HTD-1 TOC
Proceedings of IMECE2002
ASME International Mechanical Engineering Congress & Exposition
November 17-22, 2002, New Orleans, Louisiana
IMECE2002-39392
SINGLE-PHASE FLOW CHARACTERISTICS AND EFFECT OF DISSOLVED GASES ON HEAT
TRANSFER NEAR SATURATION CONDITIONS IN MICROCHANNELS
Satish G. Kandlikar
[email protected]
Mark E. Steinke
Prabhu Balasubramanian
Mechanical Engineering Department
Rochester Institute of Technology
Rochester, NY 14623
ABSTRACT
An experimental investigation is carried out to study the
heat transfer and pressure drop in the single-phase flow of water
in a microchannel. The effect of dissolved gases on heat
transfer and pressure drop is studied as the wall temperature
approaches the saturation temperature of water, causing air and
water vapor mixture to form bubbles on the heater surface. A
set of six parallel microchannels, each approximately 200
micrometers square in cross section and fabricated in copper,
with a hydraulic diameter of 207 micrometers, is used as the test
section. Starting with air-saturated water at atmospheric
pressure and temperature, the air content in the water is varied
by vigorously boiling the water at elevated saturation pressures
to provide different levels of dissolved air concentrations. The
single-phase friction factor and heat transfer results are
presented and compared with the available theoretical values.
The friction factors for adiabatic cases match closely with
the laminar single-phase friction factor predictions available for
conventional-sized channels. The diabatic friction factor, after
applying the correction for temperature dependent properties,
also agrees well with the theoretical predictions. The Nusselt
numbers, after applying the property corrections, are found to
be below the theoretical values available in literature for
constant temperature heating on all four sides.
The
disagreement is believed to be due to the three-sided heating
employed in the current experiments.
The effect of gas content on the heat transfer for the three
gas concentrations is investigated. Nucleation was observed at
a surface temperature of 90.5 °C, for the reference case of 8.0
ppm. For the degassed cases (5.4 ppm and 1.8 ppm), nucleation
is not observed until the surface temperature reached close to
100°C. An increase in heat transfer coefficient for surface
temperatures above saturation is observed. However, a slight
reduction in heat transfer is noted as the bubbles begin to
nucleate. The presence of an attached bubble layer on the
heating surface is believed to be responsible for this effect.
NOMENCLATURE
A Area ( m2 )
C Concentration ( ppm )
d Channel depth ( m )
Dh Hydraulic diameter ( m )
f Friction factor
G Mass flux ( kg/m2s )
h Heat transfer coefficient ( W/m2K )
l
Length ( m )
&
m Mass flow rate ( kg/s )
Nu Nusselt number ( = q / A*∆TLMTD )
P Pressure ( kPa )
q Heat transfer ( W )
q’’ Heat flux ( W/ m2 )
Re Reynolds number ( = G*Dh / µ )
T Temperature ( °C )
w Channel width ( m )
x Vapor mass fraction at outlet
Greek
α* Aspect ration parameter used in fRe calc ( = d/w )
∆ Difference
∆TLMTD Log mean temperature difference (°C )
µ Viscosity ( Ns / m2 )
ρ Density ( kg/m3 )
1
Copyright © 2002 by ASME
Subscripts
avg Average
eff Effective
LMTD Log mean temperature difference
TS Test Section
INTRODUCTION
Dissolved gases are a part of the normal process water.
The process of removing the dissolved gas from the water is
called degasification. At chemical equilibrium at a given
temperature, the amount of gas dissolved in a liquid is
expressed by Henry’s law:
XA=Kh * PA
(1)
Where XA is the solubility of the gas in the liquid, expressed as
the mole fraction, Kh is the Henry’s law constant, specific for
each gas and temperature dependent, and PA is the partial
pressure of the dissolved gas above the liquid.
The solubility of air decreases with an increase in water
temperature. This results in gas release as the liquid is heated.
