Proceedings of the Sixth International ASME Conference on Nanochannels, Microchannels and Minichannels
ICNMM2008
June 23-25, 2008, Darmstadt, Germany
ICNMM2008-62192
SURFACE ROUGHNESS EFFECTS ON HEAT TRANSFER IN MICROSCALE SINGLE PHASE
FLOW: A CRITICAL REVIEW
Perry L. Young
Rochester Institute of Technology
[email protected]
ABSTRACT
There has been increasing interest in research regarding
microscale transport phenomena over the past decade. The
increased surface area to volume ratio of a microchannel
presents enhanced heat transfer characteristics when compared
to conventional channels. For this reason, there has been
heightened interest in the use of microchannels to meet the high
heat dissipation demands of electronics. The fundamental
understanding of microscale transport phenomena is an
increasingly important area of research, and one area where
such understanding is lacking is the effects of surface roughness
on transport phenomena. There is very little published literature
discussing the effects of surface roughness on the heat transfer
characteristics of microchannels, and what literature exists
exhibits discrepancies between experimental results. This paper
serves as a critical review of literature from 2000 to the present,
both experimental and theoretical, involving surface roughness
effects on heat transfer in microscale transport phenomena.
INTRODUCTION
Faced with the obstacle of satisfying the steadily increasing
heat dissipation demands of the microelectronics industry,
Tuckerman and Pease [1] performed experiments in 1981 to
determine the feasibility of using microchannels etched in a
heat sink as a new cooling method for silicon integrated
circuits. Since a microchannel has a larger surface area to
volume ratio than a conventional pipe, the heat transfer
coefficient is larger for the microchannel, as well. Tuckerman
and Pease [1] investigated rectangular microchannels with
channel dimensions 50 μm wide by 300 μm deep etched onto
one side of a silicon wafer with a thickness of 400 μm. To
represent the heat created by a circuit, a heat source was used
on the opposite side of the silicon wafer. The microchannels
were enclosed with a cover plate, and water was used as the
fluid medium at a laminar Reynolds number of 730. These
microchannels exhibited a dramatic increase in heat transfer
characteristics, thus proving that the method of using
microchannels to meet higher heat dissipation needs was a
practical idea that should be pursued more in depth. The
Satish G. Kandlikar
Rochester Institute of Technology
[email protected]
authors concluded that while more research would be
necessary, the use of microchannels in heat sinks for meeting
the demanding heat dissipation requirements was promising.
In 1984, Wu and Little [2] investigated the heat transfer
characteristics of nitrogen flow in trapezoidal microchannels
with hydraulic diameters ranging from 134 to 164 μm. The
microchannels were extremely smooth with a roughness height
of approximately 0.01 μm and the experiment studied a
Reynolds number range from 400 to 20000. The authors
observed a departure in their experimental results from classical
theories, and that the departure increased with the Reynolds
number.
Peng et al. [3] furthered this experiment in 1993 by
studying the heat and mass flow of methanol (CH3OH) through
rectangular microchannels. Using six different microchannel
configurations machined into a steel plate, the authors found
that many aspects of the experiment had an influence on the
fluid flow characteristics. Some of these factors included the
liquid velocity, liquid properties, and the geometries of the
channels. It was concluded that the correct combination of
these factors could result in significant improvements to the
heat transfer characteristics of fluid flow through
microchannels.
The pioneering work of these authors lead to many studies
being performed on the heat and mass characteristics of fluid
flows through mini and microchannels. There are large
deviations and much scatter in the experimental results in this
area of research. This paper highlights some of the latest
research from the year 2000 to the present, and aims to provide
an in depth critical review of the possible sources of
experimental errors in hopes of providing clarity to
experimental results as well as to specify areas where further
research is necessary.
NOMENCLATURE
CH3OH
methanol
DH
hydraulic diameter
DRIE
deep reactive ion etching
H
height of microchannels
1
Copyright © 2008 by ASME
ID
KOH
SiO2
Wb
Wt
XeF2
inner diameter
potassium hydroxide
silicon dioxide
bottom width of trapezoidal microchannels
top width of trapezoidal microchannels
xenon diflouride
OBJECTIVES
In order to develop technology for producing efficient
microdevices, a thorough understanding of the fundamentals of
microscale transport phenomena is necessary. A large group of
researchers have performed experiments in order to bring clarity
to the heat and mass flow characteristics of single phase fluid
flow through microchannels, but the experimental results are
discordant with both conventional theories and other
experimental results. This paper addresses the latest research of
heat transfer in microchannel flow from 2000-2007 that either
assess the surface roughness, or study it directly. The
experimental methods and results of these experiments are
studied in order to provide insight into the discrepancies that
occur, and areas of necessary further research will be
highlighted.
ROUGHNESS EFFECTS ON HEAT TRANSFER
In the past few years there has been an increase in research
regarding heat transfer characteristics of microscale fluid flow.
There are very few studies that are focused mainly on the
effects of surface roughness on heat transfer characteristics of
single phase fluid flows at microscale. There is a much larger
body of research with the intent of investigating the heat
transfer characteristics of microscale fluid flow. Much of this
research has experimental results that lead the authors to
conclude that the surface roughness and uncertainties in channel
dimensions cause the deviations between experimental results
and classical theory.
The deviations found between
experimental data and conventional theories are scattered
among research; several researchers have found that their
experimental results are either over-predicted by classical
theories, while others report their experimental data being
under-predicted by conventional correlations. A summary of
recent research in this field is shown in Table 1. In this table,
all studies that have been performed since 2000 have been
reviewed in this paper.
COMMON SOURCES OF ERROR
There are a few common sources of error that many
researchers overlook while performing experiments. This
section provides an overview of the various difficulties with
experiments.
The entrance and exit effects of an experimental setup can
cause many problems. Many researchers neglect these effects
in their experiments, and incorporate the faulty data from these
regions into their data bank. A pressure drop measurement that
has been taken between the inlet and exit wells of a
microchannel cannot be assumed to be a fully developed
pressure drop because of the inlet and exit losses that incur.
This technique also ignores the difference between the
developing and developed flow regions. Another problem that
can be caused in the inlet and exit regions of a test section is
cavitation; if the inlet and exit are not straight, cavitation can
occur. The presence of cavitation can cause faulty data and
distort experimental results. An experimental set up needs to
be carefully designed considering the minimization of these
inlet and exit effects.
There are many machining processes that can be used to
create mini or microchannels. These processes include, among
others, micromechanical machining, x-ray micromachining,
etching processes, and surface proximity micromachining.
Each machining process causes a unique surface finish; two
samples that have been ground with a diamond wheel can
exhibit different surface finishes due to their material
composition or by differences in the grinding process such as
the speed of the grinding wheel or the grit size used. Surface
roughness has been highlighted by various authors as a possible
cause of deviations between experimental results and
theoretical correlations, and is one of the main focuses of this
paper. Many researchers use the average roughness parameter,
or relative roughness, to characterize roughness.
These
parameters do not describe the topographical surface accurately
enough for use in microfluidic applications. The use of a better
suited standard parameter for microfluidics to characterize
surface roughness would enable researchers to provide better
comparisons between experimental data. Another similar factor
that could cause experimental errors is the channel geometry.
Many etching processes used to make rectangular
microchannels end up with channels that resemble trapezoids,
and the etched shapes are not exact. It is difficult to etch or
machine the exact channel dimension desired, and to measure
the exact dimensions of the microchannel. The width of a
microchannel may vary over the length of the channel, and this
could cause erroneous data. Specific attention needs to be paid
to measuring the channel dimensions to the best of ability, and
to include uncertainties due to these measurements. An
example of the difficulties in defining a channel dimension is
shown in the SEM images shown in Figure 1, which were taken
by Liu et al. [4]. These three images of different capillary tubes
show that the surface roughness and channel geometry can be
very difficult to measure. There are many cavities and
