged photographs of the
cross-section view of the tube. For reducing the measurement
uncertainties, seven tubes were bundled together, cut and
ground to have smooth cross section surface. Each tube
diameter was measured and all values were averaged to obtain
the average tube diameter. Table 1 gives the detail dimensions
and surface roughness of these tubes. The corresponding
drawing of the test section is shown in Figure 2.
Figure 1. Enlarged photographs of the microtubes
Table 1. Detail dimensions of the tube tested
Average
di (µm)
920
Lh,1
(mm)
Lh,2
(mm)
Lh,3
(mm)
Lh,tota
(mm)
Ltotal
(mm)
28.56
50.29
68.66
78.14
181.5
Surface
roughness Ra
(µm)
0.704
Figure 2. Detail drawing of the test tube
The schematic diagram of the test facilities is shown in
Figure 3. Pressurized air and CO2 were used as the working
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fluid. High pressure gas flows through a regulator to the test
section. A mass flow meter was connected between the
regulator and the test section to measure the flow rate of the
working fluid. Since the heat transfer coefficient of gaseous
flow is so low that the heat loss may be important in the heat
transfer measurement. For minimizing the heat loss, the test
section was enclosed in a vacuum chamber. The inlet gas
temperature was measured by a resistance temperature detector
(RTD). DC power was clapped on both ends of the test tube to
heat the tube wall. The maximum heat loss to heat input ratio is
lower than 12%. The variation of heat loss ratio versus
Reynolds number is shown in Figure 4. The experimental
apparatus and derived parameters uncertainties are listed in
Table 2. The heating length and temperature measuring
positions shown in Figure 2 are also listed in Table 1.
0.14
Air
0.12
CO2
qloss/qinput
0.10
0.08
0.06
0.04
0.02
0.00
102
103
104
105
Red
Figure 4. Ratio of heat loss to total heat transfer
Figure 3. Schematic diagrams of the test facilities
Table 2. Uncertainties of the experimental apparatus and
derived parameters
Uncertainties
Apparatus
RTD
±0.1 oC
T type Thermocouple
±0.2 oC
Pressure
drop ±0.075 %
transducer
Flow meter
±1 %
Derived parameters
Red
±0.4 ~ 3.9 %
f
Air: ±3.3 ~ 20.3 %
CO2: ±2.4 ~ 25.7%
Nud
Air: ±5.5 ~ 60.6 %
CO2: ±10.2 ~ 74.3 %
LCT Temperature Measurements
The LCT method that proposed by Lin and Yang [2007]
was used in this study to measure the surface temperature of
micro tubes. For increasing the accuracy of temperature
measurement, four thermochromic liquid crystals (TLCs) with
5 oC band width from 28~33, 33~38, 38~43 and 45~50 oC and
one TLC with 3 oC band width from 75~78 were used in this
study. The diameters of the encapsulated TLCs are from 5 to 15
microns. The TLCs was painted on the tested surface with
thickness of approximately 30 µm. A black paint was also
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 constant temperature box. Electrical heating
wires were attached on inside surfaces of the box to maintain
the entire box space at designated temperatures. 7 T-type
thermocouples were evenly placed near the test tube in the box
to measure its temperature distribution. The Liquid Crystal
Thermograph and temperature measured by thermocouples
were recorded simultaneously. The temperature uniformity in
the constant box at different temperature can be maintained
within ±0.2 oC. The detail process and uncertainty of the LCT
temperature measurement was described in Lin and Yang
[2007]. the standard deviation for the calibrated temperaturehue curve was evaluated within ±0.5 oC.
Data Reduction
The heat transfer rate was measured from the DC power
input deducted by the corresponding heat loss shown in Figure
4. It equals to the enthalpy of gas flow increased. Since the
electrical power was added uniformly on the tube surface, the
local gas temperature, Tx, at the position x from the heating
entrance can be estimated by:
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x
= m c p (Tx − Ti )
L
Where m is the gas flow rate, L is the tube heating length and
Ti is the water inlet temperature. From the Newton’s Law of
cooling,
q
q" = = h (Twx − Tx )
A
The heat transfer coefficient h can be derived as:
q
h=
A (Twx − Tx )
Figure 5. Friction factors of air and CO2 in micro tube
q
1
Laminar (16/Red)
Turbulent (Blasius)
Air Compressible (Shapiro [1953])
CO2 Compressible (Shapiro [1953])
0.1
f
Where A is the heat transfer area, A = πdiL, di is the tube inside
diameter. Twx is the local inside tube surface temperature that
can be derived from the LCT measured outside surface
temperature by the method of one-dimensional heat conduction
analysis. The temperature difference between the inside and the
outside wall was calculated as less than 0.1 oC which is among
the experimental uncertainty range. Since the Kn numbers in
the present study are from 2.8 x 10-5 to 2.28 x 10-6 which is far
below the slip-continuum flow boundary (10-3) that suggested
by Beskok and Karniadakis [1999], continuum flow condition
was considered in the present study. The Reynolds number and
Nusselt number are defined as the following:
hd
Gd i
and Nu d = i
Re d =
kf
µ
Where G is the water mass flux, G = m/Ac, Ac is the tube crosssection area.