Natural cavities present on the heater surface act as nucleation
sites for the gas bubbles to form and grow, evaporating some of
the water as well. Apparent nucleate boiling is thus initiated at
a temperature lower than the saturation temperature of the pure
water corresponding to the system pressure.
The single phase flow of liquids in microchannels has been
studied by a number of investigators. Table 1 gives a summary
of some of the relevant investigations. Richter et al. [1]
conducted a study on flow through triangular microchannels in
liquid dosing applications. The channels were etched by KOH
solution producing 54.7° side angles for the triangular channels.
The top width was between 28 and 182.7 µm and the length of
the flow channel was fixed to 2 mm. The flow rate was between
0.01 to 1000 µl/min. The flow was laminar with Re less than 1.
Richter et al. [1] compared their experimental results with the
predictions using the standard triangular channel friction
factors. The agreement was very good over the entire range.
They also noted that the flow rate was quite sensitive to the
temperature as the viscosity of water changed considerably with
temperature over the experimental range from 20 to 50°C.
Pfahler et al. [2] conducted experiments with N-propanol in
two different sized rectangular microchannels. The larger ones
were made of silicon with <110> orientation, 53 µm deep by
135 µm wide, while the smaller channels were made of silicon
with <100> orientation, only 1.7 and 0.8 µm deep, and100 µm
wide. Their results indicate that for the all test sections with the
exception of the smallest depth of 0.8 µm, the conventional
theory predicted the friction factor quite well. For the test
section with 0.8 µm depth, a threefold increase in the friction
factor was noted. The results indicated a large contribution due
to developing length. For such small channels, accurate height
measurement was difficult. From this study, it can be concluded
that the conventional theory is applicable to channels as small
as 1.7 µm in depth.
The
effect
of
dissolved gases on the heat transfer due to early nucleation was
clearly demonstrated by Behar et al. [3] in both pool boiling
and flow boiling conditions. They identified two saturation
temperatures, one accounting for the partial pressure of
dissolved air in the water, Tsg, and the other representing the
normal saturation temperature of water at the system pressure,
Ts. When the wall temperature is above Tsg, but much lower
than Ts, the bubbles essentially consist of dissolved gas. As the
wall temperature increases, the vaporization of liquid starts to
play a role. Their results indicate that the heat transfer
improves with dissolved gas content due to the nucleation
phenomena. This increase continues well into saturated boiling.
At high heat fluxes however, the influence of dissolved gases
diminishes. The effect is very prominent in case of organic
liquids, which can dissolve up to ten times more air than in
water. Another interesting fact noted by Behar et al [3] was that
the pressure drop did not increase in forced convection until the
beginning of the vaporization region, when the wall temperature
reached Ts. This meant that the heat transfer enhancement
could be achieved without a pressure drop penalty so far as the
wall temperature was below the saturation temperature of water
corresponding to the total system pressure.
O’Connor et al. [4] studied the effect of dissolved gases on
pool boiling heat transfer of FC-72 over smooth copper and
microporous surfaces. Their results were similar to Behar et al.
[3], except that the increase in heat transfer was noted in the
entire range including the critical heat flux levels. The effect
was more pronounced for the treated surfaces.
Cui et al. [5] studied the effect of dissolved gases on the
evaporation of impinging droplets. The release of the gases at
high temperatures aided the formation of a gas cushion
supporting the film boiling heat transfer.
An exhaustive study of dissolved gas effects on subcooled
flow boiling of fluorocarbons was presented by Murphy and
Bergles [6]. They presented equations for predicting the onset
of nucleation by considering the partial pressure of the
dissolved gases. At higher heat fluxes, they noted that the
difference between the gassy and degassed liquids diminished
and the two boiling curves merged.