protrusions that affect the measurement of the channel diameter
and the surface roughness parameters. One possible way to
minimize errors with these measurements is to take repeated
measurements and find an average value, which would result in
much more accurate measurements. It is important to consider
these errors when calculating experimental uncertainties.
Another issue with many experimental setups is that the
use of many channels etched into a silicon wafer can cause maldistribution effects. Even when all channels are etched to be
the same size, it is impossible to have channels that are
perfectly shaped, and completely alike. Even small differences
in channel dimensions could lead to data with higher
Figure 1: SEM Images of microtubes used by Liu et al. [4]
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Copyright © 2008 by ASME
Author(s)
Yang & Lin
Year
Flow Medium
2006
H2O
Shape
capillaries
DH (µm)
Roughness
123-962
1.16 < Ra < 1.48
0.146 < ε/D < 1.14
Re
Nu
Error
<10,000
Laminar Nu: agreement
Turbulent Nu: agreement
Nu ± 7.8 %
Re ± 2.1 %
Re < 1000: Nu ±16%
1000 < Re < 2500: Nu ±9.8%
Re > 2500: Nu ±7.8%
Qi et al.
2006
Liquid Nitrogen
capillaries
1931, 1042,
834, 531
0.67 < Ra < 2.31
0.000347 < ε/d < 0.00435
10000-90000
Nu under-predicted
higher deviation for higher roughness
higher deviation for smaller channels
Liu et al.
2006
H2O
capillaries
242, 315, 520
-
100-7000
Laminar Nu: under-predicted
Turbulent Nu: poorly predicted
Lelea et al.
2004
H 2O
capillaries
500, 300, 125.4
-
<800
agreement
Lee et al.
2004
H2O
rectangular
318-903
-
300-3500
h: under-predicted
Wu & Cheng
2003
N2, H2, Ar
trapezoidal
-
0.00109 < ε/d < 0.00985 %
<1000
Laminar Nu: increases with roughness
Nu ±7.8%
Nu ± 22.25 %
h ± 22.24 %
Re ± 1.8 %
h±
8.9 %
6-17% for Nu
Bucci et al.
2003
H2O
capillaries
172, 290, 520
1.498 < ƐA < 2.166
100-6000
Laminar Nu: under-predicted
Turbulent Nu, 520, 290 um: agreement
Turbulent Nu, 172 um: under-predicted
Kandlikar et al.
2003
H2O
capillaries
620, 1067
1 < Ra < 3 (µm)
0.161 < ε/d < 0.355 %
500-3000
Nu over-predicted
Nu ±5%
1280-13000
Nu over-predicted
higher deviation for smaller channels
-
Hegab et al.
2001
R-134a
rectangular
112-210
0.16 < ε/d < 0.89 %
Qu et al.
2000
H2O
trapezoidal
62.3-168.9
0.8 < ε < 2 µm
-
Nu over-predicted
-
Adams et al.
1997
H 2O
capillaries
760, 1090
-
2600-23000
Under-predicted
-
Ling et al.
Rhaman & Gui
1994
1993
Air
H2O
rectangular
rectangular
900-3200
0.07<H/W<0.1
-
10000-70000
100-15000
Nu: under-predicted
Nu: under-predicted
-
Wu & Little
1984
N2
trapezoidal
134-164
0.01 µm
400-20000
departure from classical
-
Harmas et al.
1983
H2O
rectangular
404-1923
0-0.02 µm
173-12900
Nu: under-predicted
-
Table 1: Summary of recent research for heat transfer in microchannels
uncertainties, and faulty data. This mal-distribution effect is
worse when the channels etched into a test section are of
various shapes and sizes. A larger channel will have a larger
mass flow rate than a smaller, neighboring channel, and
assuming that a uniform flow rate occurs in every channel can
lead to erroneous data. Wu and Cheng [5] etched thirteen
different microchannels into a single silicon chip, and studied
the effects of channel size and surface properties on the heat
transfer characteristics. Although their experimental results
show good accordance with theory, their experiments may have
mal-distribution effects and thus have faulty data. One possible
way to avoid mal-distribution effects is to design an
experimental setup that uses a single microchannel, and take
extremely careful channel dimension measurements.
At low Reynolds numbers, the increase in temperature can
be very large across a microchannel, causing a variable property
effect. The large temperature gradient implies that the the
themophysical properties cannot be assumed as constant. This
causes the bulk temperature of the fluid to vary in a non-linear
form in the flow direction, which may cause deviations between
experimental data and theoretical predictions. Due to this large
temperature gradient, assessing all thermal properties at the
mean temperature can lead to large errors. To avoid errors
caused by the variable property effect, careful control of the
heating source to prevent large temperature gradients should be
undertaken.
Another common source of error that is often not taken into
consideration is axial conduction. Most experimental setups
assume that the conduction in the heated portion of the test
section has one dimensional conduction. If the conductive
material for the experimental setup consists of a large area to be
heated, the assumption of one dimensional heat conduction may
not be accurate since heat can conduct axially and thus cause
experimental deviations from theory. In many experimental
apparatuses, three dimensional conduction is present, and thus
leads to errors when a uniform heat flux assumption is made.
Using microtubes is one method for minimizing errors
stemming from axial conduction; since the walls of most
microtubes are thin, the axial conduction becomes negligible.
To minimize these errors for other geometric shapes of
microchannels, care should be taken to have a thin heated
section with which an accurate assumption of one dimensional
conduction can be made.
CLASSIFICATIONS OF RESEARCH
For the purpose of bringing some order to the analysis of
this field of study, the research examined in this paper has been
categorized into three sections. The first of the three categories
is experimental results that are under-predicted by classical
theory. Experimental data that lies above the theoretical curves
could be influenced by surface roughness. This category will
be assessed to determine whether the roughness of the channel
was measured, or if some considerations were made for surface
roughness. The next section consists of the research that has
been found to be over-predicted by theoretical correlations.
Experimental data that lies under the theoretical correlations is
most likely to have a source of error, such as poor channel
dimensions measurements, or geometry issues due to
microfabrication difficulties. These papers will be assessed in
depth to determine whether all possible sources of error have
been considered. The last category includes research that
produced experimental results that agreed well with classical
theory. There could still be issues with experimental results
from this group of research, so this research will also be
assessed to verify that all necessary considerations were made
and that sources of error were minimized if possible.
UNDER-PREDICTED BY CLASSICAL THEORY
Liu et al. [4] investigated the single-phase heat and mass
characteristics of deionized water flow through three quartz
microtubes with inner diameters of 242, 315, and 520 μm. Two
heating methods were employed that will be discussed more in
depth later in the following paragraph. The first heating
3
Copyright © 2008 by ASME
method allowed for a uniform heat flux assumption, and the
second heating method allowed for a constant temperature
assumption for the experimental heat transfer calculations. The
laminar and turbulent flow regimes were both studied as the
Reynolds number varied from 100 to between 5000 and 7000
for the three microtubes. Two pressure apparatuses were made
for the experimental setup to force the water flow. The first
pressure apparatus consists of a nitrogen bottle at 12 MPa, a gas
storage reservoir, a precision pressure-regulating valve, a threelayer filter, and a quick opening valve. The gas storage
reservoir is intended to minimize fluctuations, the precision
pressure-regulating valve precisely regulates pressure, and the
three-layer filter removes impurities from the water flow. This
pressure system works for experiments with pressures
requirements of up to 1.6 MPa. The second pressure system
can supply higher pressures up to 10 MPa and consists of a
reciprocating plunger gauge pump that can provide flow rates
up to 4500 mL/h. Stainless steel tubes were connected to the
test section and the pressure systems were connected to these
stainless steel tubes. A filter with 1 μm pore size was placed
between the pump and the liquid storage reservoir to remove
impurities. Two k-type thermocouples were placed at the inlet
and exit of the test section in order to measure the inlet and
outlet temperatures. All experimental data except for the flow
rate was measured and acquired with a data acquisition system.
The flow rate was measured with a precision graduated cylinder
after the system had reached steady-state. Steady-state was
determined to be when the inlet and outlet temperatures remain
constant with the flow rate.
Two different heating methods were employed in this
experimental setup; the first setup provided an approximately
constant heat flux while the second setup provided a constant
temperature. The heating setup that allowed for a uniform heat
flux assumption used an 80 μm brass wire that was uniformly
wrapped around the outside of the microtubes with a machine.
Silica gel is placed around this brass wire to minimize contact
resistance between the wire and the exterior surface of the
quartz microtubes, as well as to help secure the wire in place.
The brass wire was heated by a connection to a DC power
supply that provided low voltage but high current. The second
heating method allowed for the assumption of constant
temperature using constant temperature heating. The test
section was heated by steam provided by a steam generator.
The quartz microtube was set up to be completely immersed in
saturated steam.
For theoretical analysis, Liu et al. [4] compared the
experimental data in the laminar regime to the Shah, Hausen
and the Sieder-Tate correlations. The Shah correlation is shown
in equation 1.

