developing flow pressure drop and friction factor of water in copper microchannels
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Journal of Mechanics Engineering and Automation 3 (2013) 641-649
Developing Flow Pressure Drop and Friction Factor of
Water in Copper Microchannels
Mirmanto
Mechanical Engineering Department, Faculty of Engineering, Mataram University, Mataram 83125, Indonesia
Received: April 23, 2013 / Accepted: May 31, 2013 / Published: October 25, 2013.
Abstract: Experiments of de-ionized water flowing in microchannels made in copper blocks were carried out to obtain pressure drop
and friction factor and to investigate any possible discrepancies from conventional theory. Three channels with widths of 0.5 mm, 1.0
mm, 1.71 mm, a depth of 0.39 mm and a length of 62 mm were tested. For adiabatic tests, the temperature of the working fluid was
maintained at 30 °C, 60 °C and 90 °C without any heat fluxes supplied to the test section. The experimental conditions covered a range
of Reynolds numbers from 234 to 3,430. For non-adiabatic tests, the inlet temperature and heat flux applied were 30 °C and 147 kW/m2
and only for the 0.635 mm channel. The friction factors obtained for the widest channel (Dh = 0.635 mm) are reported for both adiabatic
and non-adiabatic experiments to assess possible temperature effects. The paper focuses on the effect of hydraulic diameter on pressure
drop and friction factor over the experimental conditions. The pressure drop was found to decrease as the inlet temperature was
increased, while the friction factors for the three test sections did not show significant differences. The experimental friction factors
were in reasonable agreement with conventional developing flow theory. The effect of temperature on friction factor was not
considerable as the friction factor with and without heat flux was almost the same.
Key words: Microchannel, single-phase flow, pressure drop, friction factor.
Nomenclature
Aht Heat transfer area (m2)
C Constant
cp Specific heat (J/kg · K)
Dh Hydraulic diameter (m)
f Fanning friction factor
H Channel height (m)
I Current (A)
K(∞) Incremental pressure drop
K Loss coefficient
L Channel length (m)
L* Dimensionless channel length (L/Dh Re)
m& Mass flow rate (kg/s)
P Electrical power input (W)
∆pmeas Measured pressure drop between inlet plenum and
outlet plenum (Pa)
∆pch Pressure drop in the channel (Pa)
∆ploss Sum of pressure losses due to turns, sudden
contraction and sudden enlargement (Pa)
q ′′ Heat flux, based on heated area (W/m2)
qrem Heat removal rate (W)
Corresponding author: Mirmanto, Ph.D., research field:
fluid mechanics. E-mail: mmirmanto@gmail.com.
qloss Heat loss rate (W)
Re Reynolds number ( )µρ /hch DV
Re* Laminar-equivalent Reynolds number
T Temperature (°C)
V Voltage (V)
chV Mean velocity in the channel (m/s)
pV Mean velocity in the plenum (m/s)
W Channel width (m)
z Distance from channel inlet (m)
Greek Symbols
β Channel aspect ratio
ρ Density (kg/m3)
μ Dynamic viscosity (kg/m·s)
Subscripts
app Apparent
c Contraction
ch Channel
e Enlargement, entrance
FD Fully developed flow
i Inlet
o Outlet
DAVID PUBLISHING
D
Developing Flow Pressure Drop and Friction Factor of Water in Copper Microchannels
642
1. Introduction
MEMS (micro electro mechanical systems) have
generated significantly interest in the area of
microscale heat transfer because of their capability for
removing high heat fluxes. They also have been used in
many practical applications and numerous scientific
researches. Commonly the microchannels are used in
cooling systems for electronics, laser diode/weapon,
gas turbine blade, bearing and cutting tool.
A microchannel concept was introduced by
Tukerman and Pease in the early 1980s. They invented
a microchannel heat sink cooling concept. They used a
silicon microchannel with a total area of 1 cm2. The
channel width, depth and fin thickness were 50 µm,
302 µm and 50 µm, respectively. Water was used as the
working fluid [1].