Mullersteinhagen, et al. [7] conducted a detailed
experimental study on the effect of various gases on water and
heptane. Their results were similar to those obtained by earlier
investigators. They noted that the effect of dissolved gases was
relatively small in water. The combination of heptane and
carbon dioxide produced the most pronounced effect.
Adams et al. [8] studied the effect of dissolved gases on the
flow of water in microchannels. They noted an increase in the
heat transfer rate due to early gas bubble nucleation.
In addition, there are a number of studies available in the
literature that support the observations made above, for
example, Torikai, et al. [9], You et al. [10], Jeschar et al. [11],
and Hong, et al. [12].
The pressure drop and the heat transfer processes are
affected by the changes in fluid properties at the wall during
diabatic flows. For liquids in laminar flow, a common
methodology is to apply the viscosity correction factor as given
by the following equations for Nusselt number and friction
factor:
2
Copyright © 2002 by ASME
Table 1 – Summary of Literature on Effect of Dissolved Gases on Heat Transfer near Saturation Condition
Author
System details
Results
Comments
of
gas
substantially The enhancement due to nucleation of
Behar, et al., The effects of dissolved gases on Presence
1966
subcooled boiling are studied at improves heat transfer in free and dissolved gases in the otherwise
forced convection. Improvement single-phase flow of pure liquids is
different conditions.
increases with gas content and is very clearly demonstrated.
pronounced with organic liquids
which dissolves gases up to ten times
more than the water.
O’Connor, et Pool boiling of FC-72 on a plain Presence of gas promotes nucleation The results indicate that the presence
al., 1988
copper surface and an enhanced at temperatures well below saturation of gas bubbles improves the heat
surface is studied as a function of temperature of the pure fluid. transfer significantly in subcooled
Significant enhancement is observed pool boiling.
dissolved gas content.
in the heat transfer with increased gas
content.
The effect of dissolved gas (CO2)
and solids (NaHCO3 & Na2CO3) in
water droplets boiling on hot
stainless steel surfaces are studied.
Distilled water is degassed by
placing it inside a Dewar flask
filled with dry ice. Once the water
gets frozen, the space above it is
evacuated for an hour. The water is
then allowed to melt. This process
of freezing and evaporation was
repeated two or more times
A theoretical analysis for boiling
incipience of a liquid containing a
substantial amount of dissolved gas
is presented.
At surface temperature below
nucleate boiling it was found that
droplet life time was determined by
heat and mass transfer around the
periphery of the droplet.
Dissolved CO2 enhanced the
evaporation
rate
slightly
and
dissolved NaHCO3 & Na2CO3 both
reduced the evaporation rate
Qualitative results are presented.
Dissolved CO2 came out of water and
formed a film above Leidenfrost
temperature.
Transition boiling
characteristics are affected.
Dissolved gases serve to promote
incipience resulting in a lower
incipient wall temperature and heat
flux. The presence of large amount of
dissolved gases very substantially
reduces the superheat requirement in
the lower flux portion of the boiling
curve.
The effect of gas decreases in the
fully developed flow boiling mode.
The boiling curves for the two cases
merge with little difference between
degassed and gassy liquids.
Mullersteinhagen, et
al., 1988
The effect of various dissolved
gases on subcooled boiling heat
transfer was investigated for flow
of water and heptane in an annulus
with a heated core.
Subcooled boiling heat transfer
coefficients for liquids containing
dissolved gases are always higher
than for the degassed liquid owing to
superposition of desorption and
evaporation. The convective heat
transfer is not influenced by the
gases.
The
study
focuses
on
the
enhancement due to early nucleation
in the presence of dissolved gases.
The range did not extend in the
saturated boiling region.
Adams, et al.,
1999.
Copper microchannel, 0.76 mm
diameter, was fabricated using
EDM.
Nichrome heater wire
provided heat input. Heat transfer
coefficient measured with degassed
water, and water saturated with air.
The presence of dissolved air
increases the heat transfer co-efficient
by as much as 17%.
The results provide overall effects.