Equation 1 can be used for constant heat flux in a microtube for
the condition ranges shown. If R e f ⋅Pr f ⋅ d / L ≥33.3,
the Shah correlation is shown in equation 2.
   

d
0.19 Re f ⋅Pr f⋅
L
Nu=3.66
(2)
0.8

0.467


d
L
R e f 2200 , 0.5Pr 17000

0.044 f 9.8 , R e f⋅Pr f 10
w
10.117 Re f ⋅Pr f
(3)
If Re f ⋅Pr f 10, then the Sieder-Tate correlation should
be used for microtubes with constant wall temperature. This
correlation is shown in equation 4.
1
0.14
 

d 3 f
⋅
w
L
Nu=1.86 R e f⋅Pr f
(4)
For the transitional flow regime in microtubes, the Hausen
correlation for uniform heat flux was used. This correlation is
shown in equation 5.


2
3
f
1
3
f
    
d
Nu f =.116 Re −125 Pr 1
L
2
3
f
w
0.14
(5)
4
2200Re10 , Pr f 0.6
Another correlation for the the transitional and turbulent flow
regimes through microtubes is the Gnielinski correlation, which
is shown in equation 6 for a Reynolds number between 3000
and 5⋅10 6 .
Nu=
f=
(1)
0.14
f
w
The Hausen correlation for the laminar flow regime is used for
microtubes with constant wall temperature, and is shown in
equation 3 for the conditions ranges shown.
0.14
 

