International Journal of Heat and Mass Transfer 136 (2019) 851–863
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International Journal of Heat and Mass Transfer
journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer enhancement of turbulent channel flow using dual
self-oscillating inverted flags: Staggered and side-by-side
configurations
Yujia Chen, Yuelong Yu, Di Peng, Yingzheng Liu ⇑
Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
Gas Turbine Research Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
a r t i c l e
i n f o
Article history:
Received 27 December 2018
Received in revised form 5 March 2019
Accepted 8 March 2019
Keywords:
Inverted flag
Heat transfer
Side-by-side flags
Staggered flags
TSP
a b s t r a c t
This study experimentally determined the flapping dynamics of dual self-oscillating inverted flags placed
inside turbulent channel flows in side-by-side and staggered configurations and their ability to enhance
wall heat removal. Three clearance-distance to channel-width ratios (Gc/W = 0.19, 0.31, and 0.5) and
three streamwise-distance to channel-width ratios (Gy/W = 0, 2, and 4) were used to examine distinct flag
behaviors. A single flag mounted to the heated wall with various gap clearances was chosen as the benchmark. The flags’ time-varying motions were recorded by a high-speed camera system. Three dynamic
regimes were identified on the basis of the flags’ dimensionless stiffness and the channel flow’s
Reynolds number: the biased mode, the flapping mode, and the deflected mode. Temperature sensitive
paint (TSP) measurements demonstrated that the best cooling enhancement, with a local Nusselt number
ratio of over 1.6, was achieved for the single flag system at Gc/W = 0.19. Adding another inverted flag to
the side-by-side configuration at Gc/W = 0.19 further enhanced the heat removal performance on both
channel walls, and the flapping period increased by nearly 50%. However, placing two side-by-side flags
close to each other (Gc/W = 0.31) led to chaotic flapping motions, resulting in diminutive augmentation in
heat transfer and an appreciable penalty in pressure drop. In the staggered configuration at Gy/W = 2 and
4, the two inverted flags synchronously flapped with a stable phase difference, and the flapping periods
were similar to those of the single flag. The peak Nusselt number ratio was 1.9 for Gy/W = 2, which was
attributed to the concerted influence of the staggered inverted flags. The system with staggered flags
placed close to the heated wall had a higher thermal enhancement factor than the system with flags
mounted in tandem along the channel centerline.
Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction
The heat transfer of channel flow plays an important role in
industry applications, e.g., in gas turbines and heat exchangers,
and can be considerably intensified by various turbulence
enhancement mechanisms (e.g., ribs, pin fins, protrusions, and
dimples [1–4]). However, such strategies significantly deteriorate
in turbulent channel flows with low Reynolds numbers (104),
which are common in electronic products due to their highly limited effective areas and the increased cost of pressure drop. To
overcome this issue, active vortex generators, such as piezo fans
and magnetic fans [5,6], have been developed, but these depend
⇑ Corresponding author at: Key Lab of Education Ministry for Power Machinery
and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University,
800 Dongchuan Road, Shanghai 200240, China.
E-mail address: yzliu@sjtu.edu.cn (Y. Liu).
https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.048
0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
on reliable external power supplies. Recent studies have shown
[7] that placing a flexible flag in the channel and then forcing it into
a self-oscillating motion produces substantial gains in heat transfer
in the extended area [8], probably due to the flag’s instability and
the highly unsteady channel flow behind the flag.
A few preliminary attempts have been made to promote wall
heat removal by placing a flag or multiple flags in the channel.
For laminar channel flow at a very low Reynolds number
(Re = 600), two vertically wall-mounted flexible flags [9,10] were
forced into self-oscillating motions with a moderate amplitude to
flag-length ratio, A/L > 0.35; the numerical results suggested an
optimized heat transfer performance with nearly 100% enhancement in mean heat flux. However, recent experimental attempts
[11] have indicated that such intense flapping is hard to generate
in a turbulent channel flow. A computational study of laminar
channel flow at Re < 800 [12] showed that the flow-induced vibra-
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Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
Nomenclature
A
B
C*
E
F
f
fT
Gc
Gx
Gy
Hc
H
h
I
KB
L
Lp
Nu
Nu*
P
Dp
R
ReW
S
T
t*
Dt*
U0
V
flapping amplitude [m]
^ m]
flexural rigidity [NA
length to channel width ratio C* = L/W
young’s modulus of the inverted flag [GPa]
friction factor
flapping frequency of the inverted flag [Hz]
TSP function
gap clearance between the flag and wall [m]
separation distance between two flags in the transverse
(x) direction [m]
separation distance between two flags in the streamwise (y) direction [m]
height of the wind channel [m]
height (or span) of the inverted flag [m]
thickness of the inverted flag [m]
luminescence intensity of the TSP
dimensionless bending stiffness
length of the inverted flag [m]
distance between two pressure taps [m]
Nusselt number
Nusselt number ratio
electronic power applied to the heating foil [W]
pressure drop between two pressure taps [Pa]
results calculated from variables
Reynolds number (based on the width of the channel)
area of the heating foil [m2 ]
temperature [K]
dimensionless time
dimensionless flapping period
^ s1 ]
free stream velocity [mA
measured variables
tion of a conventional flag (clamped at the leading edge and free at
the trailing edge) resulted in an appreciable convective heat transfer augmentation of over 60%. Unfortunately, the extremely soft
flag used in the numerical study was nearly unavailable in engineering applications. A real flag in the conventional configuration
can be experimentally excited by the channel flow at a high Reynolds number, up to 105 [13,14]; however, this is challenging for
Re 104 [15]. A single inverted flag (free at the leading edge and
fixed at the trailing edge) with a length to channel-width ratio of
C* = 0.5 was excited to an intense flapping motion at the channel
laminar flow (Re < 800) by Park et al. [16], who reported heat transfer enhancement of 150%, but with a penalty of nine times the
mechanical energy loss. Subsequently, Yu et al. [17] experimentally examined the heat transfer enhancement performance of
three inverted flags of different lengths (C* = 0.125, 0.25, and
0.375) in the range of Re = 1.2 104 –2.3 104 . They found the
local Nusselt number increased by 20% for a short flag
(C* = 0.125), and the pressure drop increased by 69%. As the longest
flag (C* = 0.375) was in flapping mode, it achieved the best cooling
performance, with a remarkable augmentation of up to 70%, but at
a substantial cost in pressure drop, which increased by a factor of
3.17. This increase in pressure drop was attributed to the energetic
vortex shedding process behind the flag, and was confirmed by the
time-resolved particle image velocimetry (TR-PIV) measurement of
the unsteady flow [17]. Using tandem flags (C* = 0.25) along the
channel centerline, Chen et al. [8] successfully doubled the local
Nusselt number for the extended streamwise area, but the total
pressure drop still exceeded the smooth channel without flags by
a factor of four. In these studies [8,17], the considerable penalty
in pressure drop was the result of a large blockage of the long flag
W
x
y
z
X
Y
Z*
width of the channel [m]
transverse direction [m
streamwise direction½m
spanwise direction½m
normalized transverse coordinate
normalized streamwise coordinate
normalized spanwise coordinate
Greek symbols
thickness of the turbulent boundary layer [m]
d99
g
thermal enhancement factor
t
Poisson’s ratio of the inverted flag
k
thermal conductivity of the air [Wm1 K1 ]
qf
fluid density [kg m3 ]
qs
density of the inverted flag [kg m3 ]
Subscripts
0
smooth channel
ref
reference
air, in
inlet air
Abbreviation
CCD
charge coupled device
CMOS
complementary metal oxide semiconductor
FFT
fast fourier transform
TSP
temperature sensitive paint
TR-PIV time-resolved particle image velocimetry
UV-LED ultraviolet light-emitting diode
to the high-speed mainstream, which is needed for a flag placed in
the channel centerline to generate a large flapping motion and
sweep out the thermal boundary layer. It is well established that
placing short inverted flags in proximity to a heated wall introduces strong disturbance to the near-wall flow, intensifying wall
heat removal at a reduced pressure drop across the entire channel,
and that the effective heat transfer enhancement area can be
extended by different configurations of the paired flags.
Building on Chen et al. [8], this study quantified the coupling
flapping dynamics of dual inverted flags in proximity to the wall
and the resultant heat transfer enhancement. Using a single flag
as a benchmark, two representative configurations of the paired
flags, staggered and side-by-side, were compared. A total of three
clearance-distance to channel-width ratios (Gc/W = 0.19, 0.31,
and 0.5) and three streamwise-distance to channel-width ratios
(Gy/W = 0, 2, and 4) were varied to examine their distinct behaviors. In the experiment, a high-speed camera was installed to identify the flags’ flapping motions; the spatially varying temperature
field on the heated wall surface was determined using the temperature sensitive paint (TSP) technique.