If we examine the flow speed in each tube, we may find
that it approaches to moderate subsonic flow to near sonic flow.
Figure 5 shows the discrepancy between the experimental
results and the Blasius predictions begins near these Reynolds
numbers. While the Reynolds number is higher than these
values, the flow is entered the high subsonic flow regime. The
Blasius equations developed for the incompressible flow will
no longer be appropriate for friction factor prediction.
Shapiro [1953] developed a theoretical equation for
friction coefficient that includes the effect of gas flow
compressibility as:
2
2
D ⎡p -p
p ⎤
f = h ⎢ 1 2 2 - 2 ln 2 ⎥
L ⎣ G RT
p1 ⎦
The friction coefficients evaluated by the above equation
are shown in Figure 6. They agree very well with those
predicted by the Blasius equation. It shows that the mechanism
of frictional flow in micro tube is the same as that in the
conventional larger tubes beside the compressibility effect.
RESULTS AND DISCUSSIONS
Friction Factors
The measured friction factors of air and CO2 flow in the
tubes and shown in Figure 4. In laminar flow regime, the
friction factors can be well predicted by Poiseuille theory.
However, in turbulent flow regime, the tested friction factors
are significantly lower than those predicted by Blasius
equation. The discrepancy between the experimental and
predicted values increased with decreasing tube diameters.
These results are the same as those tested by Yang et al. [2003].
0.01
0.001
102
104
105
Red
1
Figure 6. Friction factors of air and CO2 in micro tube
evaluated by the Shapiro [1953] equation
Laminar (16/Red)
Turbulent (Blasius)
Air Incompressible
CO2 Incompressible
Heat Transfer
To compare the measuring difference between
thermocouple and LTC, both methods were used to measure the
micro tube wall temperature in the present study. Figures 7 and
8 show the measured Nusselt numbers versus Reynolds
numbers for air and CO2 heated in the microtubes respectively.
In turbulent flow regime, the measured Nusselt numbers agree
well with those predicted by the Gnielinski [1976] correlation
for air flow but slightly higher than it for CO2. However, in the
laminar flow regime, owing to the high measurement
uncertainties, the measured Nusselt number data points
scattered around the theoretical value, Nud = 4.36. This shows
f
0.1
0.01
0.001
102
103
103
104
105
Re
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that the conventional heat transfer correlation for large tubes
can be well applied for predicting the heat transfer performance
of gaseous flow in micro tubes in both laminar and turbulent
flow regime. There is no significant size effect for water flow
in tubes within this diameter range.
Air
Laminar (Nud=4.36)
Turbulent (Gnielinski)
T/C
LCT
Nud
100
10
102
103
104
105
Red
Figure 7. Air Nusselt number versus Reynolds number
CO2
100
Turbulent (Gnielinski)
Laminar (Nud=4.36)
T/C
LCT
for predicting the fully developed gaseous flow heat transfer
performance in microtubes. There is no significant size effect
for water flow in tubes within this diameter range.
NOMENCLATURE
A
Heat transfer area (m2)
Ac Tube cross section area (m2)
Specific heat (J/kg K)
cp
Tube inside diameter (m)
di
Tube outside diameter (m)
do
f
Friction factor, dimensionless
G
Mass velocity (kg/m2 s)
h
Heat transfer coefficient (W/m2 oC)
Water conductivity (W/m oC)
kf
L
Tube heating length (m)
Lfd Thermal entrance length (m)
Lm Wall Temperature measuring position (m)
LCT Liquid crystal thermography
m
Mass flow rate (kg/s)
Nud Nusselt number, dimensionless
Pr
Prandtl number, dimensionless
q
Heat transfer rate (W)
q"
Heat flux (W/m2)
Average roughness (m)
Ra
Red Reynolds number, dimensionless
Inlet water temperature (oC)
Ti
Local water temperature (oC)
Tx
Twx Local tube inside wall temperature (oC)
TLC Thermochromic liquid crystal
x
Axial position of tubes (m)
µ
Viscosity (N/m2 s)
Nud
ACKNOWLEDGMENTS
The study was supported by the National Science
Council,Taiwan.
10
102
103
104
105
Red
Figure 8. CO2 Nusselt number versus Reynolds number
CONCLUSIONS
This study measured the heat transfer coefficients for air
and CO2 flow through microtube with inside diameter of 920
µm by the method of Thermocouple and Liquid Crystal
Thermography. The test results show that both two measuring
methods provide almost the same accuracy for the wall
temperature measurement. The conventional heat transfer
correlation for laminar and turbulent flow can be well applied
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