0.0722⋅Re⋅Pr⋅d  f
Nu f = 4.364
w
L
d
R e≤2200 and R e f ⋅Pr f⋅ ≤33.3
L

Nu f =1.953 Re f ⋅Pr f
1
3
d
L
 
f
Re f −1000  Pr f
2

f
112.7
2
1
  Pr −1
1
2
2
3
 3.64log Re−3.28
(6)
2
The last correlation used by Liu et al. [4] was the DittusBoelter correlation for the turbulent flow regime. This
correlation is shown in equation 7.
0.8
0.4
Nu f =0.023 Re f Pr f
(7)
The experimental Nusselt numbers obtained by Liu et al. [4]
were compared to the correlations in equations 1 to 7. The
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Copyright © 2008 by ASME
the authors did not identity may be the surface roughness of the
microtube; the same surface roughness in a smaller tube can
cause a higher relative roughness than than in a larger tube.
The increasing deviation with decreasing channel size also
occurs with the constant temperature heating method. In the
SEM photos, shown in Figure 1, taken of the cross sections of
the microtubes, it is evident that the interiors are not completely
smooth. Since these SEM images only show one cross section
of the microtubes, many more of these surface imperfections
may occur at other locations within the microtubes. This
undesired surface roughness may have an impact on the fluid
flow heat and mass characteristics of water through the
microtubes, and lead to the deviations shown in the research by
Liu et al. [4].
Liu et al. [4] also examined the turbulent flow regime. A
comparison between the turbulent flow data for the largest and
smallest microtubes studied for the constant temperature
assumption is shown in Figure 3. For the turbulent flow, the
Figure 2: Liu et al. [4] comparison between large and small
microtubes
experimental data for the laminar regime at Reynolds numbers
less than 2500 was plotted for both the uniform heat flux and
the constant temperature assumptions. The turbulent flow
correlations do not depend on the heating assumption such as
for the laminar flow regime, but the experimental data in both
heating cases was compared to the two turbulent flow regime
correlations. The trends of the experimental data with respect
to the theoretical correlations are similar for both heating
methods, but the magnitude of the Nusselt numbers are slightly
different. For the laminar flow regime, a comparison between
the smallest and largest microtubes studied by Liu et al. [4] is
shown in Figure 2. In this figure, it is evident that there is a size
effect occurring in the microtubes. The deviations between the
experimental data and the theoretical correlations are much
larger for the smallest microtube with an inner diameter of 242
μm than for the largest microtube with an inner diameter of 520
μm. The authors stated that the deviation at the lower Reynolds
numbers could be caused by the fact that the temperature rise
along the microchannel can be quite large, causing a variable
property effect. Another possible source of this deviation that
Figure 3: Comparison of experimental data and theoretical
correlations for (top) a microtube with ID 242 μm and
(bottom) microtube with ID 520 μm, constant temperature
assumption. From Liu et al. [4]
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Copyright © 2008 by ASME
experimental data is under-predicted by all three turbulent
correlations. However, the trend of the experimental data
follows the Gnielinski and Hausen correlations, yet the DittusBoelter correlation has a different slope than the experimental
data.
In 2004, Lee et al. [6] investigated whether classical
correlations could be used to predict thermal characteristics of
deionized water flow through ten parallel rectangular
microchannels etched in copper. These microchannels ranged
in width from 194 μm to 534 μm, and the channel depths were
typically five times the channel width in order to maintain an
aspect ratio of 5. A combination of four cartridge heaters were
machined into the copper block housing the microchannels, and
the average wall temperature of the microchannels was found
by extrapolating temperature results of type T thermocouples
placed in a series beneath the microchannels. The Reynolds
number ranged from 300 to 3500, covering both the laminar and
turbulent flow regimes, and the surface roughness of the
channels was not assessed. These authors mainly used
numerical simulation to check the experimental results, but
some comparisons were drawn between the experimental results
and classical correlations.
The laminar data was only
compared to numerical results, but the experimental data for the
turbulent flow regime was found to be under-predicted by the
Gnielinski correlation, which is shown in equation 6. The
authors concluded that there were wide disparities between the
experimental data and theoretical correlations, but that there
was good agreement between the experimental data and
numerical analysis with specifically matched boundary and inlet
conditions.
Focusing on the turbulent regime with a Reynolds number
ranging between 10,000 to 90,000, Qi et al. [7] studied the
single-phase heat and mass transfer characteristics of liquid
nitrogen flow through microtubes. The microtubes studied had
inner diameters of 1931 μm, 1042 μm, 834 μm, and 531 μm.
The roughness of each channel was measured with an Acuor
Alpha-step 500 surface profiler. The average roughness for the
largest channel of inner diameter 1931 μm was found to be 0.67
μm, and the relative roughness was found to be 0.0347%. For
the tube with inner diameter 1042 μm, the average roughness
was 0.86 μm and the relative surface roughness was 0.0825%.
The next smallest microtube with an inner diameter of 834 μm
had an average roughness value of 1.72 μm and a relative
roughness value of 0.206%, and the smallest microtube of inner
diameter 531 μm had an average roughness of 2.31 μm and a
relative roughness of .435%. The experimental data by these
authors was compared to two classical correlations; the Dittus
Boelter correlation for fully developed turbulent flows and the
Gnielinski correlation. These correlations were shown in
equations 7 and 6, respectively. The experimental data was
also compared to two non-classical correlations that have been
modified for microchannels. The first of these is the Adams
modification to the Gnielinski correlation, which is shown in
equation 8.
Nu Adams =NuGnielinski 1F 
where
  
