micromachines

Article
Experimental and Numerical Study of a Trapezoidal Rib and Fan
Groove Microchannel Heat Sink
Lufan Jin 1,2,3, *, Junchao Wang 4 , Yixun Cai 4 , Guangzhao Yang 4 , Xuebing Hua 1 , Zhenggeng Zhong 1 , Xiao Pan 1 ,
Chengyu Cai 1 , Jia Qin 1 and Mingxuan Cao 4, *

1 College of Optoelectronic Manufacturing, Zhejiang Industry and Trade Vocational College,

Wenzhou 325003, China; 13819729461@163.com (X.H.); 15990722700@163.com (Z.Z.);
caichengyu@zjitc.edu.cn (C.C.); qinjia@zjitc.edu.cn (J.Q.)
2 Institute of Laser and Opto-Electronics, School of Precision Instruments and Opto-Eletronics Engineering,
Tianjin University, Tianjin 300072, China
3 Penta Laser (Zhejiang) Co., Ltd., Wenzhou 325000, China
4 School of Mechanical and Automation Engineering, Wuyi University, Jiangmen 529020, China;
w13137051728@163.com (J.W.); 13575282936@163.com (Y.C.); yangguangzhao1121@163.com (G.Y.)
* Correspondence: jinlufan@126.com (L.J.); mingxuancao@tju.edu.cn (M.C.)

Abstract: A novel microchannel heat sink (TFMCHS) with trapezoidal ribs and fan grooves was
proposed, and the microchannel was manufactured using selective laser melting technology. Firstly,
the temperature and pressure drop at different power levels were measured through experiments
and then combined with numerical simulation to explore the complex flow characteristics within
TFMCHSs and evaluate the comprehensive performance of microchannel heat sinks based on the
thermal enhancement coefficient. The results show that, compared with rectangular microchannel
heat sinks (RMCHSs), the average and maximum temperatures of TFMCHSs are significantly reduced,
and the temperature distribution is more uniform. This is mainly caused by the periodic interruption
and redevelopment of the velocity boundary layer and thermal boundary layer caused by ribs and
grooves. And as the heating power increases, the TFMCHS has better heat dissipation performance.
When P= 33 W and the inlet flow rate is 32.5 mL/min, the thermal enhancement factor reaches 1.26.

Keywords: trapezoidal ribs; fan grooves; numerical simulation; experiments; thermal enhancement
Citation: Jin, L.; Wang, J.; Cai, Y.; factor
Yang, G.; Hua, X.; Zhong, Z.; Pan, X.;
Cai, C.; Qin, J.; Cao, M. Experimental
and Numerical Study of a Trapezoidal
Rib and Fan Groove Microchannel 1. Introduction
Heat Sink. Micromachines 2024, 15, 713. Due to the rapid development of electronic devices towards integration and minia-
https://doi.org/10.3390/mi15060713 turization, the heat flux of these devices has significantly increased. Highly integrated
Academic Editor: Jinyuan Qian circuits and microelectronic devices are widely used in aerospace, intelligent manufac-
turing, and high-tech industries. These include applications such as cooling high-power
Received: 25 March 2024 semiconductor lasers, thermal management of aviation communication equipment, and
Revised: 14 April 2024
heat dissipation of microelectronic devices. If the temperature increase in the device cannot
Accepted: 15 April 2024
be effectively managed, it may cause the device to malfunction, significantly impacting
Published: 28 May 2024
its stability and service life. Therefore, there is an urgent need for efficient heat transfer
devices to eliminate the large amount of heat generated by electronic devices. One solution
for effective cooling is the single-phase liquid-cooled microchannel radiator first proposed
Copyright: © 2024 by the authors.
by Tuckman and Pisse in 1981 [1]. Compared with traditional radiators, it has higher heat
Licensee MDPI, Basel, Switzerland. transfer performance, smaller geometric dimensions, and lower coolant requirements.
This article is an open access article At this point, a lot of papers have looked at the basic flow and heat transfer prop-
distributed under the terms and erties of single-phase convection in microchannel radiators. Among them, methods to
conditions of the Creative Commons enhance the heat dissipation performance of microchannels include nanofluids [2,3], in-
Attribution (CC BY) license (https:// let cross-section design [4,5], ribs and groove structures [6,7], porous media [8,9], wavy
creativecommons.org/licenses/by/ microchannels [10,11], etc. Adding ribs and groove structures to microchannels through
4.0/). flow destruction technology is an effective approach. K. Derakhshanpur et al. conducted