2. Experimental setup
2.1. Flag dynamics measurement apparatus
Fig. 1(a) presents a schematic diagram of the experimental
setup to measure the flag flapping dynamics. Two rectangular
and flexible inverted flags made of transparent polyethylene
terephthalate (density qs ¼ 1:38 103 kg=m3 , Young’s modulus
E = 2:2GPa;and Poisson’s ratiot ¼ 0:39) were set parallel to the
Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
853
Fig. 1. Flag flapping dynamics: (a) schematic diagram of experimental setup; (b) single flag configuration; (c) side-by-side flags configuration; and (d) staggered flags
configuration.
flow. The flags shared the same thickness (h = 0.025 mm), height
(or span) (H = 60 mm), and length (L = 7.5 mm, C* = 0.19). These
dimensions led to a high aspect ratio (H/L = 8) that guaranteed
two-dimensional flapping motions near the mid-span position.
The inverted flag was clamped at its trailing edge with two pieces
of carbon fiber plate that were 3 mm in length and 0.5 mm in
thickness. The right-hand coordinate origin was situated at the
mid-span of the upstream flag trailing edge, and the x, y, and z axes
denoted the transverse, streamwise, and spanwise orientations,
respectively. All of the coordinates were normalized by the channel
width W, i.e., X* = x/W, Y* = y/W, and Z* = z/W. The measurements
were conducted in a subsonic open-circuit wind tunnel with an
80 mm (height, Hc) 40 mm (width, W) cross section that had
been previously installed by Chen et al. [8]. The wind tunnel was
equipped with a contraction section (contraction ratio 7:1) to
straighten the air flow entering the test segment. The top-hatted
inlet velocity profile, with a turbulent boundary layer thickness
of d99 = 0.25 W, was measured by moving the hot-wire probe along
the normal-wall (x) direction; the turbulence intensity was below
2% for the current free-stream velocity range U0 = 5:8 9:4 m/s
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Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
(ReW = qf U0W/lf ranged from1:55 104 to2:52 104 ). The dimen2 3
f U0 L ,
which characterizes the
sionless bending stiffness [7] KB=B=q
relative magnitude of the bending force to the fluid inertial force
exerted on the flag, ranged from 0.198 to 0.075. Herein,
qf = 1.2 kg/m3 denotes the air density (1 atm, 395 K)
3
andB ¼ Eh =12ð1 t2 ) is the flexural rigidity of the flag.
To visualize the flag motions, a 5 W continuous-wave semiconductor laser (532 nm) was used to illuminate the mid-span of the
flags, as shown in Fig. 1(a). A 12-bit high-speed CMOS camera
(dimax HS4, PCO, USA) was installed on the top of the wind channel to record the flapping dynamics of the inverted flags. The camera was operated at a speed of 2000 fps (the flag flapping
frequency, f, was around 100 Hz for all of the experiments) with
a resolution of 1500 600 pixels (0.1375 mm/pixel), allowing the
instantaneous flag profiles of the two inverted flags to be captured
simultaneously. Inspired by the side-by-side and staggered flag
systems proposed by Cerdeira et al. [18], Ryu et al. [19], and Huang
et al. [20], three configurations were tested, as shown in Fig. 1(b)–
(d): (b) a single flag, (c) side-by-side flags, and (d) staggered flags.
In Fig. 1, Gc is the gap clearance between the flag and the wall, Gx is
the separation distance in the transverse (x) direction, and Gy
denotes the separation distance in the streamwise (y) direction.
To improve the clarity of the discussion of the results in following
sections, the upper and lower walls in Fig. 1(b)–(d) are marked as
wall side 1 and wall side 2, respectively.
2.2. Heat transfer performance measurement apparatus
The heat transfer measurements were conducted in the same
wind tunnel. The spatially varying temperature field on the heated
wall was quantified using the temperature sensitive paint (TSP)
[21] technique. TSP is a molecular temperature sensor consisting
of luminescent molecules and a binder. When illuminated by light
of a certain wavelength (385 nm in this study), the luminescent
molecules in the TSP layer are excited into an unstable elevated
energy state, which is susceptible to shifting to a ground state
through two mechanisms: thermal deactivation and luminescent
deactivation (i.e., luminescence wavelength around 600 nm). As
the temperature rises, thermal deactivation increases and luminescent deactivation decreases, leading to attenuated luminescence
intensity. The temperature field, accurately indicated by the luminescence intensity, can be determined by examining their relationship, which is generally described by the function fT in the
following equation:
Iref
¼ f T T; T ref ;
I
Fig. 2. Schematic diagram of the heat transfer experimental setup.
ð1Þ
where Iref is the luminescence intensity at a specified reference temperature Tref (usually room temperature) and I is the luminescence
intensity at arbitrary temperature T. The process for calibrating
function fT is discussed below.
Fig. 2 shows the schematic diagram of the heat transfer experiment apparatus. To produce the TSP layer, an oxygenimpermeable
automobile
clearcoat
(Dupont ChromClear
HC7776S) was used as a binder, and Ru (dpp) (GFS Chemical,
Inc.) was selected as the temperature sensor [22–24]. The TSP sensor was dissolved in methanol and mixed with the clearcoat binder. Then, the TSP solution was air-sprayed onto a thin stainless
steel plate (500 mm in length, 40 mm in width, and 0.5 mm in
thickness), and left for several hours until dry. To provide an adjustable and uniform heat flux, the whole upper surface of the stainless steel plate was covered with a heating foil (0.1 mm thick,
Backer Calesco, Sweden). A direct current (DC) source provided
continuous and stable electronic power to the heating foil; the
electronic power could be measured by the built-in voltmeter
and ammeter inside the DC source. A suitable cavity in the upper
channel wall (made of Plexiglas) was carefully designed to embed
the heated plate so that the flow distortion would be eliminated. A
thermal insulation layer (10 mm thick, thermal conductivity < 0.025 W/mK) was used to minimize heat loss from thermal
conduction; heat loss through the insulated wall was estimated
to be less than 1% of the power input. Eighteen T-type thermocouples were attached to the heating foil to monitor the plate temperature. Their locations in relation to the inverted flags are plotted in
Fig. 2. Two additional thermocouples were installed at the channel
inlet and outlet to obtain the airflow temperature. The experiments
were conducted in a constant-temperature room in which the air
conditions and inlet air temperature was kept at around 295 K.
All of the temperature signals were simultaneously captured by a
data acquisition system (Fluke 2638A, USA). The pressure drop
was measured by a manometer placed between the two pressure
taps situated on the lower transparent Plexiglas wall (accessible
as a light path) at Y* = 3.5 and 6, respectively. Under excitation
by the 385 nm UV-LED (UHP-T-LED-385, Prizmatix), the TSP layer
emitted luminescent signals, which were captured by a 14-bit CCD
camera (PCO 1600, USA) with a resolution of 1600 1200 pixels
(0.1837 mm/pixel). The camera lens (Nikon 35 mm f/2.8) was
equipped with a band-pass filter (575 25 nm) to exclude any
excitation light from the UV-LED.
The local Nusselt number Nu is widely used as a dimensionless
index to measure cooling performance, and is defined as follows:
Nu ¼
PW
;
Sk T T air;in
ð2Þ
where S denotes the heating foil area, P is the power of DC source, k
is the thermal conductivity of air, and T and T air;in represent, respectively, the local wall temperature and inlet airflow temperature
measured after the heat-balanced state was established. The stainless steel plate was under the dual influence of the electronic heating, with constant power P, and cold air cooling, which depended on
surface temperature T; as T gradually increased, a heat-balanced
state was eventually reached when the heating power was equivalent to the heat convection toward the cold air, guaranteeing a fully
development of the heat transfer before measurement. The stainless
steel plate was deemed to be in the heat-balance state when the
maximum variation in temperature measured by every single thermocouple was less than 0.1 K over a 5-min period, with a calculated
diversity of 0.045% between the heat input and heat transferred to
the cold air. The temperature difference T Tair,in in the heatbalanced state was maintained at 15–30 K for all of the experimental cases.
Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
The TSP measurement procedure and the in-situ calibration
process for the function fT were performed simultaneously. Firstly,
the luminescent intensity distribution Iref was acquired at room
temperature, Tref. Then, the heat power and the wind tunnel were
turned on. After the establishment of the heat-balance state, the
image intensity I captured by the camera and the corresponding
temperature value T measured by the thermocouples were collected simultaneously. Experimental data (scatter points) from all
of the successful runs were applied to fit the calibration curve fT,
shown in Fig. 3, and the deviation between the measurement data
and the fitted curve was below 0.2%. The accuracy of the T-type
thermocouples was 0.5 K. The uncertainty of the TSP measurement was estimated to be within 0.7 K. Based on the fitted calibration curve and the image intensity distribution, I, measured
on the heated plate, the global temperature distribution T was
accurately determined.
The uncertainty analysis was based on a confidence level of 95%
proposed by Moffat [25]. The results, R, of the experiment are
assumed to be calculated from a series of variables, Vi, as follows:
R ¼ RðV 1 ; V 2 ; V 3 ; . . . ; V N Þ:
ð3Þ
Then, the comprehensive relative uncertainty was determined
as follows:
DR
¼
R
(
N
X
@R
i¼1
@V i
DV i
R
2 )1=2
;
ð4Þ
where DR and DV i denote the uncertainty in R and Vi, respectively.
Substituting Eq. (2) into Eq. (4) gave a comprehensive relative
uncertainty of the local Nu as 7%. The Nusselt number ratio
[8,17,22] Nu* = Nu/Nu0 indicates the magnitude of the enhancement
of the heat transfer performance relative to the smooth channel.