D
F =7.6⋅10 ⋅Re 1− i
Df
−5
2
(8)
In this correlation, Df is equal to 1.161 mm. The second of
these correlations is the Wu and Little correlation for flows
with a Reynolds number higher than 3000. This correlation is
shown in equation 9.
1.09
Nu=0.0022 Re ⋅Pr
0.4
(9)
The experimental results were plotted against these four
correlations, and the graphs can be seen in Figure 4. The
experimental data was under-predicted by both the DittusBoelter and Gnielinski correlations, and the deviation increases
as the channel size decreases and as the channel roughness
increases. The authors modified the Gnielinski correlation,
taking surface roughness into consideration, by using the
Colebrook correlation with the corresponding relative surface
roughness to determine the friction factor. The experimental
results had better accordance with theory, as you can see in
Figure 4: Results by Qi et al. [9]
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Copyright © 2008 by ASME
graph (a) of Figure 4. When the experimental data was
compared to microchannel correlations, as seen in part (b) of
Figure 4, it was found that the experimental data was overpredicted by the Adams modification and the Wu and Little
correlation. The deviations between the experimental data and
the Wu and Little correlation may be due to the fact that the Wu
and Little correlation was derived for nitrogen gas. Qi et al. [7]
concluded that large surface roughness can improve heat
transfer performance in microtubes, and that when the
Gnielinski correlation is modified to take surface roughness into
account, a reasonable agreement between experiment and
theory is found.
OVER-PREDICTED BY CLASSICAL THEORY
To add to the confusion as to whether heat transfer
characteristics for fluid flow at microscale depart from
macroscale correlations, some researchers have found that their
experimental data is over-predicted by classical theory.
Hegab et al. [8] investigated the flow of R-134a refrigerant
through rectangular microchannels in 2001. The objective of
the work was to study the effect of channel geometry and the
Reynolds number on convective heat transfer in microchannels.
The hydraulic diameters used ranged from approximately 112
μm to 210 μm with a variety of aspect ratios between 1 and 1.5.
To minimize the uncertainty with channel dimensions, special
attention was paid to measurements. A profilometer was used
to measure the channel roughness and height, and a microscope
and video camera system were used to measure the channel
widths. The channel length was measured with digital dial
calipers with an accuracy of 25 micrometers. Mainly turbulent
flow was investigated, with a Reynolds number range of
2000-4000. The wall temperatures of the microchannels were
measured by averaging the temperatures recorded by seven
thermocouples on the back of the wafer. Consideration was
paid to the temperature difference between the wall and the
back of the wafer through a conduction heat transfer analysis.
The temperatures measured by the thermocouples were adjusted
by this difference to determine the wall temperatures. The
authors found that both the friction factor and the Nusselt
number of the fluid flow through the microchannels were overpredicted by conventional correlations.
The deviations
between the experimental data and classical theory ranged from
6% to 84%. These deviations were found to increase as channel
diameter decreased or Reynolds number increased. Since the
Reynolds number range investigated was in the transitional and
turbulent flow regimes, the authors compared their experimental
values for the Nusselt number to Gnielinski's correlation, which
was shown in equation 6.
In 2000, Qu et al. [9] performed experiments with the
objective of investigating and explaining the heat transfer
characteristics of deionized ultra filtered water flow in
trapezoidal microchannels in mind. For the experimental
apparatus used by Qu et al. [9], ultra filtered deionized water
was pumped from a liquid reservoir through a 0.1 μm filter in
order to prevent particles and bubbles from flowing through the
test section. Water from the filter flowed through a precision
flow meter that was calibrated and designed for low flow rates.
The water then flowed into the microchannel test section. A
variety of trapezoidal microchannels were microfabricated with
anisotropic etching techniques in silicon with a range of
hydraulic diameters from 62.3 μm to 168.9 μm. The roughness
height in the microchannels was approximately 0.8 μm for
smaller channels, and 2 μm for larger channels. The relative
roughness ranged from 3.5 to 4.5%. The microchannel plates
were bonded with an epoxy resin to the test assembly to avoid
water leakage. Since each silicon plate had five microchannels
with the same dimensions etched into it, the authors stated that
there were no mal-distribution effects. However, at the
microscopic level, it is impossible to etch two microchannels
that are exactly alike, so some mal-distribution effects are
unavoidable. A film heater was attached to the bottom wall of
the microchannel plate. A thermal compound was placed
between the heater and the bottom wall of the silicon plate in
order to reduce contact resistance. The film heater was
connected to a power supply that provides a low voltage and a
high current in order to provide a uniform heat flux condition.
The test setup and film heater were insulated with thermal
insulation materials to reduce convective and radiative heat
loss. A diaphragm type differential pressure sensor was
attached to the inlet and outlet to measure the pressure drop
across the microchannels. Three t-type (copper-constantan)
thermocouples were attached to the bottom wall of the silicon
microchannel plate to measure the longitudinal temperature
distribution, and two t-type thermocouples were mounted at the
ends of the microchannels to measure the inlet and outlet fluid
temperatures. All of the thermocouples were calibrated before
use. A data acquisition system was used to take temperature
and pressure drop measurements, and to control the pump so
that a constant flow rate at steady state was driven through the
microchannels. The microchannels were tested up to a pressure
drop of 250 psi or until microchannel breakage occurred. This
microchannel breakage usually occurred at a pressure drop of
over 250 psi across the entire mircochannel. As a result of this,
the Reynolds number for smaller microchannels was restricted
to only a couple hundred. The experimental uncertainties were
calculated; the uncertainty for the calculations of the Reynolds
number was found to be 4.6%, and the uncertainty for the
Nusselt number was found to be 8.5%.
The numerical analysis applied by Qu et al. [9] assumed
that entrance effects were negligible, due to the small hydraulic
diameter of the channel compared to the length. The flow was
also assumed to be laminar and both hydraulically and
thermally developed. The bottom of the microchannel was
assumed to have constant heat flux, and the top of the
microchannel has an adiabatic boundary condition due to the
insulation. The sides of the microchannel are also assumed to
have an adiabatic boundary condition. When the experimental
results were compared to the numerical analysis of the
microchannel as a unit cell, Qu et al. [9] found that their
experimental data was lower than for the numerical results,
although both follow the same trends for the microchannels
with the smallest hydraulic diameters. The microchannels with
the largest hydraulic diameters showed some deviation from the
laminar theory numerical trends. The authors contributed the
deviations between the numerical analysis and experimental
data to the fact that the relative roughness of the channels was
quite high (3.5 to 4.5%) and stated that the roughness may have
profound effects on the velocity field and heat and mass flow
characteristics. To make up for the effect of the surface
roughness, the authors looked into the roughness viscosity
model proposed by the same authors, Mala and Li [10], in
earlier research. This roughness viscosity model takes the
7
Copyright © 2008 by ASME


 R A⋅Rek⋅ R h −l min 
=
1−e

k
−
Rek
⋅ Rh −l min 
Re
k

2
(11)
In this equation, A can be calculated as shown in equation 12.
 
R
A=5.8 h
k
0.35
 
e
 
Re 0.94 5.0×10−5⋅
Rh
−0.0031
k

(12)
Rh represents half of the hydraulic radius of the microchannel
which for this case represents half of the hydraulic diameter.
lmin represents the shortest distance from a point in the
microchannel to the wall of the microchannel, and Rek
represents the local roughness Reynolds number which can be
calculated as shown in equation 13.
Re k =
W k f k
f
(13)
Wk represents the velocity at the top of a roughness element,
and can be found using the following relationship shown in
equation 14.
 