Micromachines 2024, 15, 713. https://doi.org/10.3390/mi15060713 https://www.mdpi.com/journal/micromachines

Micromachines 2024, 15, 713 2 of 14

numerical research on microchannels with semicircular ribs and found that an increase
in the curvature of the semicircular ribs resulted in a significant increase in heat transfer
coefficient and a slight increase in pressure drop [12]. Ergin Bayrak et al. used numerical
simulation methods to study the heat dissipation of microchannels with different geometric
shapes, discovering that microchannels with holes can mix the fluid at the center of the
channel with the fluid near the wall, thereby improving heat transfer performance [13].
Datta et al. conducted a study on composite channels with ribbed grooves on the side walls.
By comparing the Nusselt number, friction coefficient, and thermal performance changes,
it was found that the composite channel had the best comprehensive performance [14].
Peitao et al. investigated the effects of rib height and cavity depth on the heat transfer
performance of triangular ribbed microchannels. The optimal size of microchannels reduces
the temperature difference at the bottom of the channel from 26 K to 17 K, resulting in an
overall performance improvement of 1.2305 times [15].
However, while these numerical modeling efforts indicate that complex microchannel
designs are constantly improving, fabrication of such heat sinks via conventional subtractive
techniques (e.g., micromachining [16], laser processing [17], and anisotropic chemical
etching [18]) has limitations. Advances in additive manufacturing (AM) technologies have
made it possible to manufacture complex microchannels. Kirsch and Thole experimentally
tested the wavy microchannels of additive manufacturing. The results indicate that the
wall roughness generated by the AM process enhances heat transfer and also increases
pressure loss [19,20]. Ganesan Narendran et al. used AM to manufacture single-layer
and double-layer microchannel heat sinks. The influence of different materials on the
performance of microchannels was explored and compared with traditional processing
methods. The results showed that the 3D printing channel had a higher pressure drop
and a larger Nusselt number [21]. Guang Pi et al. used selective laser melting (SLM)
technology to manufacture microchannel structures with pits and cavities. Compared
with straight microchannels, it increased the heat transfer performance by more than
10% [22]. Han et al. made a new type of biomimetic microchannel heat sink through 3D
printing. The temperature difference inside the 3D-printed heat sink was 57% lower than
that of the spider web heat sink, resulting in better temperature uniformity [23]. Joshi et al.
conducted an experimental comparison between microchannel heat sinks manufactured
with AM and those with conventional processing. The heat dissipation performance of AM
microchannels improved by 46%, but the pressure drop increased by 91%, mainly due to
the high surface roughness of AM microchannels [24].
As previously mentioned, numerous studies have demonstrated that the addition
of rib and groove structures within microchannels through flow disruption techniques is
an effective method to enhance microchannel performance. Selective laser melting is an
effective technique for fabricating complex microchannels. In this study, we proposed a
microchannel with an asymmetric rib and groove structure and fabricated the microchannel
heat sink using SLM and CuCrZr powder. We conducted experiments to test the heat
dissipation in the microchannels using deionized water as the working fluid. The thermal
performance of the TFMCHS was compared with that of conventional straight channels to
explore the feasibility of enhancing heat transfer. The results show that compared with the
RMCHS, the average and maximum temperatures of the TFMCHS are significantly reduced,
and the temperature distribution is more uniform. This is mainly caused by the periodic
interruption and redevelopment of the velocity boundary layer and thermal boundary
layer caused by ribs and grooves. And as the heating power increases, the TFMCHS has
better heat dissipation performance. When P= 33 W and the inlet flow rate is 32.5 mL/min,
the thermal enhancement factor reaches 1.26.
Micromachines 2024, 15, 713 3 of 14