The local surface temperatures, and
the nucleation phenomena were not
studied.
Cui, et
2000
al.,
Murphy and
Bergles, 1972
3
Copyright © 2002 by ASME
µ 
f
=  w 
f cp  µ m 
0.58
;
Nu  µ w 

=
Nucp  µ m 
−0.14
(2)
the average dimensions of the channels. The average channel
dimensions are: 214 µm wide by 200 µm deep and 57.15 mm
long. All of the measured values fall within ± 5% of the
average values.
There is no experimental study available on confirming the
above relationship for single-phase flow in microchannels.
Since these are empirically derived relations, they need to be
verified, although they are expected to hold as no additional
mechanisms of heat or momentum transfer are introduced.
OBJECTIVES OF THE PRESENT WORK
From the work of Richter et al. [1], the pressure drop for
microchannels is expected to be similar to that of conventional
channels. The present work is aimed at validating the singlephase friction factors for laminar flow under adiabatic and
diabatic conditions.
In literature, the effect of heat transfer on pressure drop is
not experimentally verified for microchannels. Specifically, the
effect of temperature on the friction factor described by eq. (2)
needs to be validated. Also, the Nusselt number is expected to
be somewhat different for the present case of three sided
heating around the microchannel.
Finally, the effect of dissolved gases on the changes in the
nucleation characteristics and their effect on heat transfer and
pressure drop will be investigated.
EXPERIMENTAL SETUP
The experimental setup for the horizontal microchannel
flow loop is designed to deliver a constant mass flow rate to a
microchannel heat exchanger. In addition, the water delivery
system must deliver de-ionized water with different air
concentrations. Figure 1 shows the schematic of the water
delivery system. The system includes a pressure chamber, a flat
plate heat exchanger, a throttling needle valve, a flow meter, a
test section, and a condensate collection container.
The test section details are shown in Fig. 2. The test
section is a combination of three layers. The top layer is made
of Lexan, an optically clear polycarbonate material. The water
inlet and outlet plenums are machined into the polycarbonate
layer. This is done to eliminate the heat transfer in the inlet and
outlet manifolds. The second layer is a copper block that
contains the microchannels. The copper is an Electrolytic
Tough Pitch alloy number C11000. It is comprised of 99.9%
copper and 0.04% oxygen (by weight).
The thermal
conductivity is 388 W/m-K at 20°C. The third piece is a
Phenolic. It is a laminate of epoxy and paper. It has a very low
thermal conductivity and acts as an insulator on the lower
surface of the copper plate. It is used to secure the
microchannel test section with the help of ten mounting screws.
A cartridge heater is used to provide a constant input power.
There are six parallel microchannels machined into the
copper substrate. Using a microscopic vision system, the
channel depth and width are measured at six distinct locations
along the channel. These measurements are used to determine
High-Speed
Camera
Constant
water supply
Microchannel
Test Section
pressure
Condenser
Flow
meter
Figure 1: Fluid Delivery System. Pressure Chamber, Flat
Plate Heat Exchanger (not shown, before flow meter),
Throttling Needle Valve, Flow Meter, Test Section,
Condensate Collection.
1
2
3
4
Figure 2: Test Section Cross Section. (1) Lexan Cover Plate,
(2) Copper Microchannel, (3) Cartridge Heater, and (4)
Phenolic Retaining Plate.
The pressure drop for the microchannel was measured
between the inlet and exit plenum locations. The pressure drop
was used to calculate the friction factor for the microchannels,
after accounting for the entrance region, area changes, bends,
and exit losses.
Images of nucleation phenomena are recorded using a highspeed, microscopic image acquisition system. A high-speed,
digital CCD camera was used to gather the images. It is
capable of recording at 8,000 frames per second. However, the
majority of the images are recorded at 1,000 fps. The lens used
is a long distance microscope lens. It has a field of view of 0.5
mm at a focal length of 15 cm.