The Nu0 at the corresponding Reynolds numbers for the smooth
channel without a flag were also measured. To further clarify the
heat transfer enhancement performance, the results are presented
by Nu* below.
3. Results and discussion
3.1. Single flag
The flapping dynamics of a single flag next to the wall at three
typical gap clearances, Gc/W = 0.19, 0.31, and 0.5, and the resultant
heat transfer enhancement were first investigated to establish a
benchmark. When Gc/W = 0.19, the clearance was equal to the flag
855
length, i.e., Gc = L; any further reduction in Gc would disturb the
flapping motions of the flag because of the latent physical contact
between the flag and the wall. When Gc/W = 0.5, the inverted flag
was mounted along the centerline of the channel. Gc/W = 0.31
was designed to keep the distance between the channel centerline
and the flag at L, such that the two flags would not touch when
configured side-by-side, as discussed in Section 3.2. Three distinct
dynamic regimes, the biased, flapping, and deflected modes, were
recognized with consecutive increases in the Reynolds number,
ReW, (indicating that the dimensionless bending stiffness KB
decreased), as shown in Fig. 4(a). No obvious wall confinement
effect was observed on the flag flapping dynamics, and when Gc/
W varied, the dynamic regimes remained almost unchanged, with
a similar ReW range. In biased mode (1), the flag mainly flapped
asymmetrically to one side with moderate amplitudes of A/
L = 0.7–1.2 at ReW = 1:64 104 –1:73 104 ; for the following
experiments, the flag flapping amplitude A was defined as the maximum tip-to-tip displacement in transverse direction. The instantaneous motions of the inverted flag were recognized by a
monitor point located 0.8 L (curvilinear distance along the flag)
away from the trailing edge, as shown in Fig. 4(a). Fig. 4(b) gives
a typical trajectory of the monitor point in the biased mode for
Gc/W = 0.5 and ReW = 1:64 104 , showing a periodical flapping
motion of the inverted flag restricted to a single side (x/L > 0) with
respect to the free state. In the flapping mode (2), a symmetric
oscillation with a significant amplitude of nearly 1.8 L was identified for the ReW range of 1:81 104 to2:34 104 . The trajectory of
the monitor point in the flapping mode approximated a sineshaped curve (Fig. 4(c)). In the deflected mode (3), as ReW increased
further, the restoring bending force inside the flag was no longer
comparable to the aerodynamic force exerted on the flag; therefore, the flag entirely deformed to the channel wall with a diminutive amplitude of less than 0.2 L, as shown in Fig. 4(d). These three
dynamic regimes have been observed in previous studies [8,15,17],
which also reported bi-stable states with small Reynolds number
ranges in both the biased to flapping mode transitions and flapping
to deflected mode transitions. In this study, the heat transfer
experiments were conducted without the bi-stable states to avoid
the effect of mode transition. In Fig. 4(b)–(d), dimensionless time is
defined as t* = tU0/L, where t denotes the physical time.
The additional turbulence was introduced by the energetic flapping flag, which facilitated the heat transfer enhancement from the
heated plate. Yu et al. [15] reported that the channel turbulent
kinetic energy can be locally elevated by over 80 times due to
the presence of the flapping inverted flag. The performance of a
single flag as a cooling mechanism across the three dynamic
regimes has been widely investigated, using both numerical [16]
and experimental [8,17] methods, and the results have consistently
shown that an inverted flag in the flapping mode provides the best
cooling performance among the three regimes. Consequently, this
study quantified the heat transfer performance in the flapping
mode. Fig. 5 depicts the contours of the distribution of the Nusselt
number ratio, Nu*, for Gc/W = 0.19 (a and b), 0.31 (c and d), and 0.5
(e) at ReW = 2:08 104 . The relative heat transfer enhancement
performance indicated by the dimensionless Nusselt number was
confirmed [8,17] to be insensitive to the Reynolds number in the
flapping regime, as the flags’ self-oscillating behaviors were simi-
Fig. 3. In-situ calibration result for the TSP.
lar. Thus, a moderate ReW = 2:08 104 in the flapping mode was
chosen as a representative demonstration. In addition, the poor
dependency of the heat transfer performance on the Reynolds
number is further clarified in Fig. 7. For Gc/W = 0.19 and 0.31, the
inverted flag was mounted away from the centerline; in such configurations, the cooling performance of the near side and far side
(wall sides 1 and 2, respectively, as shown in Fig. 1) should be measured individually. However, in this study’s original experimental
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Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
Fig. 4. Single flag dynamics: (a) dependency of the flapping amplitude and flapping dynamics on the Reynolds number, ReW, and dimensionless bending stiffness, KB, for
various clearances Gc; (b and d) trajectories of the monitor points for biased, flapping, and deflected modes, respectively.
set-up (Fig. 2), only wall side 1 with the heated plate was available
for heat transfer measurements, while wall side 2 consisted of a
transparent Plexiglas plate where the heat transfer was absent.
To circumvent this issue, another experiment was conducted, with
the inverted flag placed in the symmetric position along the centerline. For instance, the inverted flag mounted at Gc/W = 0.81
was the counterpart for Gc/W = 0.19; the heat transfer measured
at side 1 for Gc/W = 0.81 (Fig. 5(b)) could then be regarded as the
result measured at side 2 for Gc/W = 0.19. The inverted flags along
with their shadows are plotted as grey areas of various sizes in
Fig. 5: for Gc/W = 0.19, side 1, (Fig. 5(a)), the inverted flag was far
from the camera and LED source; accordingly the size of the
blocked grey area is small. In contrast, for Gc/W = 0.81, side 1,
(i.e., Gc/W = 0.19, side 2, Fig. 5(b)), the inverted flag was close to
the camera and LED source, so the grey area is enlarged.
Figs. 5 and 6 demonstrate that as the gap clearance between the
inverted flag and the wall decreased, Nu* increased. Fig. 5(a) shows
that when Gc/W = 0.19, Nu* increased remarkably to 1.5 for
0.5 < Y* < 1.75 at wall side 1 before gradually decreasing for
Y* > 2. In contrast, Fig. 5(b) shows that the best cooling region
shifted to 2.5 < Y* < 4, with a Nu* value around 1.2 at side 2
(0.81 W away from the flag). The difference in cooling performance
between wall sides 1 and 2 can be explained by the vortex shedding process that takes place behind the inverted flag. PIV measurements [7,15,17] and numerical studies [26] have confirmed
that the shedding vortex emits toward the wall and transports
downstream. The shedding vortex attached to wall side 1 was
immediately behind the flag and swept out the thermal boundary
layer, which significantly strengthened the heat transfer performance of the configuration with the small gap clearance Gc/
W = 0.19. The spanwise-averaged Nu* distributions in Fig. 6 (red1
1
For interpretation of color in Figs. 6, 9, 11 and 15, the reader is referred to the web
version of this article.
Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
857
Fig. 5. Contours of the Nu* distribution for a single flag at ReW = 2:08 104 : (a and b) Gc/W = 0.19, wall sides 1 and 2, respectively; (c and d) Gc/W = 0.31, wall sides 1 and 2,
respectively; (e) Gc/W = 0.5.
Fig. 6. Spanwise-averaged Nu* distribution of a single flag with various Gc values at
ReW = 2:08 104 .
solid line) also showed that the maximum Nu* = 1.6 rose at Y* = 1. As
the flag was farther from wall side 2 (gap clearance 0.81 W), the
vortex dissipated and was transported downstream before attaching
to the wall; the weaker peak Nu* = 1.27 then shifted downstream at
Y* = 3 (Fig. 6, red dashed line). A similar phenomenon was observed
for Gc/W = 0.31 and 0.5; that is, as shown in Fig. 6, the maximum Nu*
was attenuated to 1.5 (purple solid line) at Y* = 1 when the inverted
flag moved to Gc/W = 0.31. However, compared with the red dashed
line (Gc/W = 0.19, side 2), the heat transfer performance for side 2 at
Gc/W = 0.31 was substantially augmented with an elevated Nu* value
exceeding 1.4 at Y* = 2.5. When the inverted flag was mounted along
the centerline for Gc/W = 0.5, the heat transfer performance on sides
1 and 2 should be the same, because the two walls are symmetric;
consistent with this prediction, a moderate peak Nu* = 1.46 was
obtained at Y* = 1.5.
There was a heat transfer performance trade-off between the
two walls: a larger Nu* was achieved with a closer gap clearance,
Gc, at side 1 due to the vigorous vortex shedding process from
the inverted flag; however, Nu* significantly declined because the
shedding vortex dissipated before sweeping out the thermal
boundary layer on wall side 2. To evaluate the comprehensive heat
transfer performance of inverted flags with various Gc values, a
thermal enhancement factor g [8,16,27,28] that accounted for both
heat transfer benefit, Nu=Nu0 , and pressure drop penalty, F/F0, was
defined as follows:
g¼
Nu=Nu0
ðF=F 0 Þ1=3
;
ð5Þ
where Nu is the global space-averaged Nusselt number for the two
wall sides, subscript 0 denotes the smooth channel value at the corresponding Reynolds number, F = 2DpW=Lh qf U 20 is the friction factor, Dp is the pressure drop between two pressure taps located at
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Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
Y* = -3.5 and 6, Lh ¼ 9:5W is the distance between the two pressure
taps, and qs is the air density. It is not reasonable to compare only
the Nusselt number with that of the clean channel, because the
channels modified with vortex generators such as flags and ribs
always require more pumping power than a clean channel at the
same Reynolds number. The thermal enhancement factor g is
defined as the ratio of the Nusselt number of a modified channel
to that of a smooth channel at a constant pumping power [27].
