developing flow pressure drop and friction factor

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: [email protected].

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


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


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.


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


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


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


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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649

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developing flow pressure drop and friction factor

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