2. Data reduction
We conducted experiments to examine the flow and heat transfer features at different
flow rates, from 15 to 40 mL/min. The average Nusselt number (Nu) and heat transfer
coefficient (h) are given by the following method:

hDh
Nu = , (1)
λf

qw A f ilm Dh
h= · , (2)
∆TAch Lch λ f
∆T = Tw − 0.5( Tin + Tout ), (3)
where h, qw , A f ilm , ∆T, and Ach are the heat transfer coefficient W/ m2 · k , the heating

wall heat flux W/m2 , the bottom substrate heating area m2 , the temperature difference
between the channel walls and fluid (K), and the contact surface area between the fluid
and solid wall (m 2 ). Tw , Tin , and Tout are the average temperatures of the heating film area
and the inlet and outlet fluid temperature, respectively, all measured in K.
The experimentally measured pressure drop across the microchannel is used to calcu-
late the experimental friction factor given in Equation (4):

∆PDh
f ave = . (4)
2ρ f Lu2m

The theoretical friction factor is predicted using the Hagenpoiseuille equation given
by Equation (5):
64
f ave = . (5)
Re
At the channel inlet, the following formula defines the Reynolds number (Re):

ρ f uin Dh
Re = , (6)
µf

where uin is the inlet velocity of the channel.

The following equations can be used to calculate the hydraulic diameter:

4Wch Hch
Dh = . (7)
2(Wch + Hch )

The total thermal resistance of the heat sink and the pumping power is calculated
as follows:
Tmax − Tin Tmax − Tin
Rth = = , (8)
Q A f ilm · q
where Rth is the thermal resistance of microchannel heat sinks, Tmax is the maximum value
of the temperature field, and Tin is the inlet temperature.
The pumping power is expressed as follows:

Wpp = N · AC · uin · ∆p, (9)

where Wpp is the pumping power by the MCHS, N is the number of channels, AC is the
cross-section area of each channel, and ∆p is the total pressure drop across the microchannel.
The thermal enhancement factor (PEC) is defined as the ratio of the heat transfer coef-
ficient of the enhanced channel to that of the non-enhanced channel at an equal pumping
power and is given by [25]:
   1
Nu f 3
PEC = / , (10)
Nu0 f0
 3. Experiment and Simulation
3.1. Heat Sink Design
Figure 1 shows the isometric view of the straight-channel heat sink test piece and its
Micromachines 2024, 15, 713 dimensions. The channel height H c h is 1.1 mm, the channel width Wch is 1.1 mm, 4 of the
14
Lch WS
channel length is 20 mm, the wall thickness between the channels is 1.1 mm, the
total width of the heat sink W H S is 10 mm, the total length of the heat sink LHS is 30 mm,
where 0 represents
and the total height theofrectangular channel,
the heat sink H HS
isi.e., a Rec.
5 mm.
The TFMCHS was created based on the conventional RMCHS. The design parameters
3. Experiment and Simulation
of the TFMCHS are presented in Figure 2. The geometric structure of ribs and grooves is
3.1. Heat Sink Design
mainly designed with the goal of reducing the boundary layer. Among them, for the rib
Figurethe
structure, 1 shows
upper and the isometric
lower edges view of right-angle
of the the straight-channel heat0.11
trapezoid are sink
mm test piece
and 0.15 and
mm,
its dimensions.
respectively, andThethechannel
height ofheight Hch is 1.1
the trapezoid mm,mm.
is 0.15 the channel
The depth of theWfan-shaped
width ch is 1.1 mm, the
groove
channel length L is 20 mm, the wall thickness between the channels W
is 0.2 mm, and the included angle is 30°. The spacing between the ribs and grooves is 0.8
ch S is 1.1 mm, the
total
mm,width
with aofperiod
the heat of sink WHS
2 mm. The is rest
10 mm, thedimensions
of the total lengthofofthe
theTFMCHS
heat sinkareL HSthe
is 30 mm,
same as
and the total height of the heat sink
those of the RMCHS. Figure 3 shows the H is 5 mm.
HS isometric view of the TFMCHS test piece.

Figure1.1.Isometric
Figure Isometricview
viewofofstraight-channel
straight-channelheat
heatsink
sinktest
testpiece
pieceand
anditsitsdimensions.
dimensions.

The TFMCHS was created based on the conventional RMCHS. The design parameters
of the TFMCHS are presented in Figure 2. The geometric structure of ribs and grooves is
mainly designed with the goal of reducing the boundary layer. Among them, for the rib
structure, the upper and lower edges of the right-angle trapezoid are 0.11 mm and 0.15 mm,
respectively, and the height of the trapezoid is 0.15 mm. The depth of the fan-shaped
groove is 0.2 mm, and the included angle is 30◦ . The spacing between the ribs and grooves
Micromachines 2024, 15, 713 is 0.8 mm, with a period of 2 mm. The rest of the dimensions of the TFMCHS are the5 same
of 15
as those of the RMCHS. Figure 3 shows the isometric view of the TFMCHS test piece.