W k=
∂w
∂n

k
(14)
Using the roughness viscosity model shown here, Qu et al.
[9] modified their numerical relationship, and found a better
agreement between their numerical and experimental results. A
comparison of the experimental and numerical results for the
smallest microchannel with a hydraulic diameter of 62.3 μm
before and after the roughness modification is shown in Figure
5. A comparison of the results for the largest hydraulic
diameter studied by Qu et al. [9] is shown in Figure 6. From
this figure, it is evident that the experimental data doesn't
follow a flat line for the laminar theory. Instead, the Nusselt
numbers at lower Reynolds numbers are lower than predicted
and increases linearly until a constant value is reached around
the Reynolds number of 600.
Figure 5: Comparison between experimental and numerical
results with and without roughness viscosity modification
for microtube of ID 62.3 μm. From Qu et al. [9].
additional momentum transfer into consideration by introducing
a roughness-viscosity. Using this model, the viscosity used in
calculations can be calculated as shown in equation 10.
app = R f
(10)
In this equation, μapp is the new viscosity for calculations, μR is
the roughness viscosity, and μf is the fluid viscosity, evaluated
at the mean fluid temperature. The ratio of the roughness
viscosity to the fluid viscosity can be found using equation 11.
WELL PREDICTED BY CLASSICAL THEORY
In contrast with the deviations found by many researchers,
other scientists find that fluid flow at microscale does not
depart from conventional theory. In 2006, Yang and Lin [11]
studied the flow of water through six stainless steel microtubes
with inner diameters ranging from 123 to 962 μm. The
experiment studied flows up to a Reynolds number of 10,000.
Liquid crystal thermography procedures were used to obtain the
temperature on the surface of the microtube, which was heated
by a DC power source that was clamped to both sides of the
tube. The microtubes had average roughness values ranging
between 1.16 and 1.48 μm. Yang and Lin [11] found that their
experimental Nusselt number for the laminar flow regime
agreed well with the theoretical value of 4.36 for fully
developed flow with constant heat flux. For the turbulent flow
regime, they found that the experimental Nusselt numbers
8
Copyright © 2008 by ASME
to a DC power supply. Ten out of the 13 microchannels had a
surface material of Si, and the remaining three had a thermal
oxide deposition layer with a thickness of 5000 angstroms (10-4
micrometers). These three microchannels thus had SiO2 as the
surface material.
This deposition increased the surface
hydrophilic capabilities in order to provide some insight onto
the effect of surface hydrophilic properties on the flow and heat
transfer data. Other variations between the microchannels
included differences between channel dimensions, channel
depths, Wb to Wt ratios, H/Wt ratios, and the relative
roughnesses of the microchannels. To acquire a variety of
surface finishes, KOH etch was used with varying
concentrations, temperatures, and application times. The
relative roughnesses examined in the experimental study ranged
from 0.00326 to 1.09%.
Wu and Cheng [5] separated the data into two sets, and
used two conventional correlations to study the experimental
data. For a Reynolds number range from 10-100, the
correlation shown in equation 15 was used.
0.946
Nu=C 1 Re
Pr
0.488

1−
Wb
Wt
3.547
    
Wt
H
k
Dh
Dh
L
(15)
In this equation, C1 is a property based on the surface
hydrophilic properties. For a silicon surface, C1 is equal to 6.7,
and for a thermal oxide, C1 is equal to 6.6. Equation 15 is valid
for the following ranges: 4.05≤Pr≤5.79, 0≤Wb/Wt≤0.934,
0.038≤H/Wt≤0.648,
3.26x10-4≤k/Dh≤1.09x10-2,
191.77≤L/Dh≤4.53.79. For a Reynolds number range of 100 to
1500, the correlation shown in equation 16 was used.

Nu=C 2 Re.148 Pr .163 1−
Figure 6: Comparison between experimental and numerical
results with and without roughness viscosity modification for
large microtube of ID 168.9 μm. From Qu et al. [9].
agreed perfectly with the Gnielinski correlation.
The
experimental results in the developing regime were found to
agree well with the Shah and Bhatti correlations. The authors
concluded that there were no size effects within the range of
microtubes studied in these experiments.
In 2003, Wu and Cheng [5] conducted studies on the heat
transfer characteristics of water flow through trapezoidal silicon
microchannels with a variety of surface finishes. The goal of
this research was to experimentally investigate the effects of
geometric parameters, hydrophilic properties, and surface
roughness on the heat and mass flow through the microchannels
investigated. Focus was placed on the laminar flow regime,
with the Reynolds number ranging from 10 to 1500. The
authors microfabricated a silicon wafer with 13 different etched
microchannels, and heated the wafer with a film heater attached
Wb
Wt
0.908
1.001
.798
     