Since then, many studies on microchannels have
been reported. Some authors explained that the
single-phase pressure drop in microchannels still
obeyed the conventional theory and macroscale
correlations. Gao et al. [2] investigated the
single-phase flow and the associated heat transfer in the
channels of large-span rectangular cross-section with
heights ranging from 0.1 mm-1 mm. The fluid used
was demineralized water with a pH of 7.8. They found
that the friction factors still obeyed the conventional
theory. A review of 150 papers (500 data sets) with
hydraulic diameters ranging from 8 µm to 990 µm and
Reynolds number ranging from 0.002 to 5,000 was
carried out by Steinke and Kandlikar [3]. They
concluded that in microchannels, generally, the
conventional theory was applicable. Costaschuk et al.
[4] investigated water flowing in an aluminum
rectangular microchannel with a hydraulic diameter of
169 µm and Reynolds numbers ranging from 230 to
4,740. They found that the Poiseuille numbers
confirmed the conventional theory. Silverio et al. [5]
studied pressure drop and heat convection for a
single-phase fully-developed for laminar flow in
microchannels of diverse cross-sections. They used
distilled water as the working fluid and channel
hydraulic diameters ranging from 200 µm to 500 µm.
The Reynolds number applied was 800. They stated
that the deviation from the laminar theory was not
observed.
In contrast, some studies showed that the
conventional theory was not applicable to
microchannels as described in the following
publications. Pfund et al. [6] investigated pressure
drops in microchannels with heights ranging from 128
µm to 521 µm and a width of 10 mm. The channels
were formed in a sandwich structure which consisted of
polycarbonate, spacer and 0.05 inch thick polyimide
(DuPont CIRLEX film). They used water as the
working fluid with Reynolds numbers ranging from 60
to 3,450. Although the experimental uncertainties and
systematic errors were included in the results analysis,
the deviation from conventional theory remained
significant. Jiang et al. [7] studied fluid flow and heat
transfer characteristics in rectangular microchannels 80
mm long, 900 µm wide and 350 µm deep, and the
channels were separated by 500 µm thick walls. The
test plate was made of oxygen free copper with a
thickness of 3 mm, width of 20 mm and length of 80
mm. They used a parallel microchannel with 13
channels and water as the working fluid. They found
that the friction factors were only 20% to 30% of the
theoretical value. The critical Reynolds number found
was 1,100 which was also lower than that of
conventional theory. The causes of the discrepancy
were not mentioned by the authors. Akbari et al. [8]
conducted an experimental observation on pressure
drop of de-ionized water flowing in a rectangular
microchannel with aspect ratios ranging from 0.13 to
0.76 and Reynolds numbers varying from 1 to 35.
According to their analytical model and experimental
data, the Poiseuille numbers were found to be only a
function of microchannel geometry in the range of
tested Reynolds numbers. The friction factors were
therefore different with that of conventional theory.
Kohl et al. [9] investigated the discrepancies in
previously published data using straight channel test
Developing Flow Pressure Drop and Friction Factor of Water in Copper Microchannels
643
sections with integrated miniature pressure sensors
along the flow direction. The channel hydraulic
diameters ranged from 25 µm to 100 µm and the
Reynolds numbers applied varied from 4.9 to 2,068.
This technique provided a way to consider the entrance
effects and hydrodynamic developing flow. The
authors suggested that the friction factor for
microchannels could be accurately determined from
data for standard large channels. In addition, they
explained that the inconsistency in previous research
could be due to instrumentation errors and
compressibility effects. Furthermore, they explained
that the pressure drop inside the channel associated
with the developing flow was found to be higher 17%
of the fully developed flow pressure drop.