Figure 2. Complex-channel
Figure 2. Complex-channel cross-sectional view and
cross-sectional view and water
water inlet
inlet flow
flow direction.
direction
Micromachines 2024, 15, 713 5 of 14
Figure 2.
Figure 2. Complex-channel
Complex-channel cross-sectional
cross-sectional view
view and
and water
water inlet
inlet flow
flow direction
direction

Figure3.3.
Figure
Figure 3.Isometric
Isometricview
Isometric viewof
view ofcomplex
of complexheat
complex heatsink
heat sinktest
sink testpiece
test pieceand
piece andits
and itsdimensions.
its dimensions.
dimensions.

3.2.
3.2.Processing
3.2. Processingof
Processing ofMicrochannel
of MicrochannelHeat
Microchannel HeatSinks
Heat Sinks
Sinks
This
This study
This studyused
study usedCuCrZr
used CuCrZrpowder
CuCrZr powderto
powder toprepare
to preparethe
prepare themicrochannels.
the microchannels. The
microchannels. The particles
The particles are
particles are
are
spherical and
spherical and
spherical have
and have a diameter
have aa diameter between
diameter between
between 30 30 and
30 and 50
and 50 µm.
50 µm. The
µm. The microchannel
The microchannel heat
microchannel heat sink
heat sink was
sink was
was
prepared
preparedusing
prepared usingSLM
using SLM
SLMtechnology, as shown
technology,
technology, as shown
as in Figure
shown 4a. Figure
in Figure
in Figure 4b shows
4a. Figure
4a. Figure 4bthe
4b actualthe
shows
shows molding
the actual
actual
effect inside theinside
microchannel, with Rz withvaluesR measured at the bottom surface of the
molding
molding effect
effect the microchannel,
inside the microchannel, with R zz values
values measured
measured at the
at the bo
bo om surface
om surface
microchannel
of the ranging
the microchannel from
microchannel ranging 75 to
ranging from 90
from 75 µm.
75 to
to 90
90 µm.
µm.
of

Figure
Figure 4.Heat
Figure4.4. Heat
Heat
sinks andand
sinks
sinks
packaging test. (a)
packaging
and packaging
Heat
test.
test. (a)sink,
(a) Heat
Heat
(b) sink,
SEM images of microchannels,
(b) SEM
sink, (b) SEM images of
images
(c) packaging of
of microchannels,
microchannels, (c)
(c)
heat sink.
packaging of heat sink.
packaging of heat sink.
3.3. Preprocessing and Packaging of Microchannel Heat Sinks
Firstly, the conductive wire of the heating plate was connected to the DC power
supply, and then the heating plate was fixed to the top surface of the microchannel heat sink
using thermally conductive
silicone. The thermal conductivity of the thermally conductive
silicone was 5 W/ m2 · k . In order to achieve a good encapsulation effect for microchannel
heat sinks, a dedicated positioning fixture was designed. The fixture was divided into upper
and lower parts, which were fastened with two M4 screws to ensure a stable and water-tight
testing process. A multichannel thermometer was used to measure the temperature curve
of the bottom surface and the inlet and outlet of the radiator. Finally, the water pipe was
tightly connected to the inlet and outlet of the heat sink. The fully encapsulated heat sink is
shown in Figure 4c.
 divided into upper and lower parts, which were fastened with two M4 screws to ensure a
stable and water-tight testing process. A multichannel thermometer was used to measure
the temperature curve of the bo om surface and the inlet and outlet of the radiator.
Finally, the water pipe was tightly connected to the inlet and outlet of the heat sink. The
Micromachines 2024, 15, 713 fully encapsulated heat sink is shown in Figure 4c. 6 of 14