EXPERIMENTAL PROCEDURE
The experimental procedures for preparing gas saturated
water, degassed water and the experimental data collection are
4
Copyright © 2002 by ASME
outlined in this section. 8 MΩ de-ionized water was used in the
experiments.
For preparing gassy water, the de-ionized water is poured
into a pressure chamber. The chamber is pressurized using air.
The water is isolated from the air by a membrane. The
membrane fills with air and expands, thereby pressurizing the
surrounding water. The resulting oxygen concentration is
measured to be 8.0 ppm.
For all of the experiments, the
oxygen content is measured using an Omega dissolved oxygen
meter.
For preparing the degassed water, the same de-ionized
water is used. The water is added to a commercially available
pressure cooker equipped with different deadweights for
different pressure settings above the atmospheric pressure. Once
the pressure is attained as the cooker is heated, the deadweight
is removed and the chamber is allowed to blow down and return
to atmospheric pressure. Thus, a very vigorous boiling occurs
within the chamber. The air dissolved in the water is forced out
of the chamber along with the steam as the chamber
depressurizes.
The chamber is once again pressurized
following the heating.
A deadweight corresponding to 5 psi and 15 psi is used on
the pressure cooker. After the above degassing process, the
water is degassed to a saturation temperature of 108 °C and 121
°C, respectfully.
The remaining dissolved air will not
precipitate from the water as long as it stays below the
respective degassing temperatures. However, steam continually
escapes from the chamber when the deadweight is again
applied.
The above procedure is repeated once more to get the final
degassed water. The concentration of dissolved oxygen, O2, is
measured as a benchmark. For a temperature of 22 °C, the
concentration of oxygen was 8.0 ppm for the gassy water and
for the two levels of degassed water it was 5.4 ppm and 1.8
ppm. This reduction of measured oxygen content can be related
to the reduction of air content between the gassy and the
degassed water.
Once the test section is assembled and well insulated, heat
loss experiments are conducted. The heat losses are determined
as a function of the copper block temperature. The heat loss
data is used in calculating the actual heat carried away by water
flowing in microchannels.
The experiment was first performed with gassy water and
then with degassed water. In both cases, water is drawn from
the bottom of the pressure vessel and passes through a flat plate
heat exchanger (not shown in Fig. 2) to adjust the water inlet
temperature to the test section. A flow meter is used to measure
the flow rate. The accuracy of the flow meter is 3% of the full
scale, or 0.25 cc/min. LabVIEW is used to monitor the
thermocouples measuring temperature.
The accuracy of
temperature measurement is ± 0.1 °C. Flow is started in the
channel and the cartridge heater is powered. The mass flux is
held constant while the input power is varied through the
desired range. The resulting thermal performance was recorded
in terms of water flow rate, inlet and outlet water temperatures,
six temperatures inside the copper block along the flow length,
and the inlet and exit pressures.
The images are acquired after the system has reached
steady state to detect nucleation in the flow channel.
A
macroscopic lens is used to get a view of all six channels. This
was used to determine channel interaction and to locate
nucleation sites. Once the entire channel is imaged, the
microscopic lens is used to gather detailed images of specific
features and events.
The uncertainty of the experimental data was determined.
The accuracy of the instruments is reported as: T = ± 0.1 °C, DP
= ± 0.01 psi, Volts = ± 0.05 V, I = 0.005 Amp. The bias and
precision errors were estimated, and the resulting uncertainty in
the heat transfer coefficient is 8.6 % and in the friction factor is
7.2 %.
RESULTS
Experiments are performed to obtain heat transfer and
pressure drop data. The mass flux was held constant and the
heat flux was varied for each data set. The flow is in the
laminar range with Reynolds number ranging from 20 to 390.
The heat flux ranged from 2.07 x 104 W/m2 to 2.65 x 105 W/m2.