Temperature of fluid may affect the deviation in
results from conventional theory. Shen et al. [10]
studied flow and heat transfer in microchannels with
rough wall surfaces. They applied three different inlet
temperatures: 30 °C, 50 °C and 70 °C. The
microchannel was a copper rectangular multi-channel
with 26 channels. The channel width and depth were
300 µm and 800 µm, respectively. The tested Reynolds
numbers varied from 162 to 1,257 and de-ionized water
was used as the working fluid. They revealed that the
effect of surface roughness (relative roughness
4%-6%) on laminar flow was significant and the effect
of inlet temperature on pressure drop indicated that
higher inlet temperature decreased the pressure drop. In
addition, the Poiseuille number found was greater than
that of conventional theory and also dependent on the
Reynolds number. Urbanek et al. [11] investigated the
temperature dependence on the Poiseuille number of
flow in microchannels. They used propanol, pentanol
and water as the working fluids. The microchannels
used were trapezoidal and triangular with hydraulic
diameters of 5 µm, 12 µm and 25 µm. They claimed
that the Poiseuille numbers increased by as much as
25% and 10% for the 12 µm and 25 µm channels,
respectively, as the temperature increased from 0 °C to
80 °C. This indicates that the experimental results
show a deviation from conventional theory. In contrast,
Toh et al. [12] conducted a numerical computation of
fluid flow and heat transfer in microchannels using
water as the working fluid. The channel widths and
depths ranged from 50 µm to 64 µm and 280 µm to 320
µm, respectively. The microchannels were parallel
silicon microchannels with 150-200 channels. They
found that increasing the temperature decreased the
pressure drop and hence decreased the Poiseuille
numbers. For cold water, the Poiseuille number was in
good agreement with that predicted using conventional
theory, whilst for hot water the Poiseuille number was
lower than that of conventional theory.
2. Experimental Facility
A schematic diagram of the test facility is shown in
Fig. 1. The working fluid was de-ionized water which
was drawn from the main tank and circulated through
entire the flow loop by a magnetically coupled gear
pump (Micropump GA-T23, PFSB) equipped with a
programmable variable speed drive (Ismatec Reglo
ZS-Digital). The mass flow rate of the working fluid
was measured using a Coriolis flowmeter
(Micromotion Elite CMF010) with an uncertainty of
±1 × 10-5 kg/s. Two filters were fitted in the flow loop
to remove any particles suspended in the working fluid.
Electric pre-heaters with PID controllers were installed
in the upstream loop, before the microchannel test
section, to heat the fluid to the desired inlet
temperature. After exiting the test section, the working
fluid returned to the main tank.
The microchannel test sections are shown in Fig. 2,
which was made of an oxygen-free copper block of
overall dimensions 12 mm wide × 25 mm high × 72
mm long. A single rectangular microchannel was cut in
the top surface of the block between the 2 mm diameter
inlet and outlet plenums using a Kern HSPC 2,216
high-speed micro-milling machine. The microchannel
length was 62 mm. Three identical test sections but
different widths were manufactured, as shown in Table
1. The measurements were accurate to ±1 µm giving
Developing Flow Pressure Drop and Friction Factor of Water in Copper Microchannels
644
Fig. 1 Schematic diagram of the test rig.
Fig. 2 Test section construction showing the main parts (all dimensions in mm).
Table 1 Dimensions and surface roughness of the test
section.
Test
section
Width
W
(mm)
Height
H
(mm)
Hydraulic
diameter
Dh (mm)
Aspect
ratio β
Length
L
(mm)
Surface
roughness
Ra (μm)
1 0.50 0.39 0.438 0.78 62.0 1.012
2 1.00 0.39 0.561 0.39 62.0 1.048
3 1.71 0.39 0.635 0.23 62.0 1.190
mean uncertainties of hydraulic diameter ±0.34%,
±0.37% and ±0.42%, respectively. Each test section
was clamped with a transparent polycarbonate cover
and sealed with an O-ring.
For non adiabatic experiments, heat input to the
microchannel test section was provided by a cartridge
heater which utilized an AC electrical power controlled
by a variable transformer. The electrical power
dissipated by the test section cartridge heater was
determined from voltage and current measurements
obtained using calibrated digital multimeters (Black
Star 3,225) with uncertainties of ±0.3 V and ±0.01 A,
respectively.