3.4. Experimental Procedures

A schematicProcedures
3.4. Experimental diagram of the experimental apparatus is shown in Figure 5. It consisted
of a Atest section, a power supply
schematic diagram system, a data
of the experimental acquisition
apparatus system,inand
is shown a drainage
Figure system.
5. It consisted
Deionized water with a working fluid of 298.15 K was used. The ceramic
of a test section, a power supply system, a data acquisition system, and a drainage system. heating plate
was energized by a DC power supply with a range of 0–30 V and
Deionized water with a working fluid of 298.15 K was used. The ceramic heating plate was 0–10 A. After being
pumped by
energized by aa peristaltic
DC powerpump, supplythe coolant
with a rangein the constant-temperature
of 0–30 V and 0–10 A. After water
beingtank entered
pumped
thea peristaltic
by experimental pump,section and carried
the coolant in theaway the heat of the heating
constant-temperature water tankplate through
entered thea
microchannel
experimental heat and
section sink.carried
The heated
away the coolant
heat ofentered the plate
the heating waterthrough
tank. The inlet water
a microchannel
temperature
heat sink. The was
heated controlled at 298.15
coolant entered the kwater
throughtank.aTheconstant-temperature
inlet water temperature bath.wasThe
peristaltic pump had a filter at the front end to prevent pollutants from entering.
controlled at 298.15 k through a constant-temperature bath. The peristaltic pump had a filter The flow
atrate was accurately
the front end to preventcontrolled
pollutantswithin the rangeThe
from entering. of flow
10~100
ratemL/min by adjusting
was accurately controlledthe
rotational
within speedof of
the range the peristaltic
10~100 mL/min bypump, adjustingwith thean uncertainty
rotational speedofof 1.5%. Using a
the peristaltic
multichannel
pump, with anthermometer
uncertainty of to 1.5%.
measureUsingthe atemperature
multichannel at the inlet, outlet,
thermometer to and bo om
measure theof
temperature at the inlet,
the microchannel, outlet, andwas
the uncertainty bottom
0.2 K.ofUsing
the microchannel, the uncertainty
a pressure controller was
and pressure
0.2 K. Using
sensor a pressure
to measure the controller
pressure in and
thepressure
inlet andsensor
outlettosections,
measurethe theuncertainty
pressure inwasthe inlet
0.5%.
and
These devices were connected to a PC for monitoring and recording temperatures for
outlet sections, the uncertainty was 0.5%. These devices were connected to a PC and
monitoring and recording
pressures during temperatures and pressures during the experiments.
the experiments.

Figure5.5.Schematic
Figure Schematicdiagram
diagramofofexperimental
experimentalapparatus.
apparatus.

Duringthe
During theexperiment,
experiment,packaging
packagingtesting
testingwas
wascarried
carriedout
outfirst.
first.Then,
Then,the
theinlet
inletflow
flow
rate
ratewas
wasset
setthrough
throughaaperistaltic
peristalticpump,
pump,the theinlet
inletwater
watertemperature
temperaturewas wasset
setthrough
throughaa
constant-temperature
constant-temperaturewater
watertank,
tank,and
andthe
therequired
requiredheating
heatingplate
platepower
powerwas
wasalso
alsoset.
set.After
After
aastable
stablewater
watersupply
supplyfor
forhalf
halfananhour,
hour,the
theexperimental
experimentaldata
datawere
wererecorded.
recorded.

3.5. Uncertainty Analysis

Due to errors in all the experimental data collected, a detailed uncertainty analysis
was carried out on relevant parameters using the procedure described by Holman [26]. The
uncertainty of each parameter was based on the uncertainty of the measured parameter,
and these errors are listed in Table 1, respectively. According to the analysis, the uncertainty
of the Nusselt number and friction coefficient were ±3.22% and ±3.94%, respectively.

Table 1. Maximum uncertainty of measured and calculated parameters.

Maximum Maximum
Parameters Parameters
Uncertainty (%) Uncertainty (%)
Dh 1.37 Re 2.03
Qv 2.1 ∆p 1.98
P 0.327 Tav 1.45
Micromachines 2024, 15, 713 7 of 14

3.6. Numerical Simulation

A three-dimensional numerical model of the microchannel heat sink was established
using ANSYS FLUENT 16.0 software, and the convective heat transfer and fluid flow
processes inside the microchannel were analyzed. The upper surface of the channel was in
contact with the heating plate, and the remaining surfaces were set for natural heat dissipa-
tion. The pressure velocity was coupled using the SIMPLEC algorithm, and the momentum
and energy equations were discretized using a second-order upwind scheme [27]. The
entire microchannel was selected as the computational domain, and in order to simplify
the problem, the following assumptions were made for the model:
(1) The fluid is a Newtonian fluid, and the flow is laminar, incompressible, and steady-
state [28];
(2) Except for the viscosity of water, the properties of fluids and solids are constant [29];
(3) Radiative heat transfer is neglected [30];