Eq. (5) allows a comparison between the clean channel and the
modified channel. Table 1 summarizes the heat transfer performance and friction characteristics of the single inverted flag mode.
The highest thermal enhancement factor of g = 1 was achieved at
Gc/W = 0.19, which is around 4% higher than that of Gc/W = 0.5. Placing the self-oscillating inverted flag in proximity to the channel wall
improved the heat transfer performance.
The effect of the Reynolds number on heat transfer performance
of the inverted flags is demonstrated in Fig. 7. Keeping the inverted
flags in the flapping mode for Gc/W = 0.19 in the ReW range of
1:81 104 –2:34 104 resulted in an almost unchanged
spanwise-averaged Nu* distribution for side 1, with a similar peak
Nu* value around 1.6 at Y* = 1. For side 2, the maximum Nu* slightly
Fig. 7. Spanwise-averaged Nu* distribution for a single flag with Gc/W = 0.19 at
various ReW values.
increased from 1.23 to 1.31 as the ReW rose from 1:81 104
to2:34 104 . It seems that the trends of Nu* distributions are similar in the whole Reynolds number range of flapping regime, which
is consistent with previous studies [8,17]. Accordingly, ReW was
kept at the fixed value of 2:08 104 for the side-by-side and staggered flags systems, as described in the following sections.
3.2. Side-by-side flags
Promoting heat removal in the channel flow by placing a single
inverted flag close to the wall had an inevitable disadvantage: the
near wall (side 1) received sufficient cooling enhancement, but the
far wall (side 2) had poor cooling. Placing two inverted flags sideby-side (Fig. 2(c)) seems to be an effective method for obtaining
adequate heat transfer augmentation on both channel walls. Two
typical gap clearances were investigated, Gc/W = 0.19 and 0.31,
which tested distances between the two flags in the transverse
direction of Gx/L = 3.33 and 2, respectively. Fig. 8 demonstrates that
the flapping amplitude and dynamics of the side-by-side flags were
dependent on KB and ReW. Comparing these with the single flag
configurations, the three distinct dynamic regimes were located
in similar ReW ranges for the side-by-side configurations at Gc/
W = 0.19 and Gc/W = 0.31, but the transition ReW between the
biased, flapping, and deflected modes, declined slightly to
1:73 104 and2:26 104 , respectively.
However, the flapping dynamics of the side-by-side inverted
flags for Gc/W = 0.19 and 0.31 were totally different. Fig. 9 depicts
the snapshots of flag movement and the trajectories of the monitor
points at ReW = 2:08 104 . For Gc/W = 0.19 (Fig. 9(a) and (b)), the
two flags flapped in phase with periodic and synchronous motions;
in contrast, the flapping motions for Gc/W = 0.31 were chaotic
(Fig. 9(c) and (d)), as the two flags alternately flapped toward
one single side or both. For instance, flag 2 (Fig. 9(d), red line)
flapped symmetrically at 20 < t* < 80, whereas it flapped toward a
single side at 0 < t* < 230. Fig. 9(c) shows the profiles of the chaotic
Table 1
Heat transfer performance and friction characteristics of single inverted flag for
various Gc.
Gc/W
Nu=Nu0
F/F0
g
0.19
0.31
0.5
1.18
1.19
1.17
1.65
1.78
1.80
1.00
0.98
0.96
Fig. 8. Side-by-side flag dynamics. The flapping amplitude and dynamics depend on
the Reynolds number, ReW, and the dimensionless bending stiffness, KB, for various
gap clearances, Gc.
inverted flags at t* = 0–20. Flag 1 flapped symmetrically, whereas
flag 2 purely oscillated toward the bottom wall. Such irregular flapping motions were also observed experimentally by HuertasCerdeira et al. [18], and may be the result of strong interactions
between the two flags.
Fig. 10 compares the Nu* distributions of the side-by-side flags
(Fig. 10(b) and (d)) with that of a single flag (Fig. 10(a) and (c)) at
ReW = 2:08 104 . Compared with the single inverted flag at Gc/
W = 0.19 (Fig. 10(a)), Fig. 10(b) shows a remarkable rise in Nu*
above 1.6 behind the side-by-side flags from Y* = 0.75 to 2, which
can be attributed to the additional turbulence caused by the second self-oscillating inverted flag. Furthermore, the peak Nu* rose
to 1.8 at Y* = 1 (Fig. 11, green line). As the side-by-side flags were
close to the wall (Gc/W = 0.19) and far from each other
(Gx = 3.33L), they still flapped with large amplitudes and symmetric motions, and the heat transfer performance, indicated by Nu*,
was significantly elevated. However, the results differed when
the two side-by-side inverted flags were placed close to each other
(Gx = 2L, i.e., Gc/W = 0.31). A diminutive elevation in Nu* was
observed in the side-by-side flags (Fig. 10(d)) compared to the single flag (Fig. 10(c)) for Gc/W = 0.31. The peak Nu* slightly increased
to 1.54 at Y* = 1.25 for the side-by-side inverted flags (Fig. 11, blue
Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
859
Fig. 9. Snapshots of the side-by-side flags and the trajectories of the monitor points: (a and b) Gc/W = 0.19 and (c and d) Gc/W = 0.31.
line), a little higher than peak Nu* = 1.49 at Y* = 1 for the single
inverted flag (Fig. 11, purple line). In addition, Nu* for the sideby-side case was even smaller than for the single inverted flag at
0.25 < Y* < 1. This small enhancement in heat transfer can be
explained by the chaotic motions of the side-by-side flags at Gc/
W = 0.31. At times, the side-by-side flags only flapped toward a single side with smaller amplitudes; therefore, the resulting turbulence of the surrounding fluid may be incomparable to that of
symmetrically flapping flags.
Table 2 compares the heat transfer performance and friction
characteristics of the side-by-side flags with those of the single
inverted flag. For Gc/W = 0.19, the global averaged Nusselt number
ratio, Nu=Nu0 , was augmented to 1.30 for the side-by-side configuration, and a benefit of around 10% was successfully achieved relative to the single flag ratio of Nu=Nu0 = 1.18. However, the friction
ratio, F/F0, increased by 68% because of the additional flag’s blockage, which overall reduced efficiency g by 7%. In contrast to the
single inverted flag for Gc/W = 0.31, Nu=Nu0 was enhanced by 3%
for the side-by-side flags, and the F/F0 increased by approximately
70%, resulting in an uneconomic thermal enhancement efficiency
of g = 0.86.
3.3. Staggered flags
The flapping dynamics and heat transfer characteristics of the
staggered inverted flags were investigated. As the single flag and
side-by-side flags configurations gave the best heat transfer
performance at Gc/W = 0.19, the gap clearance for the staggered
flags was maintained at the same value. The separation distances
in the streamwise direction were Gy/W = 2 and 4, as shown in
Fig. 1(d). The staggered flags’ flapping dynamics and the resultant
heat transfer performances were compared with those of the sideby-side flags, i.e., Gy/W = 0. Fig. 12 shows that the flapping amplitude and flapping dynamics depended on the ReW and KB of the
staggered inverted flags. For the staggered configurations Gy/
W = 2 and 4, the flapping amplitude and dynamic regimes were
also similar to those of the single flag. The two staggered flags
flapped synchronously with nearly the same amplitude throughout
the entire ReW range. For brevity, Fig. 12 only depicts the flapping
amplitude of the front flag 1.
The trajectories of the monitor points revealed the time history
of the flag motions for Gy/W = 0 (side-by-side) and 2 and 4 (staggered), as shown in Fig. 13. For the side-by-side system Gy/W = 0,
the two flags flapped symmetrically toward both sides with no
phase delay. However, their dimensionless flapping period, Dt*,
remarkably increased from 10.9 (isolated single flag, Fig. 4(c)) to
16.4, indicating that the side-by-side flags oscillated more slowly
than the single flag. As for the staggered systems Gy/W = 2 and 4,
Fig. 13(b) and (c), show that the two flags flapped in coupled
motions with a constant phase delay and their flapping periods,
Dt*, recovered to around 10.4, which is comparable to the single
flag value of Dt* = 10.9. We can infer that the interactions between
the staggered flags were weaker than those between the side-byside flags. Therefore, placing the dual flags in a staggered configuration might eliminate the chaotic motions observed in the side-
860
Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
Fig. 10. Contours of the Nu* distribution for various Gc values at ReW = 2:08 104 : (a) single flag at Gc/W = 0.19, wall side 1; (b) side-by-side flags at Gc/W = 0.19; (c) single flag
at Gc/W = 0.31, wall side 1; and (d) side-by-side flags at Gc/W = 0.31.