All temperatures were measured using 0.5 mm
diameter K-type sheathed thermocouples with an
Exploded view of
microchannel
1. Cover plate, polycarbonate; 2. Channel cover, polycarbonate; 3. O-ring seal; 4. Cartridge heater; 5.
Copper block; 6. Nitrile foam rubber insulation; 7. Bottom plate, polycarbonate.
Developing Flow Pressure Drop and Friction Factor of Water in Copper Microchannels
645
uncertainty of ±0.025 K. All pressures were measured
using differential pressure sensors (Honeywell 26PCC
type) connected between the tapping points and
atmosphere with an uncertainty of ±0.2 kPa.
The average surface roughness Ra of the channel
base was measured using a Zygo NewView 5,000
surface profiler with a resolution of 1 nm.
3. Data Reduction
The pressure drop along the microchannel, Δpch, due
to the friction and the developing flow, is obtained by
subtracting the inlet and outlet pressure losses from the
total measured pressure drop, Δpmeas. The inlet and
outlet plenum pressure losses were estimated using Eq.
(1).
( )ecchploss KKVKVp ++=∆ 290
2
2
12
2
1ρρ (1)
where K90 is the loss coefficient associated with each of
the 90° turns at the channel inlet and outlet and is
approximately 1.2. According to Ref. [13], Kc and Ke
are the inlet and exit loss coefficients for the sudden
contraction and the sudden enlargement and can be
estimated from Ref. [14] based on the ratio of the
channel area to the plenum flow area and the flow
regime (laminar or turbulent). The values of Kc and Ke
for the three test sections are presented in Table 2. The
experimental fanning friction factor based on the
channel pressure drop is given by
22 ch
hchch
VL
Dpf
ρ
∆=
(2)
To estimate the heat flux in non-adiabatic
experiments, the rate of heat loss from the test section
to the ambient was determined by energy balance tests
and found to be approximately 6.8% of the input
electrical power. The rate of heat removal, qrem, by the
working fluid is expressed as
( ) PqPTTcmq lossioprem 932.0=−=−= & (3)
where P is equal to the product of the voltage V and
current I supplied to the cartridge heater. The average
heat flux at the heated walls of the channel is defined as
q" = qrem/Aht, where Aht = (2H + W)L since the
Table 2 Values of Kc and Ke for the three test sections.
Test
section
Area
ratio σ
Kc Ke
Laminar Turbulent Laminar Turbulent
1 0.062 1.10 0.75 0.96 0.98
2 0.124 0.95 0.61 0.79 0.83
3 0.212 0.88 0.54 0.59 0.66
polycarbonate channel cover is assumed to be
adiabatic.
The propagated experimental uncertainties were
calculated based on the method described in Ref. [15]
and are given in Table 3 together with experimental
conditions.
4. Experimental Results and Discussion
The experimental results are presented in the form of
graphs and were obtained from the tests performed
with and without applying the heat flux. Channel
pressure drops obtained at three different inlet
temperatures are presented in Fig. 3 for the 0.438 mm
and those obtained from the three different hydraulic
diameter channels at the same fluid temperatures of 30
°C, 60 °C and 90 °C are presented in Figs. 4a-4c. In
general, the pressure drop increases with Reynolds
numbers, which is as expected since the pressure drop
is a function of mass flow rate. The pressure drop also
increases as the channel hydraulic diameter decreases
in this work. At the fluid temperature of 30 °C, Fig. 4a,
the pressure drop increased by approximately 51%, 108
% and 214% when the hydraulic diameter decreased by
12%, 22% and 31%, respectively.
Local pressure measurements are plotted in Fig. 5 at
equi-spaced locations along the Dh = 0.438 mm test
section from the inlet plenum (z/L = 0) to the exit
plenum (z/L = 1) for several Reynolds numbers, at fluid
temperature of T = 30 °C. The marked decrease in
pressure evident between the inlet plenum and z/L = 0.2
includes contributions due to the flow area change, the
losses associated with the 90° turn and sudden
contraction in the channel inlet, in addition to the
pressure drop due to wall shear stress and flow
development. Similarly, the pressure change between
z/L = 0.8 and the outlet plenum includes contributions
Developing Flow Pressure Drop and Friction Factor of Water in Copper Microchannels
646
Table 3 The uncertainty and the range of measurement.