The surface temperature is determined from the two rows
of thermocouples that are located at different depths from the
microchannel surface. Six thermocouples are spaced uniformly
along the length of the microchannels.
The surface
temperatures are calculated using the average heat flux value.
The log-mean temperature difference method was used to
calculate the heat transfer coefficient. The present setup closely
resembles the constant wall temperature boundary condition
due to the thick copper block employed in the test section. The
maximum temperature variation in the copper block from the
inlet section to the outlet section was measured to be less than 1
°C. The heat transfer coefficient is found using eq. 3.
h=
qTS
A * ∆TLMTD
(3)
The heat transfer surface area used for the calculation was
found using the channel dimensions measurements described
earlier. The present microchannels are heated from three sides.
The Nusselt number was calculated from eq. 4.
Nu =
hDh
kf
(4)
The theoretical value of the Nusselt number for the case of
constant wall temperature is given by eq. 5, where α* = d/w.
The resulting Nusslet Number is corrected for temperature
dependent properties using eq. 2.
1 - 2.61α * +4.97α *2 -5.119α *3
NuT = 7.541
4
5
 2.702α * -0.548α *
+
 (5)


The predicted Nusselt number is 2.97 for the current test
section with an aspect ratio of 0.935. The experimental values
5
Copyright © 2002 by ASME
coming out of water at this point and forms an insulating layer
of air bubbles. As the surface temperature of the channel
approaches the saturation temperature, the gassy case heat
transfer coefficient increases above the degassed cases. The first
two data points in each case have a very small temperature
difference, with a very large uncertainty. The reported values of
uncertainty are based on the third data set corresponding to a
surface temperature of 56 °C. The reduction in heat transfer
coefficient due to gassy nucleation has not been previously
reported. However, there is an enhancement in heat transfer
coefficient for the gassy case at higher surface temperatures.
This agrees with previous work.
The exit quality was determined for each case. The heat
loss for each data point is determined. The actual heat
transferred into the test section is used in determining the exit
quality. The results of heat transfer coefficient verses exit
quality is plotted in Figure 5. The exit quality ranges from
-0.12 to 0.12.
12
10
havg ( kW/m K )
350
6
2
0
0
Con O2 = 5.4 ppm
250
Con 02 = 8.0 ppm
Con O2 = 5.4 ppm
Con O2 = 1.8 ppm
4
Con O2 = 8.0 ppm
300
100
200
300
400
q'' ( kW/m2 )
Con O2 = 1.8 ppm
Figure 4: Heat Transfer Coefficient vs. Heat Flux. For: C1
= 8.0 ppm, C2 = 5.4 ppm, C3 = 1.8 ppm; G = 380 kg/m2s; 2.0
x 104 W/m2 < q’’ < 3.5 x 105 W/m2, -0.1 < x < 0.1.
200
150
100
12
50
10
havg ( kW/m2K )
q'' ( kW/m2s )
8
2
of the constant property Nusselt number ranged from 1.79 to
1.94, with an average value of 1.88. Note that the test section
was heated from the three sides, while the predicted value from
equation 5 [13] corresponds to uniform temperature on all four
sides.
Three different concentrations of dissolved oxygen are
investigated. Normal tap water has an oxygen concentration of
8.6 ppm at standard temperature and pressure. The de-ionized
water used for these experiments has an oxygen concentration
of 8.0 ppm. The 8.0 ppm concentration will be the reference
case and, is referred to as the gassy case. The first level of
degassing gives a Oxygen concentration of 5.4 ppm. The final
case of degassing has an oxygen concentration of 1.8 ppm.
The high speed imaging system was used to detect the
onset of nucleation. The images where studied to determine at
which surface temperature and location in the flow direction
nucleation occurs. Bubble attachment and growth was observed
for all cases.
The resulting plot of heat flux versus the wall temperature
near the exit of the channel can be seen in Figure 3. The
transition from the single-phase to two-phase is seen as a
marked change in slope. Nucleation occurs at a lower surface
temperature than the saturation temperature. Following early
nucleation, a reduction in heat flux is seen for the gassy case.