Fig. 11. Spanwise-averaged Nu* distribution of the single flag and side-by-side flags
for various Gc values at ReW = 2:08 104 .
by-side system with close flag distances, which is a common configuration for narrow channels.
Fig. 14 plots the contours of the Nu* distribution for the staggered flags at ReW = 2:08 104 . For Gy/W = 2, Nu* quickly rose to
1.7 behind the front flag at Y* = 0.6 (Fig. 14(b)), with a peak value
1.65 at wall side 1, before the heat transfer performance decayed
at Y* > 1.7. Fig. 15 demonstrates that the spanwise-averaged Nu*
for the staggered flags was 0.15 higher (purple solid line, Gy/
W = 2, wall side 1) at Y* > 3.5 than the single flag (red solid line).
This can be attributed to the rear flag’s vigorous flapping motion.
The Nu* distribution was distinct at wall side 2 (Fig. 14(c)), as the
cooling augmentation behind the front flag was almost ignorable
before Y* = 1.8: the front flag was far from wall side 2 and the shedding vortex did not sweep out the thermal boundary layer at
Y* < 1.8. In addition, the rear flag was mounted in proximity to wall
side 2, which gave the region 2.2 < Y* < 3.5 favorable heat removal
conditions, resulting in a high Nu* value that exceeded 1.7. The
peak Nu* was observed at nearly 1.9 (Fig. 15, purple dashed line),
which was even higher than that of the side-by-side configurations’ Nu* = 1.8 (Fig. 15, blue solid line), perhaps because for a single inverted flag, the Nu* peak was observed 1 W and 3 W
downstream from the flag at wall sides 1 and 2, respectively, as
shown in Fig. 6. Similarly, for the staggered system Gy/W = 2, the
front flag was mounted at Y* = 0, and the best cooling region was
located at around Y* = 3 for wall side 2; the rear flag was mounted
in proximity to wall side 2 at Y* = 2, and its best cooling region was
at about 1 W behind the rear flag, i.e., Y* = 3. The concerted influence of the dual staggered flags substantially enhanced the heat
removal performance, with a maximum Nu* of around 1.9 at
Y* = 2.75, wall side 2. When the rear flag moved to Y* = 4 (Fig. 14
(d) and (e)), the heat transfer performance at side 1 was similar
to that of Gy/W = 2 (Fig. 14(b)); however, the peak Nu* region for
wall side 2 shifted downstream to 4.4 < Y* < 5 (Fig. 14(e)). Table 3
indicates that the most economic cooling performance with a ther-
Table 2
Heat transfer performance and friction characteristics of the side-by-side inverted
flags for various Gc values.
Configuration
Gc/W
Nu=Nu0
F/F0
g
Single
Side-by-side
Single
Side-by-side
0.19
0.19
0.31
0.31
1.18
1.30
1.19
1.22
1.65
2.78
1.78
2.81
1.00
0.93
0.98
0.86
Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
861
4. Conclusions
Fig. 12. Staggered flag dynamics: flapping amplitude and dynamics depend on the
Reynolds number, ReW, and the dimensionless bending stiffness, KB, for various
separation distances, Gy, at a fixed gap clearance of Gc/W = 0.19.
mal enhancement efficiency of g = 0.94 was achieved at Gy/W = 2.
In contrast to our previous study [8], g = 0.87 was obtained by placing inverted flags (C* = 0.25) in tandem along the channel centerline with a similar Reynolds number. Accordingly, placing the
shorter inverted flags (C* = 0.19) proximate to the wall in staggered
configuration could further improve heat transfer performance.
This study investigated the flapping dynamics of dual selfoscillating inverted flags close to the walls within a turbulent channel flow in both side-by-side and staggered configurations. It
examined the resultant heat transfer enhancement performance
on the channel walls. The time varying curving profiles of the
deformed inverted flags were chronologically recorded by a highspeed camera and then identified using a structure boundary
detection algorithm. The heat transfer performance indicated by
the Nusselt number ratio Nu* was measured quantitatively using
the TSP measurement technique.
Three distinct dynamic regimes based on the Reynolds number,
ReW, and the dimensionless bending stiffness, KB, i.e., the biased,
flapping, and deflected modes, were identified for a single inverted
flag with gap clearances of Gc/W = 0.19, 0.31, and 0.5. The wall confinement effect of the different gap clearances on the flapping
dynamics was ignorable. The best heat transfer enhancement with
g = 1.00 was achieved when the flag was placed close to the channel wall with Gc/W = 0.19, and the maximum Nu* of around 1.6 was
observed at Y* = 1 for wall side 1 at ReW = 2:08 104 . As the gap
clearance increased and the flag was moved farther away from
the wall to Gc/W = 0.5, the peak Nu* region shifted downstream at
Y* = 1.5 and the Nu* value declined by 1.46. No obvious Reynolds
number effect was found on the heat transfer performance in the
flapping mode for the ReW range from 1:81 104 to2:34 104 .
Two inverted flags arranged in side-by-side configurations were
subsequently studied. The same three dynamic regimes were
Fig. 13. Trajectories of the monitor points for the fixed gap clearance Gc/W = 0.19 and various separation distances: (a–c) Gy/W = 0, 2, and 4, respectively.
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Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
Fig. 14. Contours of the Nu* distribution for staggered flags at ReW = 2:08 104 and Gc/W = 0.19: (a) Gy/W = 0; (b and c) Gy/W = 2, wall sides 1 and 2, respectively; (d and e) Gy/
W = 4, wall sides 1 and 2, respectively.
Table 3
Heat transfer performance and friction characteristics of the staggered inverted flags
for various Gy at Gc/W = 0.19.
Fig. 15. Spanwise-averaged Nu* distribution of staggered flags for various Gy values
at ReW = 2:08 104 .
examined. The two flags periodically and synchronously flapped
with the same phase for Gc/W = 0.19 at ReW = 2:08 104 ; however,
the dimensionless flapping period increased to Dt* = 16.4, much
longer than for the isolated single flag Dt* = 10.9. In contrast to
the single flag with Gc/W = 0.19, an elevated maximum Nu* = 1.8
was recognized at Y* = 1 for the side-by-side flags with
Gy/W
Nu=Nu0
F/F0
g
0
2
4
1.30
1.29
1.24
2.78
2.61
2.47
0.93
0.94
0.91
Gc/W = 0.19. Although the global averaged Nusselt number ratio,
Nu=Nu0 , rose to 1.30, the friction factor ratio, F/F0, simultaneously
increased by 68%, which led to an overall downward trend in thermal enhancement efficiency of g = 0.93. As for Gc/W = 0.31, the two
side-by-side flags were closer to each other, resulting in chaotic
flapping motions: the two inverted flags alternated between a
symmetric flapping motion toward both wall sides and an asymmetric flapping motion toward a single side.Nu=Nu0 = 1.22 was
slightly augmented by 3% for the side-by-side flags with Gc/
W = 0.31; however, F/F0 was augmented by 70% due to the large
blockage of the two flags, which eventually led to a significant
decrease in thermal enhancement efficiency of g = 0.86.
The two staggered flags’ coupling flapping behaviors were
determined at ReW = 2:08 104 for Gy/W = 2 and 4. Unlike the
side-by-side system, the oscillating dynamics of the staggered flags
was similar to that of the single flag, i.e., with a comparable flapping period Dt* = 10.4 and amplitude A/L = 1.8. The maximum heat
transfer enhancement Nu* = 1.9 was achieved at Y* = 2.75, which
could be attributed to the concerted influence of two staggered
Y. Chen et al. / International Journal of Heat and Mass Transfer 136 (2019) 851–863
flags for Gy/W = 2. The resultant thermal enhancement efficiency
g = 0.94 was superior to g = 0.87, which was obtained by mounting
tandem flags along the channel centerline [8]. This shows that
placing flags close to the wall in a staggered configuration is more
economical than the single flag and side-by-side double flag
configurations.
Conflict of interest
The authors declare that they have no conflict of interest in relation to this study.
Acknowledgments
The authors gratefully acknowledge financial support for this
study from the National Natural Science Foundation of China
(11725209).
Appendix A. Supplementary material
Supplementary data to this article can be found online at
https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.048.
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International Journal of Heat and Mass Transfer 136 (2019) 597–609
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer
journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer enhancement in microchannel heat sink with
bidirectional rib
Guilian Wang a,⇑, Nan Qian a, Guifu Ding b
a
b
School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, 333 Longteng Road, Shanghai 201620, People’s Republic of China
National Key Laboratory of Science and Technology on Micro/Nano Fabrication, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
a r t i c l e
i n f o
Article history:
Received 10 September 2018
Received in revised form 25 January 2019
Accepted 9 February 2019
Keywords:
Bidirectional rib
Microchannel
Heat transfer
Pressure drop
a b s t r a c t
The heat transfer and flow characteristics of the microchannel heat sink (MCHS) with bidirectional ribs
(BRs) are experimentally and numerically studied in the present paper. The BR, composed of vertical
rib (VR) and spanwise rib (SR), can interrupt the thermal boundary layer and induce recirculation in both
vertical and spanwise directions. Its cooling effectiveness is compared with that of the widely-used VR
and SR for the Reynolds number ranged from 100 to 1000. The results show that the Nussalt number
of the microchannel with BRs (BR-MC) is up to 1.4–2 and 1.2–1.42 times those of microchannels with
VRs (VR-MC) and SRs (SR-MC), respectively. This implies that the BR can strengthen the heat transfer
more sufficiently. Meanwhile, the utilizing of BR gives rise to the larger pressure drop penalty due to
its broader obstruction areas. In addition, the higher relative rib height of VR (eVR) and relative rib width
of SR (eSR) are revealed to enhance the heat transfer but induce pressure drop in the BR-MC. The thermal
enhancement factor can keep larger than 1 when eVR < 0.316 and 0.026 < eSR < 0.357.