Parameter Range of measurement Uncertainty
Inlet temperature, Ti 30 °C, 60 °C and 90
°C ±0.2 K
Outlet temperature, To 33-56 °C ±0.2 K
Mass flow rate, m 4.98-153 g/min ±0.6 g/min
Mass flux, G 332-4,883 kg/m² · s ±0.7%-14%
Pressure, p 2-106 kPa ±0.2 kPa
Pressure drop, p∆ 1.2-79.2 kPa ±0.38%-13.7
%
Reynolds number, Re 234-3,430 ±2%-14%
Friction factor, f 0.0101-0.0602 ±3.7%-32%
Heat flux, q" 147 ±8.4%
Fig. 3 Channel pressure drop for the 0.438 mm channel at
30 °C, 60 °C and 90 °C.
due to the flow area change and the losses at channel
exit.
In this work, hydrodynamic development occurred.
However, it depended on the Reynolds number applied
and the diameter of the test section. The length of this
entry region is more significant at higher Reynolds
numbers and for the larger hydraulic diameter. The
hydrodynamically entrance length can be estimated
using, Le = 0.056 Dh Re, as shown in Ref. [16]. All
flows were evidenced partially or completely in the
developing regions. Accordingly, the laminar flow
results are compared with a developing flow equation
proposed by Shah [17] to predict the apparent friction
factor, fapp, for developing flow in circular and
noncircular ducts, given by
( )( )
2
3.44
3.44 4 * *
*1
*
FD
app
Kf Re
L Lf
CRe LRe
L
∞+ −
= +
+
(4)
where L* is the dimensionless channel length and K(∞)
Fig. 4 Channel pressure drop obtained in the three test
sections at 30 °C, 60 °C and 90 °C.
Fig. 5 Pressure distribution along the test section for the
0.438 mm channel at a fluid temperature of 30 °C.
is the fully developed incremental pressure drop. For
rectangular channels, K(∞) is presented in graphical
form in Fig. 7, Chapter VII, in Ref. [16]. The
corresponding value of K(∞) and the constant C in Eq.
(4) which depend on the aspect ratio, β (the short wall
side/the long wall side).
T = 30 °C
T = 60 °C
T = 80 °C
ΔP
ch (
kP
a)
Dh = 0.438 mm
Dh = 0.561 mm
Dh = 0.635 mm
Dh = 0.438 mm
Dh = 0.561 mm
Dh = 0.635 mm
Dh = 0.438 mm
Dh = 0.561 mm
Dh = 0.635 mm
1,000 10,000 100
T = 30 °C
T = 60 °C
T = 90 °C
1,000 10,000 100
Re = 159
Re = 1,578
Re = 573
Re = 2,016
Re = 1,079
Re = 2,172
Dh = 0.438 mm
β = 0.78
T = 30 °C
Reynolds number, Re
Reynolds number, Re
Developing Flow Pressure Drop and Friction Factor of Water in Copper Microchannels
647
The friction factor for fully developed laminar flow
in a rectangular channel can be calculated using the
following equation given in Ref. [16]. 2
3 4 5
1 1.3553 1.946724
1.7012 0.9564 0.2537FD
fRe
β β
β β β
− += − + −
(5)
In the turbulent regime, the experimental friction
factor results are compared with Eq. (6). Due to Ref.
[13], the laminar-equivalent Reynolds number, Re*,
appearing in Eq. (6) was proposed by Jones [18] for
rectangular channels and is defined by Eq. (7).