This effect can be seen in Figure 3 as well in Figure 4. In
Figure 4, the heat transfer coefficient first decreases and then
increases above the degassed cases.
0
20
40
60
80
100
Ts ( °C )
Figure 3: Heat Flux vs. Exit Surface Temperature. For: C1
= 8.0 ppm, C2 = 5.4 ppm, C3 = 1.8 ppm; G = 380 kg/m2s; 2.0
x 104 W/m2 < q’’ < 3.5 x 105 w/m2, -0.1 < x < 0.1.
The heat transfer coefficient remains almost constant in the
single-phase region. As nucleation begins, the heat transfer
coefficient begins to increase steadily with heat flux. The effect
of gas content is seen by an actual reduction in heat transfer
coefficient, as nucleation occurs. The dissolved air is now
8
6
Con O2 = 8.0 ppm
4
Con O2 = 5.4 ppm
2
Con O2 = 1.8 ppm
0
-0.120 -0.070 -0.020
0.030
0.080
0.130
Exit Quality, x
Figure 5: Heat Transfer Coefficient vs. Exit Quality. For:
C1 = 8.0 ppm, C2 = 5.4 ppm, C3 = 1.8 ppm; G = 380 kg/m2s;
2.0 x 104 W/m2 < q’’ < 3.5 x 105 W/m2, -0.1 < x < 0.1.
6
Copyright © 2002 by ASME
Figure 6 shows the observed nucleation surface
temperature verses the Oxygen concentration. The gassy case
had observed nucleation begin at a surface temperature of 90.5
°C. The degassed case of 5.4 ppm and 1.8 ppm has nucleation
beginning at surface temperatures of 99.65 °C and 99.88 °C,
respectively.
experiments. The presence of a bubble boundary layer attached
to the wall is believed to cause this effect. The two-phase flow
shows an increase in f, as expected, above the single-phase
values. The two-phase friction factor is not correlated because
of the small number of data points.
1
14.0
12.0
Con O2 = 8.0 ppm
0.9
Abiabatic f: O2 = 8.0 ppm
Con O2 = 5.4 ppm
0.8
Adiabatic f: O2 = 1.2 ppm
Con O2 = 1.8 ppm
0.7
Standard Tap Water C O2 = 8.7 ppm
0.6
10.0
f
O2 Concentration ( ppm )
16.0
14.25 / Re
0.5
8.0
0.4
6.0
0.3
4.0
0.2
0.1
2.0
0
1.E+01
0.0
90
95
100
Ts ( °C )
Figure 6: O2 Concentration vs. Nucleation Surface
Temperature. For: C1 = 8.0 ppm, C2 = 5.4 ppm, C3 = 1.8
ppm; G = 380 kg/m2s.
1.E+02
1.E+03
Figure 7: Adiabatic Friction Factor vs. Reynolds Number.
For: C1 = 8.0 ppm, C3 = 1.8 ppm; G = 380 kg/m2s; q’’ = 0.0
W/m2.
The friction factors for the single-phase flow are compared
with the theoretical values reported in literature.
The
theoretical friction factor for the case of laminar flow is
predicted from eq. (4).
f
1 - 1.3553α * +1.9467α *2 -1.7012α *3 
 (6)
f Re = 24
4
5

+
0.9564
α
*
-0.2537
α
*


The predicted fRe from equation (6), for an aspect ratio of
0.935 for the current flow channels, is calculated to be 14.25.
The adiabatic friction factor for laminar flow is first
determined experimentally to provide validity of the test section
and measurement techniques. The adiabatic friction factor for
the microchannel is shown in Figure 7. The adiabatic friction
factor is in good agreement with the predicted friction factor.
The experimental data is generally within 10% of the predicted
value.