Ó 2019 Published by Elsevier Ltd.
1. Introduction
The inexorable miniaturization and high speed operation of
electronic devices have resulted in a tremendous increase in power
density, which will cause huge amount of heat in electronic
devices. To avoid heat accumulation and preserve their component
lifespan and reliability, many powerful heat dissipation methods
have been developed till now which include microchannel heat
sink (MCHS), jet impingement, sprays, heat pipes, piezoelectrically
driven droplets, etc. [1–5]. Among these techniques, MCHS is the
most practical choice due to its favorable and attractive features
such as light weight, compactness and high heat transfer area to
volume ratio [6–11]. The water-cooled microchannel technology
was proposed initiatively by Tuckerman and Pease [12]. They
demonstrated that a heat flux as high as 790 W/cm2 can be
removed with a maximum substrate temperature rise of 71 °C.
Although high thermal performance can be achieved by using
MCHS, several techniques, such as nanofluid, surface area increase
and thermal boundary layer redeveloping, have been proposed to
promote the heat transfer with the escalating thermal demands
of electronic devices. Arani et al. [13] numerically investigated
water/single-wall carbon nanotubes nanofluid in a double layered
MCHS. They concluded that the increase of nanoparticle volume
⇑ Corresponding author.
E-mail address: wglwrc2016@126.com (G. Wang).
https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.018
0017-9310/Ó 2019 Published by Elsevier Ltd.
fraction causes an increment of the Nusselt number but pressure
drop augmentation. Hung et al. [14] investigated the hydraulic
and thermal performances of the porous-MCHSs with different
configuration designs. They found that porous microchannels can
improve the cooling performance due to the surface area increase.
Xu et al. [15] studied experimentally and numerically the
hydrothermal characteristics of silicon MCHS which consists of
ten parallel triangular microchannels separated by five transverse
trapezoidal microchannels. They found that the proposed MCHS
can decrease the temperature by 14 °C compared with the conventional MCHS. The results demonstrated that the redeveloping of
thermal boundary layer has a significant effect on improving the
heat transfer in the MCHS.
Based on the thermal boundary layer redeveloping mechanism,
some researchers proposed the MCHS with variable cross-sections,
fins, grooves or ribs. Chai et al. [16] numerically and experimentally investigated the fluid flow and heat transfer in MCHS with
periodic expansion–constriction cross-sections. The results show
that the expansion–constriction cross-sections provide a significant influence on the heat transfer. Shafeie et al. [17] performed
detailed numerical study of the MCHS with different height of
micro pin fins. It was shown that the finned microchannels have
better heat transfer performance than the smooth microchannels
at the same pumping power. Moreover, the finned case with highest fin depth (500 mm) had the highest heat removal among studied finned heat sinks. Ahmed et al. [18] investigated numerically
598
G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609
Nomenclature
A
Cp
Dh
f
h
l
_
m
N
Nu
P
p
Q
q
DT
T
t
u
area, m2
specific heat, J kg1 K1
hydrodynamic diameter, m
frictional factor
heat transfer coefficient, W m2 K1
length, m
mass flow rate, kg s1
the number of microchannels in heat sink
Nusselt number
pitch of the rib, m
pressure, Pa
total heat transfer, W
heat flux, W m2
temperature difference, K
temperature, K
thickness, m
velocity, m s1
the MCHS with triangular, trapezoidal and rectangular grooves.
They found that there was a significant enhancement in heat transfer using grooved microchannels, and the ones with trapezoidal
groove can provide the highest Nusselt number enhancement of
51.59%.
The ribs, also called roughness elements or turbulators, have
been extensively studied and widely used due to their marked
effect on the heat transfer enhancement. Chai et al. [19] investigated the pressure drop and heat transfer characteristics of the
interrupted MCHS with rectangular ribs. Compared with interrupted microchannel without rectangular ribs and smooth
microchannel, the interrupted one with rectangular ribs can provide the higher heat transfer enhancement factor. Desrues er al.
[20] conducted numerical simulations to study the thermal performance of the microchannels with alternated vertical ribs and found
that the proposed microchannels with VRs can provide a higher
Nusselt number than the smooth ones. Jiang et al. [21] carried
out experimental and numerical studies to investigate the flow
and heat transfer characteristics of mist/steam two-phase flow in
the channel with 60 deg spanwise ribs. They showed that ribs
mounted on the sidewalls could lead to secondary flows and then
improved the heat transfer characteristics. Xie et al. [22] performed an experimental study for heat transfer enhancement in
a MCHS with various vertical crescent ribs protruded from the bottom wall. It was found that the ribs can improve the heat transfer
performance by generating vortices. Xia et al. [23] computationally
investigated the hydrothermal performance of MCHS with spanwise cavities and ribs. The results showed that Nusselt number
for the MCHS with spanwise cavities and ribs increased about
1.3–3 times more than the rectangular microchannel, while the
apparent friction factor increased about 6.5 times more.
Although thermal performance enhancement in MCHS can be
achieved by using ribs, high pressure drop is also induced due to
high-flow disturbances and blocking-flow effect. Therefore, the
geometry and arrangement of ribs should be optimized to tradeoff between the enhanced heat transfer and the pressure drop penalty. Ghani et al. [24] proposed a new configuration of MCSH with
sinusoidal cavities and ribs, and investigated numerically its geometric parameters on hydrothermal performance. The results
showed that the microchannel with relative cavity amplitude of
0.15, relative rib width of 0.3 and relative rib length of 0.5 yielded
the best overall performance with Pf = 1.85 at Re = 800. Akbari et al.
u
w
mean flow velocity, m s1
width, m
Greek symbols
l
dynamic viscosity, Pa s
q
density, kg m3
k
thermal conductivity, W m1 K1
Subscripts
c
microchannel
f
fluid
in
inlet
out
outlet
r
rib
s
smooth microchannel
w
wall
[25] performed a numerical analysis of heat transfer and flow characteristics of MCHS with different rib height. They found that the
heat transfer rate can be enhanced by increasing the rib height,
volumetric percentage of nanoparticles and Reynolds number.
However, the existence of ribs causes an increase in the average
friction factor. Wang et al. [26] also conducted parameters optimization of the slant rectangular ribs in the MCHS by comprehensive consideration of heat transfer and pressure drop. The
optimization results showed that the MCHS with the slant rectangular ribs have the best thermal performance with the attack
angles of 52.5°, the relative height of 0.3, the relative length of 1
and the relative width of 0.1, respectively.
Many other researches are focused on the effect of rib’s cross
sectional shape on hydrothermal performance of MCHS. Chai
et al. [27] studied numerically the heat transfer of the MCHS with
rectangular, backward triangular, isosceles triangular, forward triangular and semicircular ribs. The results revealed that the forward
triangular ribs can induce the largest Nusselt number in the
microchannel. Meanwhile, the one with semicircular offset ribs
brings about the best overall thermal performance. Moon et al.
[28] also conducted a numerical investigation to analyze the effect
of cross-sectional rib shapes on the heat transfer and friction loss
performances. Among the considered sixteen rib shapes, the
boot-shaped rib gave the best heat transfer performance with an
average friction loss performance. Gholami et al. [29] investigated
the effect of rectangular, oval, parabolic, triangular and trapezoidal
ribs on the forced flow and heat transfer of the MCHS. The results
indicated that the parabolic rib had the best proportion of Nusselt
number enhancement comparing to the augmentation of the friction factor.
From the review of the available literature on thermal performance in the microchannel roughened with VRs and SRs, it is clear
that VRs and SRs both can improve the heat transfer characteristic
by disturbing the thermal boundary layers and inducing the recirculation for the mixing of hot and cold fluids. However, the disturbed thermal boundary layers and induced recirculation are
only in the vertical or spanwise direction. Therefore, the heat
transfer enhancement by the VRs and SRs is restricted in single
direction, which is insufficient for improving the heat transfer ability of MCHS. In this paper, a new type of rib called ‘‘bidirectional rib
(BR)”, composed of VR and SR, is proposed to interrupt the thermal
boundary layers and induce the recirculation in both vertical and
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G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609
spanwise directions, and further intensify thermal transfer
enhancement.
2. Problem statement and numerical methods
2.1. Physical models
A novel MCHS with BRs consists of two parts as shown in Fig. 1
(a): a cover with VR-roughened microchannels; a substrate with
the SR-roughened microchannels. The VRs part contained in BRs
are in-line distributed on the bottom surface of the cover and the
SRs part are in staggered arrangement on the sidewalls.