Wt
H
k
Dh
.033
Dh
L
(16)
In equation 16, C2 is equal to 47.8 for silicon surfaces and 54.4
thermal oxide surfaces. This equation is valid for the following
ranges: 4.44≤Pr≤6.05, 0≤Wb/Wt≤0.934, 0.038≤H/Wt≤0.648,
3.26x10-4≤k/Dh≤1.09x10-2, and 191.77≤L/Dh≤453.79.
These two correlations were compared to the experimental
data through all thirteen microtubes. A plot of the comparison
between the correlations in equations 15 and 16 and the
experimental data is shown in Figure 7. The authors found
reasonable agreement between the classical correlations and the
experimental data. They concluded that the bottom to top
width ratio, the height to top width ratio, and the length to
diameter ratio have large influences on the laminar Nusselt
numbers, and that the laminar Nusselt number increases as the
surface roughness of the channels increase. This increase was
found to be more evident at the lower Reynolds numbers.
However, one factor that may have been overlooked in this
research was the mal-distribution effects that may be caused by
having a variety of microchannels etched into a single silicon
wafer. Each channel would have an unique mass flow rate, and
the assumption that the mass flow rate is constant throughout
all the channels could lead to faulty data.
In 2004, Lelea et al. [12] performed experiments to study
the heat and mass transfer characteristics of distilled water flow
through microtubes with inner diameters of 125.4 μm, 300 μm,
and 500 μm. The objective of this research was to provide
9
Copyright © 2008 by ASME
clarification to the scatter of published experimental results.
The flow was kept to the laminar flow regime, with the highest
Reynolds number studied being 800. The test section of this
experimental setup was placed in a vacuum to minimize heat
transfer losses, and the inlet temperature of the distilled water
was kept constant using a counter-flow heat exchanger. The
microtubes were heated by Joule heating, providing a uniform
heat flux to the water running through the test section.
Therefore, the fully developed Nusselt number was 4.36 for the
uniform heat flux assumption with microtubes. The roughness
of the microtubes studied was not assessed, but it was assumed
that the microtubes were smooth. The experimental results for
these experiments were compared to the Shah and London
correlation for microtubes with a uniform heat flux. This
correlation is shown in equations 1 and 2. Another form of the
Shah correlation is shown in equation 17 for the local Nusselt
number with thermally developing conditions.
3
* −0.506
Nu x=4.3648.68⋅10 ⋅x 
⋅e
−41x *
(17)
In equation 17, the non-dimensional x* can be calculated using
the following equation.
Re
DH
x* =
Re Pr
(18)
Lelea et al. [12] compared their experimental data to these
correlations, and the results can be seen in Figure 4. In this
Figure, all experimental data from all three sizes of microtubes
examined has been included and compared to the Shah and
London correlations, as well as the fully developed Nusselt
number of 4.36 for microtubes with uniform heat flux. Overall,
there appears to be agreement between the theory and
experimental data, but in the thermally developing region, there
is some scatter among the experimental results. To examine
this region more, individual graphs of the experimental data for
each microtube were examined in depth, and are shown in
Figure 9. The top graph in Figure 9 is a plot of the local Nusselt
number versus the non dimensional x for the largest microtube
of inner diameter 500 μm and an input heat of 2 watts. There is
a large scatter around the developing area of the experimental
results for this particular study, but for early developing
conditions and fully developed conditions, the experimental
data appears to match well with theoretical correlations. The
middle plot is a comparison of the experimental data for the
microtube with an inner diameter of 300 μm with an input
heating power of 2 watts and the classical correlations. There
seems to be a good agreement between the classical correlations
and the experimental data for this experiment. The bottom plot
of this series in Figure 9 is a plot of the experimental data and
classical correlations for the smallest microtube of inner
diameter 125.4 μm with an input heating power of 0.75 watts.
The differences in the heating powers were most likely done in
order to avoid the variable property effect. This plot does not
have as large a scatter as the top graph, but it does have some
scatter between the theoretical correlations and experimental
results at the end of the developing regime. In looking at these
Figure 7: Comparison of heat transfer correlations with
experimental data from Wu and Cheng [6]
three graphs, it can be concluded that the deviations seen are
approximately constant within all three channels, and no size
effect has occurred.
Interesting results were obtained by Kandlikar et al. [13]
who studied the heat transfer characteristics of water through
rough stainless steel microtubes having inner diameters of 1067
and 620 μm in 2003. Two etching compounds were used to
create a variety of surface roughness finishes inside the
microtubes. The first acid treatment was made with 8 mL of
HCl and 10 mL of HNO3 at room temperature. One sample of
both sizes of microtubes were filled with this acid treatment,
and let to sit for a minute. The surface roughness that resulted
from this acid treatment had an average roughness value of 1.9
μm for the larger microtube, and 1.8 μm for the smaller
microtube. The relative roughness values were calculated by
taking the ratio of the average roughness value and the tube
diameter. The relative roughness for the larger tube with the
first acid treatment was 0.00178, and for the smaller tube the
relative roughess was 0.00290. A second acid treatment was
created with 50 mL of HCl, 5 mL of HNO3 and 50 mL of H2O
at 50°C. This acid treatment was flushed through a sample of
both size microtubes, and let to sit for a minute. The average
roughness from this acid treatment in the larger tube was found
to be 3.0 μm, and for the smaller tube it was 1.0 μm. The
relative roughness values were 0.00281 and 0.00161 for the
larger and smaller tubes, respectively. For the original surface
finish of the microtubes, the average roughness in the larger
and smaller tubes was found to be 2.4 μm and 2.2 μm,
respectively. The relative roughness value for the large tube
that had not been exposed to any etching treatments was found
to be 0.00225, and for the smaller tube the relative roughness
was 0.00355. Mostly the laminar flow regime was studied; for
the larger microtube studied, the Reynolds number ranged from
500 to 2600, and for the smaller microtube, the Reynolds
number ranged from 900 to 3000. Electrical resistance was
used to heat up the stainless steel microtubes, and heat loss was
minimized by wrapping the tube with fiberglass insulation.
The voltage and current input were multiplied to determine the
net power input supplied to the test section, and the temperature
10
Copyright © 2008 by ASME
equation 6, as well as the Adams modification to the Gnielinski
correlation, which was shown in equation 8. When the
experimental data was plotted with the theoretical correlations,
a strong agreement was found for the largest capillary tube
examined. However, as the channel size decreased from 520
μm to 290 μm, the deviation between the experimental data and
Figure 8: Summary of experimental results by Lelea et al. [12]
distribution across the pipe was measured with three k-type
thermocouples. The entire test set up was determined to be
under thermally developing conditions. The experimental data
was compared to the Shah and London correlation for the local
Nusselt number for thermally developing flow was used. This
correlation is shown below in equation 17. All experimental
data was found to match the Shah and London correlation
within experimental uncertainties. It was found that for the
microtube with an inner diameter of 1067 μm, the experimental
data matched well with the Shah and London correlation
regardless of the surface roughness finish. However, the
experimental data for the smaller microtube with an inner
diameter of 620 μm was under-predicted by this correlation as
the surface roughness increased. The authors concluded that
more research was required to understand the effects of surface
roughness in tubes of smaller diameters.
Experiments run by Bucci et al. [14] on stainless steel
capillary tubes with inner diameters of 172 μm, 290 μm, and
520 μm also ended up with mixed results; the experimental data
for the smallest capillary tube was found to be under-predicted
by theoretical correlations, while the remaining experimental
data was found to show agreement with classical theory. The
Reynolds number for these experiments varied between 100 to
6000, covering both the laminar and turbulent flow regimes.
The capillary tubes were heated through the condensation of