0.32930.268
/1.016120.0929 *
/hL D
app
h
f ReL D
− −
= +
(6)
( )2 11
* 23 24
Re Re β β
= + −
(7)
The turbulent flow results are also compared with
the well-known Blasius equation [19] for circular
conduits and fully developed flow: f = 0.316 Re-0.25,
then when the Blasius friction factor is converted into
fanning friction factor, the friction factor becomes: -0.250.079f Re= (8)
As shown in Fig. 6, at low Reynolds number range
(Re < 1,500), the friction factor decreases with
Reynolds number. At a Reynolds number of
approximately 1,500, the friction factor reaches the
local minimum value and starts to deviate from the
laminar data. This indicates that there is an early
transition in this study. However, it is not necessarily
indicative of differences with conventional theory
because the flow in the entrance of the channel has
been disturbed by the sharp entrance and the flow was
in the developing region. After that, the friction factor
decreases further in the turbulent regime and the trend
of the friction factor in this regime is similar to that in
conventional channels. However, the experimental
friction factor in the turbulent regime is slightly higher
than that predicted by the developing turbulent flow
theory Eq. (6). There was a possibility that the pressure
tapping holes of 0.5 mm on the channel cover could
result in a slight increase in pressure drop. The
experimental friction factor for the three different
Fig. 6 Friction factor obtained for flow in the three test
section at three different inlet temperatures.
hydraulic diameters at fluid temperatures of 30 °C,
60 °C and 90 °C are in reasonable agreement with the
developing flow line calculated using Eq. (5) for β =
0.23 at laminar Reynolds numbers. The data indicate
that there is no effect of the hydraulic diameter in the
range studied here. Eq. (5) predicts that the friction
factor increases with decreasing aspect ratio in the
laminar regime.
As seen in Fig. 7, the effect of temperature and hence
the fluid properties is not significant. The experiments
were performed with and without heat flux applied.
The properties of the fluid were evaluated at the fluid
bulk temperature. The bulk temperatures ranged from
56 °C to 33 °C as the Reynolds numbers increased
1,000 10,000100
T = 30 °C
T = 60 °C
T = 90 °C
Reynolds number, Re
Developing Flow Pressure Drop and Friction Factor of Water in Copper Microchannels
648
from 383 to 2,167, while the fluid density increased
from 985 kg/m3 to 995 kg/m3 and the viscosity varied
Fig. 7 Friction factor obtained for flow in the 0.635 mm
channel with and without heat flux.
from 0.000494 kg/m·s to 0.000772 kg/m·s.
The changes in fluid properties do affect the pressure
drop, but they do not influence the friction factor
significantly. This contradicts were found by Urbanek
et al. [11] and Toh et al. [12] as they found the effect of
fluid temperature on the friction factor. All of them
used the same working fluid water in this study by
Urbanek et al. [11] found that as the fluid temperature
increased, the Poiseuille number increased as much as
25% of the theory for the 12 µm channel. In contrast,
Toh, et al. [12] found that as the temperature increased,
especially at low mass flow rates, the Poiseuille
number decreased. Similar to that, for flow with a
heating process, in this study the fluid temperature
variation was provided by heating the test section but
the inlet temperature was kept constant at 30 °C at the
constant heat flux of 147 kW/m2. Shen et al. [10] found
the effect of fluid temperature on the pressure drop.
This study then confirms the results obtained by Shen
et al. [10]. As the fluid temperature was increased, the
pressure drop decreased; however, they did not report
the effect of the fluid temperature on friction factor.
5. Conclusions
Experimental data have been presented for the
pressure drop and friction factor of single-phase flow
of deionized water in single copper microchannels of
rectangular cross-section. The effect of hydraulic
diameter on pressure drop is very significant whilst that
on friction factor is not considerable. The effect of
temperature is not significant either. In the laminar
regime, the apparent friction factor is in reasonable
agreement with the hydrodynamic entry region
correlation. In the turbulent regime, the experimental
friction factors are in reasonable agreement with a
circular tube correlation modified by substituting a
laminar-equivalent Reynolds number. The results
indicate early transition to turbulence but this could be
due to disturbances at the channel inlet and may not
indicate deviations from values predicted for larger
channels.
Acknowledgments
The author would like to acknowledge the Indonesia
Higher Education for the funding; Brunel University
for the experimental facility.
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