When the fluid flows through the BRs, the VRs part can improve
the uniformity of the temperature and flow fields in the vertical
direction. At the same time, the temperature and flow fields in
the spanwise direction can be improved by the SRs part. The
geometry dimension of the proposed MCHS with BRs is
21 mm 11.9 mm 1.5 mm (L W H). The main structural
parameters of the designed structure are shown in Table 1.
Considering that the designed MCHS is a periodic structure,
only single-branch microchannel is selected as the computational
domain to reflect the flow and heat transfer characteristics, as
shown in Fig. 2(a). In order to study the effect of rib geometry on
the fluid flow and heat transfer, other two relevant geometries,
the microchannel only with VRs (VR-MC) and the microchannel
only with SRs (SR-MC), are also considered in the present study,
as shown in Fig. 2(b–c).
2.2. Governing equations and boundary conditions
The commercial FluentTM software is used to simulate the solidfluid conjugate heat transfer process for different ribbed cases,
which can provide us a convenient and precise method for
evaluating the heat transfer and flow characteristics. Meanwhile,
the following assumptions are made to simplify the analysis: (1)
Radiation, gravitational force, viscous dissipation and thermal
contact resistance between components are neglected; (2) The
solid and fluid properties are constant; (3) The fluid flow is steady
and incompressible, and laminar flow prevails across the
microchannels.
According to the aforesaid assumptions, the basic governing
equations can be written as follows:
Continuity equation:
r ðquÞ ¼ 0
ð1Þ
Momentum equation:
ðu rÞqu ¼ rp þ lr2 u
ð2Þ
Energy equation:
u rT ¼
k
qC p
r2 T
ð3Þ
Energy equation in the solid domain is given by:
kr2 T ¼ 0
ð4Þ
where q is water density, u is the velocity at the inlet of the
microchannel, p is pressure, Cp is the specific heat of the water, l
is the dynamic viscosity, and k is the thermal conductivity of water.
The symmetric boundary conditions are applied onto the symmetric surface of model. Uniform velocity with different values
and constant temperature (Tin = 293 K) is applied in the inlet of
the microchannel. At the exit, a pressure outlet boundary condition
is specified with a fixed pressure of 1.013 105 Pa. A uniform constant heat flux of q = 100 W/cm2 is applied on the top surface. The
bottom surface has the assumed natural convection heat transfer
Fig. 1. Schematic of (a) the MCHS with BRs and (b) BR geometry.
Table 1
Microchannel geometry details.
Parameter
hc
lc
wc
hVR
wVR
lVR
hSR
wSR
lSR
P
tw
Values (lm)
500
10,000
450
150
450
100
350
150
100
1000
175
600
G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609
Fig.3. The structured grid of ribbed passage in BR.
The Reynolds number (Re) is defined as:
Re ¼ q u Dh =l
ð5Þ
is mean velocity, Dh is the hydraulic diameter of the
where u
microchannel and it is calculated as:
Dh ¼ 2wc hc =ðwc þ hc Þ
Fig. 2. Schematic of single-branch microchannels with (a) BRs, (b) VRs, and (c) SRs.
coefficient of 10 W/m2 K since it is exposed in the air environment
[30].
The aforesaid mass, momentum and energy governing equations are solved using the standard pressure and second-order
upwind discretization scheme. The SIMPLE algorithm is employed
for pressure velocity coupling to achieve the stability of solution
convergence, and the convergence criteria of 10-6 for continuity
and 10-8 for the energy equation are used in the numerical
solution.
2.3. Grid independence study
To ensure the high accuracy of simulation results, every model
adopts hexahedral elements generated by ANSYS ICEM CFD 14.5.
As shown in the Fig. 3, fine mesh is concentrated near the wall
region to resolve the large velocity gradient and thermal boundary
layer, while the grid in the other parts is relatively sparse. To this
end, the height of the first layer elements adjacent to the solid
walls is set to be small enough to ensure a dimensionless wall distance (y+) less than 1.0. To verify the mesh independence, four grid
systems separately with 340,210 elements, 633,714 elements
1,206,609 and 2,301,476 elements are generated in the BR-MC case
and then the Nusselt number and friction factor are compared with
different grid systems. The test results of the Nusselt number, friction factor and their relative error between the finest grids and
other grids are shown in Table 2. It is found that the Nusselt number and friction factor with the third grid system differ from those
with the fourth one by 300, the rate of decreasing in the apparent friction factor is
not distinct due to the prominent blocking effect of ribs.
Fig. 7. The Nusselt number as a function of Reynolds number for all ribbed
microchannels.
Fig. 8. The normalized Nusselt number as a function of Reynolds number for all
ribbed microchannels.
Table 3
Uncertainties for different parameters involved in the experimental tests.
Parameters
Uncertainty (%)
Parameters
Uncertainty (%)
Dh
A
L
Tout- Tin
Twall
_
m
0.69
0.1
0.2
2
2
0.98
4p
Re
0.98
1.79
2.1
4.89
5.93
6.75
s
Nu
f
g
3.3. Uncertainty analysis
An uncertainty analysis was carried out to give some quantitative description of the validity of test data. The uncertainties asso_ were
ciated with direct measured parameters (W, H, L, T, P and m)
obtained from the manufacturers’ specification sheets. While the
uncertainties of the calculated values (Dh, A, Tout, Tin, 4p, Re, Nu, f,
s and h) were determined using standard error analysis [32]. Their
maximum uncertainties are all listed in Table 3.
4. Results and discussions
In this section, the average Nusselt numbers and apparent friction factor for all ribbed cases are measured and predicted with the
Reynolds number varying from 100 to 1000. Detailed discussion
has been provided for the mechanisms of different ribs on modification of heat transfer and flow characteristics. Thereafter, the
effects of relative rib height of VR (eVR) and relative rib width of
SR (eSR) on hydrothermal performance are elucidated.
4.1. Overall heat transfer and pressure drop characteristics
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G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609
Fig. 9. The apparent friction factor as a function of Reynolds number for all ribbed
microchannels.
4.2. Flow field and heat transfer mechanisms
In order to deeply understand the underlying mechanisms of
the heat transfer and pressure drop characteristics among the
three considered configurations, streamlines in the 3D microchannel model are presented and discussed in this section, as shown in
Fig. 10. When the fluid passes over the VRs in the microchannel,
partial fluid is deflected to the vertical wall and then a large recirculation is created behind the VR, as shown in the Fig. 10(a). With
the existence of the recirculation, the cold fluid at the center of
microchannel is mixed with the hotter fluid closed to the vertical
walls, which can produce a larger thermal difference between wall
and coolant. At the same time, the thermal boundary layer closed
to the vertical wall is disturbed and then redeveloped between
the two adjacent VRs. However, the flow streamlines in the spanwise direction, except for the ones closing to the VR, are approximately paralleled with the streamwise. For SR-MC, the flow
streamlines are forcing to deflect in the spanwise direction and
recirculation is generated behind the SRs. Therefore, the interruption of thermal boundary layer and fluid mixing occur near the
spanwise walls.
In comparison with the VR and SR, the BR provides a larger
recirculation flow occupying most flow region in the microchannel,
which indicates more cool fluid in the mainstream region is mixed
with hotter fluid. As shown in the Fig. 10(c), it firstly flows towards
the heating cover due to the VR part and then turns to the ribbed
sidewall as result of SR part. The two deflections make the thermal
boundary layers near the vertical and spanwise walls redevelop.
Due to the successive distribution of the BRs, the thermal boundary
layers will be interrupted again before they are fully developed.
Thus, most thermal boundary layers in the BR-MC are in the developing state. This is main reason that the heat transfer efficiency of
Fig. 10. Streamlines for microchannels with (a) VRs, (b) SRs and (c) BRs between the fifth and seventh ribs at Re = 500 in 3D microchannel structure.
G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609
BR-MC is better than those of VR-MC and SR-MC, shown in the
Figs. 7 and 8.
Meanwhile, the 2D cross-sectional streamlines are also displayed to explore the flow field and heat transfer mechanisms.
Fig. 11 displays the streamlines on the y-z cross section of
x = 0.3125 mm (left) and x-y cross section of z = 0.9 mm (right) at
Re = 500, selected between the fifth and sixth ribs of the test section. Apparently, the introduction of VR, SR and BR all induces
recirculation flow in the microchannels. In Fig. 11(a), the VR can
induce a large recirculation flow between two adjacent VRs on
the y-z cross section, which disturbs the thermal boundary layer
in vertical direction and causes the fluid under the cover exchanges
with the mainstream. On the other x-y cross section, the streamlines are flat, which indicates no distinct secondary flow structure in
the spanwise. On the contrary, the SRs can induce two recirculation
flow on the x-y cross section, while there is no recirculation flow on
the y-z cross section. As shown in Fig. 11(b), one small recirculation
flow occurs at the leading bottom corner of the rib and the other
large recirculation flow is located between the two adjacent ribs.
Therefore, the VRs and SRs only generate recirculation flow and
disturb the thermal boundary in the vertical and spanwise direction, respectively. However, no obvious flow structure change
emerges in the other direction.