∇·V = 0 (11)
ρ(v · ∇v) = −∇ p + ∇(µ f · ∇ T f ) (12)
ρCP v · ∇ T f = ∇(λ f · ∇ T f ) (13)
For the solid region, the energy equation is

∇(λs · ∇ Ts ) = 0. (14)

Among them, V is the velocity of the fluid, p is the pressure in the fluid region, T f is
the fluid temperature, and Ts is the solid temperature.
This simulation uses deionized water as the fluid and CuCrZr as the solid material.
The material properties of water include a density of 1000 kg · m−3 , a thermal conductivity
of 0.6 w · m−1 · k−1 , a constant pressure heat capacity of 4178 j · kg−1 · k−1 , and a viscosity
that varies with temperature. The material properties of CuCrZr include a density of
8960 kg · m−3 , a thermal conductivity of 288 w · m−1 · k−1 , and a constant pressure heat
capacity of 377 j · kg−1 · k−1 .
The microchannel Inlet was set as a constant velocity inlet, the outlet was a pressure
outlet, and the gauge pressure was zero. A uniform heat flux was applied at the top of the
microchannel. Coupling boundary conditions were set on the fluid-solid coupling wall.
In this study, the variation range of water temperature is
298.15–363.15 K, and the
viscosity variation range is 3.17 × 10−4 −8.95 × 10−4 kg/ m · s−2 . The influence of visible
temperature on viscosity cannot be ignored. Kestin et al. confirmed the relationship
between temperature and viscosity in Equation (15) [31]:

20 − t n
 
µ(t) o
log = 1.2378 − 1.303 × 10−3 (20 − t) + 3.06 × 10−6 (20 − t)2 + 2.55 × 10−8 (20 − t)3 (15)
µ(20 ◦ C) t + 90

The governing equations are regarded as converged once all residuals fell below 10−4 .
The heat sinks were meshed with hexahedron mesh. Grid independence studies were
performed to ensure the numerical solution was not influenced by the number of grids.
Four different numbers of grids were used, and the relative error between grid 4 and the
average bottom temperature of other grids is shown in Table 2. The relative error between
Grid 3 and Grid 4 was just 0.9%, so Grid 3 was used to obtain the numerical solution.
Table 2. Check of grid independence.

Case Element Number ( ) Tav (◦ C) Err (%)

Grid 1 20.38 37.81 4.1
Grid 2 37.92 38.74 1.8
Grid 3 53.29 39.13 0.9
Grid 4 86.34 39.49 /
Micromachines 2024, 15, 713 8 of 14

4. Result and Discussion

4.1. Printing Equipment and Printing Parameters
Commercial laser-selective melting equipment (Dimetal-300, Leijia Additive Manu-
facturing Company, Guangdong, China) was used to print the designed microchannel
heat sink samples. The printing parameters were set as follows: laser power at 350 W,
scanning speed at 420 mm/s, scanning spacing of 0.06 mm, and layer thickness of 30 µm.
To enhance printing precision and ensure structural integrity inside the microchannel heat
sink, a 67◦ rotated printing method was chosen. After printing, a wire-cutting machine was
used to remove the external support structures of the microchannel heat sink, as shown in
Figure 4a. It can be observed that the external shape of the printed microchannel heat sink
sample was well formed.

4.2. Verification of Simulation and Validation of Experiment for MCHSs

In order to verify the accuracy of the numerical solution, experimental data and sim-
ulation data of the microchannel were compared. Firstly, a multichannel thermometer
was used to set five uniform temperature measurement points on the bottom of the mi-
crochannel to measure the average temperature of the bottom surface. The comparison
between the experimentally measured temperature and the simulated temperature for
MCHSs and TFMCHSs at QV = 30 mL/min is shown in Figure 6. It can be seen that under
different heating plate powers, the experimental results and simulation results are in good
agreement, and the deviation of the average temperature of the radiator bottom surface
is less than ±3.7%. The average temperature calculated by simulation is greater than the
average temperature tested by experiments. This is because the simulation calculation only
considers the convective heat transfer between fluid and solid, ignoring the roughness
Micromachines 2024, 15, 713 9 of 15
effect of 3D-printed microchannels [32]. Therefore, the simulation and experiments in this
article can ensure the accuracy of the data.