The pressure drop was measured during all of the heat
transfer experiments as well. The measured pressure was taken
across the length of the microchannel as the fluid entered and
exited the microchannel. The diabatic friction factor is further
corrected using eq. (6) to obtain the constant property friction
factors, as shown in Figure 8.
Once again, the predicted f is for single-phase flow, and is
in good agreement with the predicted values prior to nucleation.
With the onset of nucleation, the friction factors are seen to
increase.
This behavior was found consistently in all
Re
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
1.E+01
14.25 / Re
Con O2 = 8.0 ppm
Con O2 = 1.8 ppm
Re 1.E+02
1.E+03
Figure 8: Diabatic Friction Factor vs. Reynolds Number.
For: C1 = 8.0 ppm, C2 = 5.4 ppm, C3 = 1.8 ppm; G = 380
kg/m2s; 2.0 x 104 W/m2 < q’’ < 3.5 x 105 W/m2, -0.1 < x < 0.1.
CONCLUSIONS
An experimental investigation is conducted to study the
adiabatic and diabatic friction factors for laminar flow in 200
micrometer square microchannels.
The heat transfer
characteristics are also investigated for three levels of dissolved
air content in the water. The following conclusions are drawn
from the present study.
1. The adiabatic single-phase friction factor for laminar
flow of water in microchannels is accurately described
by the established relationship for large (conventional)
diameter channels.
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Copyright © 2002 by ASME
2. The diabatic friction factors can be accurately predicted
using the property ratio correction factors used for large
diameter (conventional) channels.
3. The single-phase laminar heat transfer results are 20-30
percent below the Nusselt number value reported for
large diameter square sections. The difference is
believed to be due to the three-sided heating employed in
the present test section, as the Lexan cover essentially
acts as an adiabatic wall.
4. The effect of dissolved gas is seen using three different
Oxygen concentrations; 8.0 ppm, 5.4 ppm, and 1.8 ppm.
The enhancement in heat transfer coefficient is seen for
surface temperatures above the saturation temperature,
for the gassy case. However, a reduction in heat transfer
coefficient is observed for surface temperatures below
saturation temperature. This is believed to be due to a
thin layer of air bubbles forming an insulating layer on
the heated wall surface.
5. No difference is observed between the two levels of
degassing. The surface temperatures did not reach the
values corresponding to the degassing pressure. The
behavior of the degassed cases is as expected.
6. A slight increase in pressure drop accompanied by a
slight decrease in heat transfer coefficient is noted as
the bubbles begin to nucleate. The presence of an
attached bubble layer on the heating surface may be
responsible for this effect.
The effect is more
pronounced with higher concentration of air.
ACKNOWLEDGEMENT
All of the work was conducted in the Thermal Analysis
Laboratory at RIT. The support provided by Rochester Institute
of Technology is gratefully acknowledged.
6. Murphy, R.C., and Bergles, A.E., 1972, "Subcooled Flow
Boiling of Fluorocarbons - Hysteresis and Dissolved Gas
Effects on Heat Transfer.” Proceedings of Heat Transfer
and Fluid Mechanics Inst., Stanford University Press, pp.
400-416.
7. Mullersteinhagen, H., Epstein, N., and Watkinson, P., 1988
“Effects of Dissolved Gases on Subcooled Flow Boiling
Heat Transfer.” Chem. Eng. Process, Vol. 23 (2), pp. 115124.
8. Adams, T.M., Ghiaasiaan, S.M., and Abdel-Khalik, S.I.,
1999, “Enhancement of Liquid Forced Convection Heat
Transfer in Micro Channels due to the Release of Dissolved
Noncondensables.” International Journal of Heat and Mass
Transfer, Vol. 42, pp. 3563-3573.
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13. Kakac, S., Shah, R.K., and W. Aung. 1987, Handbook of
Single-Phase Convective Heat Transfer. New York: John
Wiley & Sons.
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