For BR-MC, recirculation flow can be observed on both y-z and
x-y cross sections, as shown in Fig. 11(c). On the y-z cross section,
two small recirculations are located on the trailing of VR and one
relatively larger recirculation happens between two ribs. At the
same time, a large scale recirculation flow and a small recirculation
flow can be observed on the x-y cross section, and their positions
and shapes are similar to those in the SR-MC. With the generated
605
recirculations in multi direction, the temperature field is more uniform and the temperature difference between the wall and coolant
is smaller, which can improve convective heat transfer in the
microchannel. However, owing to the bidirectional distribution of
the BR, the cross-section area is larger than those of the SR-MC
and VR-MC, which leads to a decrease in the flow area and thus
a higher pressure drop.
Fig. 12 shows the detailed temperature field distribution
between the fifth and sixth ribs on central cross sections
(x = 0.3125 mm, y = 5.55 mm, z = 0.9 mm) for three ribbed
microchannels at Re = 500. The temperature field distributions for
all cases possess the same temperature level number. For VR-MC,
as shown in Fig. 12(a), there exists obvious boundary between
recirculation region and main stream. In the recirculation region,
the temperature field presents uniform temperature and small gradient toward the heated cover due to the recirculation flow shown
in Figs. 10(a) and 11(a). However, the thermal contour lines near
the other walls are still dense. These imply that the VRs destroy
the thermal boundary layer near the top wall and improve the
temperature uniformity in the vertical direction. For SR-MC, in
terms of temperature contour as revealed in Fig. 12(b), the temperature contour lines near the ribbed sidewalls are sparser compared
with those close to the other walls. Therefore, the VRs and SRs only
reduce the thermal boundary layer thickness in the corresponding
ribbed direction. Compared with the VR-MC and SR-MC, the temperature contour lines in the BR-MC are sparse in the whole flow
field and the temperature distribution is more uniform, as shown
in Fig. 12(c). This indicates that the BRs can make the thermal
boundary layer thinner in both vertical and spanwise direction
and induce the greater temperature difference between walls and
Fig. 11. Cross-sectional streamlines at x = 0.3125 mm (left) and z = 0.9 mm (right) between the fifth and sixth ribs for (a) VR-MC, (b)SR-MC and (c) BR-MC at Re = 500.
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G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609
Fig. 12. Temperature field distribution between the fifth rib and sixth rib on center cross sections (x = 0.3125 mm, y = 5.55 mm, z = 0.9 mm) for (a) VR-MC, (b) SR-MC and (c)
BR-MC at Re = 500.
coolant, which is advantageous to transport heat away from the
wall and will bring about more heat transfer enhancement.
Heat transfer on the four walls of three ribbed microchannels
has been demonstrated in terms of local Nusselt number (Nux),
as shown in Fig. 13. Apparently, the local Nusselt numbers on four
walls of three ribbed microchannels all display the cycle behavior
between two adjacent ribs. Moreover, the local Nusselt numbers of
BR-MC are all larger than those of the VR-MC and SR-MC. This indicates that the BRs provide the higher convective heat transfer
enhancement as a result of the thinner thermal boundary layers,
as observed in Fig. 12. For VR-MC and SR-MC, the periodic higher
heat transfer appears at the leading of the ribs due to the impingement of coolant, while the deceleration downstream of the rib due
to sudden expansion leads to a lower heat transfer on the trailing
of ribs. This trend is also observed for the BR-MC. In addition, a
higher heat transfer in the BR-MC is observed on the non-ribbed
sidewalls near the VR part, which is aroused by the impingement
and acceleration of the flow, respectively.
4.3. Effects of relative rib height of VR (eVR) and relative rib width of SR
(eSR) on hydrothermal performance
According to the prior results, it can be concluded that the BRMC significantly outperforms VR-MC and SR-MC with respect to
heat transfer performance. The next step of the present study is
aimed at analyzing the effects of rib geometry on the thermalhydraulic performance of BR-MC. The selected main geometry
parameters, relative rib height of VR (eVR) and relative rib width
G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609
607
Fig. 13. Contours of local Nusselt number on (a) top wall, (b) left wall, (c) right wall and (d) bottom wall of the considered cases at Re = 500.
of SR (eSR), are defined as the ratio of the VR height to the
microchannel height (eVR = hVR/hc) and the SR width to the
microchannel width (eSR = wSR/wc), respectively. The hVR and wSR
are in the range of 0–200 lm, whereas the other geometric parameters of BR are kept constant as listed in Table 1.
Fig. 14 depicts the variation of Nusselt number with eSR and eVR
for BR-MC at Re = 500. The figure shows that the Nusselt number
both continuously increases with the increment of eSR and eVR.
When eSR = 0.45 and eVR = 0.4, the Nusselt numbers can reach
12.05 and 11.88, respectively. With the larger eSR and eVR, the more
volume of cooling fluid is involved in mixing in each redeveloping
zone. Besides, the enlargement in eSR and eVR promotes jet
impingement and enlarges the surface area. All these factors are
contributing to the heat transfer enhancement. In addition, the
results with eSR = 0 and eVR = 0 once again confirm that the BR
can provide more sufficient heat transfer enhancement in comparison with SR and VR.
The effects of eSR and eVR on the apparent friction factor are seen
from Fig. 15. It is obvious that the apparent friction factor both
increases continuously with the increasing of eSR and eVR for the
Fig. 14. Variation of average Nusselt number with eSR and eVR for BR-MC at
Re = 500. (Correlation with eSR: Nu = 5.06648 + 19.29044eSR 9.25658eSR2, error <
3.28%; correlation with eVR , Nu = 7.00058 + 13.83435eSR 5.96057eSR2, error <
5.94%.)
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G. Wang et al. / International Journal of Heat and Mass Transfer 136 (2019) 597–609
5. Conclusion
The hydrothermal performance of MCHS with BRs has been
studied experimentally and numerically, and compared with those
with relevant rib geometries such as VRs and SRs. Mechanisms
underlying the heat transfer enhancement by BRs are clarified in
detail. Furthermore, the effects of eVR and eSR on heat transfer
and flow performance are discussed. The main conclusions can
be made as follows:
Fig. 15. Variation of average friction factor with eSR and eVR for BR-MC at Re = 500.
(Correlation with eSR: f = 0.11544–0.67269eSR + 6.92454eSR2, error < 10.1%; correlation with eVR: f ¼ 0:12525eeSR =0:18815 þ 0:02525, error < 5.2%.)
entire Reynolds numbers. When eSR = 0.45 and eVR = 0.4, the apparent friction factor are 13.6 and 6.6 times of the ones at eSR = 0 and
eVR = 0, respectively. According to the Fig. 9, the reduction of crosssection area of fluid flow leads to an increment of apparent friction
factor. Similarly, the increasing of eSR and eVR also make the crosssection area shrink and then block the fluid flow. This is the reason
that the pressure drop significantly increases with the increment of
the eSR and eVR. Therefore, the eSR and eVR cannot be too large
because they will induce much more pressure drop and weaken
the thermal performance. According to the results with eSR = 0
and eVR = 0, it is proved that the apparent friction factor in the
BR-MC is higher than SR-MC and VR-MC as result of the combined
barrier effect of SR and VR in the microchannel.
Fig. 16 shows the thermal enhancement factor as a function of
eSR and eVR for BR-MC at Re = 500. The thermal enhancement factor
firstly increases dramatically and then decreases as eSR and eVR
increase. The eVR = 0.15 and eSR = 0.17 introduce the maximal thermal enhancement factor of 1.19 and 1.16, respectively. When
eVR < 0.316 and 0.026 < eSR < 0.357, the thermal enhancement factor is all larger than unity. This implies that the BR-MC possess
high heat transfer enhancement which can offset the pressure drop
penalties caused by the BRs. While the thermal enhancement factor is smaller than unity when eVR > 0.316 and eSR > 0.357. This is
because the increase of eVR and eSR causes a more significant increment in the pressure drop penalty than the heat transfer enhancement. Owing to the serious pressure drop, the BR-MC loses its
advantages as an effective heat transfer enhancement method.
Fig. 16. The thermal enhancement factor as a function of eSR and eVR at Re = 500.
(1) With the same mass flow rate, the Nusselt number of the BRMC is nearly 1.2–1.42 times and1.4–2 times those of VR-MC
and SR-MC, which means that the heat transfer enhancement ability of BR is better than VR and SR.
(2) For all ribbed microchannels, the apparent friction factor all
increases with the rise of Reynolds number. The utilizing of
the BRs in the microchannel causes the highest apparent
friction factor which attributes to the more prominent
blocking effect.
(3) The BRs provide the higher heat transfer by interrupting
thermal boundary layer and inducing the recirculation in
both vertical and spanwise directions. Therefore, the local
Nusselt number of four walls in BR-MC is kept to be highest.
(4) For BR-MC, the rises of eVR and eSR both can improve the heat
transfer but increase the apparent friction factor. Taking the
heat transfer and pressure drop into account concurrently,
the BRs with eVR < 0.316 and 0.026 < eSR < 0.035 can provide
the thermal enhancement factor values above than 1.
Conflict of interest
The authors declared that there is no conflict of interest.
Acknowledgements
This research has been sponsored by the Young Foundation of
shanghai, China (ZZGCD16004), the National Natural Science Foundation of China (No. 51605277, No. 61803254 and No. 61601296).
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