water vapor outside the capillary tubes in order to allow for a
constant surface temperature assumption. For this heating
method, a boiler was used to create vapor, and was placed near
the experimental setup. This heating method allowed for the
exterior surface temperature of the capillary tubes to be known
without placing thermocouples directly on the exterior of the
test section; the exterior channel temperature would be
equivalent to the condensation temperature of the vapor. While
surface roughness wasn't the main concern of the paper, a laser
interferometric microscope was used to examine the capillary
tubes, and the absolute roughness height was found to be 1.609
μm for the largest capillary tube, 2.166 μm for the 290 μm
capillary tube, and 1.498 μm for the smallest capillary tube.
Bucci et al. [14] compared the laminar experimental data to
the Hausen correlation, which was developed for a long tube
with a uniform surface temperature. This correlation was
shown in equation 3. The turbulent experimental data was
compared to the Gnielinski correlation, which is shown in
Figure 9: Individual Experimental Results by Lelea et al. [12]
11
Copyright © 2008 by ASME
classical correlations increased. This trend continued, with the
smallest capillary tube with an inner diameter of 172 μm
showing the largest deviations between the experimental results
and conventional correlations. However, the smallest capillary
tube started to show an agreement with the Adams modification
to the Gnielinski correlation. The experimental results for the
heat transfer experiments with all three capillary tubes can be
seen in Figure 10. In this figure, the top plot shows the
experimental data for the largest capillary tube of inner
diameter 520 μm. In this plot, it is evident that the experimental
data matches the Hausen correlation for the laminar flow
regime, and the Gnielinski correlation for the turbulent flow
regime. The middle plot in Figure 10, which shows the
experimental data for the capillary tube of inner diameter 290
μm, starts to show deviations between the experimental data
and these two theoretical correlations. The third plot in this
series has a comparison between the experimental data and
theoretical correlations for the experimental data for the
smallest capillary tube. It is evident from this plot that the
experimental data deviates from the theoretical correlations, but
seems to match the Adams modification to the Gnielinski
correlation. From this series of graphs, it is seen that the
deviations increase as the channel size decreases, bringing into
question whether there is a size effect, and where this size effect
begins to occur. It may be that the surface roughness has a
much larger effect in the smaller channel, and that this is the
reason why the experimental data has larger deviations as the
channel size decreases.
consideration, and found that the relative roughness ranged
between 3.5 to 4.5%. This large relative roughness may be a
large factor as to why the experimental data was over-predicted
by theory. The use of a standard roughness parameter
specifically for microfluidic flows, and a process for
incorporating the surface roughness into theoretical correlations
could help to provide clarification here. Another issue where
this would help provide insight is evident in the work by
Hegab et al. [8]. The experimental data found by these authors
was also found to be over-predicted by theory. The authors
noticed that the deviations increased as channel size decreased.
This could be due to the surface roughness. A microchannel
with the same roughness elements as a smaller channel would
have a much lower relative roughness value than the smaller
DISCUSSION
The research that has been reviewed in this paper includes a
wide range of experimental approaches and results. The most
common issue with regards to experimental data is that the
surface roughness of the microchannels causes departure from
classical theories. Surprisingly, this appears to be the case for
both under and over-predicted experimental results. Kandlikar
et al. [13] found that the larger tube assessed exhibited no size
effects, while the experimental data for the smaller tube with an
inner diameter of 620 μm was found to be slightly lower than
conventional correlations with deviations that increased with
increasing surface roughness. Similar results were found by
Bucci et al. [14]. These authors noticed that the experimental
data for the smallest microtube of 172 μm were under-predicted
by conventional correlations, while good agreement was found
for the larger microchannels of 290 and 520 μm.
Liu et al. [4] also found their experimental results to be
under-predicted. The authors used a SEM microscope to obtain
images of the microtubes used. These images were used to
measure the inner diameter of the microtubes. From these SEM
images (shown in Figure 1), it is also noticeable that there is
some surface roughness that could alter the experimental
results. The likely cause of some error in this experiment stems
from the fact that the SEM images were only taken at one
location in the microtube. For more accurate measurements of
the microtube inner diameters, this imaging process could be
performed repeatedly in more than one location, and averaged,
or a roughness model could be proposed.
Qu et al. [9] found that their experimental data was overpredicted by classical theory. The trends between the data and
the theoretical curves are similar, except at the lower Reynolds
numbers. The authors took the channel roughness into
Figure 10: Experimental Results from Bucci et al. [14]
12
Copyright © 2008 by ASME
channel. A smaller channel with a larger relative roughness,
even though the roughness elements themselves are the same,
can cause a size effect due to roughness.
Wu and Cheng [5] found that their experimental data
appeared to match well with conventional correlations. The
relative roughness of the microtubes assessed are very small
and range between 0.00326 and 1.09. Since these microtubes
appear to be very smooth, the surface roughness may not have a
large impact on the experimental results. Since the test section
studied involved the use of microtubes, axial conduction is a
minimal concern at most. The temperature gradient also
appears to be too small for the consideration of errors due to
the variable property effect, so this research is most likely very
accurate.
As shown by this critical review, simply looking at surface
roughness may not be enough. Many problems can stem from
the variable property effect, and due to axial conduction.
Careful experimentation is necessary to minimize axial
conduction and other such errors to be able to isolate the effects
of surface roughness and find a way to characterize these
effects. For example, the research by Kandlikar et al. [13] and
Bucci et al. [14] was performed with capillary tubes. Capillary
tubes have thin walls, and can be accurately modeled using a
one-dimensional heat transfer model. These two bodies of
research found that their data agreed well with classical
correlations for the larger capillary tubes, and only deviated for
the smallest tubes examined. Therefore, since there may have
been very little axial conduction, the deviations for the smallest
capillary tubes could possibly be attributed to surface roughness
effects, since the effect of surface roughness becomes
heightened at smaller scales. When these typical sources of
error are identified and minimized, agreement with
conventional correlations can be found.
CONCLUSIONS
A select body of research from the years 2000 to 2007 has
been examined to provide clarity to the scatter of published
results for heat and mass transfer characteristics of microscale
flows. Many various sources of error can cause erroneous data,
leading to discrepancies between experimental data and
conventional correlations. If attention is paid to minimize the
effects of inlet and outlet losses, mal-distribution effects,
surface roughness, variable property effects, and axial
conduction, it is possible to provide experimental data that will
allow for crucial insights in this field of research to be made.
AREAS FOR FURTHER RESEARCH
To further the fundamental understanding of surface
roughness effects in microchannels, the following areas should
be carefully investigated.
● Heat transfer characteristics in the hydraulically and
thermally (and simultaneously) developing regions
● Design of experimental setup with minimal axial
conduction for microchannels with geometries other
than circular.
● A standard roughness parameter for surface
characterization for microscale fluid flows
● A procedure for incorporating this roughness
parameter into studies of microscale heat and mass
transfer
●
Determination of when surface roughness becomes a
factor in determining heat and mass transfer
characteristics of fluid flow
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