Figure
Figure6.6.Comparison
Comparisonofofmeasured
measured and numerical
and solutions
numerical for the
solutions average
for the surface
average temperature
surface of of
temperature
heat
heatsinks
sinksunder
underdifferent
differentheating
heatingpowers.
powers.

4.3. Flow
4.3. FlowCharacteristics
CharacteristicsofofHeat
Heat Sinks
Sinks
The geometric
The geometricstructure
structureofof microchannels
microchannels hashas a significant
a significant impactimpact on fluid
on fluid flow. flow.
Figure 77 shows
Figure showsthe theflow
flow velocity magnitude
velocity magnitudeand and
streamline distribution
streamline of twoofmicrochan-
distribution two
nels at different flow velocities when
microchannels at different flow velocities when P = 19 W. P =19 W
Figure 7a shows the velocity
. Figure 7a shows the velocitydistribution
cloud map of
distribution the cross-section
cloud at the entrance
map of the cross-section at theofentrance
the microchannel. It can be It
of the microchannel. seen
canthat
be the
velocity
seen that at
thethe centeratofthe
velocity thecenter
channel is the
of the highest.
channel is theThis is because
highest. This isthe closerthe
because thecloser
fluid is to
the
thefluid
wall,isthe
to the wall,the
greater theviscous
greater the viscous
force force it experiences.
it experiences. The TFMCHS The TFMCHS
generatesgenerates
four vortices
four
at thevortices at the inlet cross-section,
inlet cross-section, mainly due tomainly due toofthe
the presence ribspresence of ribs
and grooves and grooves
interfering with the
interfering
radial flowwithof thethe radial
fluid, flow ofinthe
resulting fluid, resulting
a pressure differencein aandpressure difference
the formation and the [10].
of vortices
formation of vortices [10].
From Figure 7b,c, it can be seen that the presence of ribs and grooves creates a
thro ling effect [33]. When the fluid flows through the trapezoidal rib, the sudden
decrease in inlet leads to the main flow converging towards the middle, some of the
streamline being interrupted, and the overall flow being S-shaped. A large stagnation
 Micromachines 2024, 15, 713 10 of 15
Micromachines 2024, 15, 713 9 of 14

Micromachines 2024, 15, 713 10 of 15

Figure
Figure7. 7.Flow
Flowvelocity
velocityandandstreamline
streamlinedistribution
distributionfigures
figuresforfordifferent
differentchannels:
channels: (a)
(a) the
the channel
channel inlet for
v=inlet for v(b)
1 m/s;  1m
z =/ 6.4–11.8
s ; (b) z =mm
6.4–11.8
(y = mm (y = 0.5
0.5 mm), v= mm), v  (c)
1 m/s; 1mz/ =s ;6.4–11.8
(c) z = 6.4–11.8
mm (ymm= 0.5(ymm),
= 0.5 mm),
v = 0.6 m/s.
v  0.6m / s .
From Figure 7b,c, it can be seen that the presence of ribs and grooves creates a throttling
effect [33].
Figure When
8 shows thethefluid flowsofthrough
variation pressurethe trapezoidal
drop with flow rate rib,for
thetwosudden
types ofdecrease
radiatorsin inlet
whento Pthe
leads =19 W main
. It canflow converging
be seen towards
that the pressure theofmiddle,
drop someofof
the two types the streamline
radiators increases being
with the increase
interrupted, and the in flow rate,flow
overall and being
the pressure drop A
S-shaped. of large
the TFMCHS
stagnation is greater
zone than that
is generated at
of the RMCHS. This is because the pressure drop in a straight channel
the rear end of the rib, resulting in lower heat transfer efficiency. At the same time, due to is mainly caused
thebypresence
friction lossof on the inner
grooves, wall
the of the channel,area
cross-sectional and the static
of the pressure
channel graduallyand
increases, decreases
the velocity
along the flow direction. For complex channels, a pressure
of the fluid flowing through the grooves slows down, resulting in a stagnation drop not only includes friction
zone. A
loss along the inner wall of the channel but also includes pressure loss caused by direct
vortex is generated in the stagnation zone, pulling the hot fluid inside the groove towards
fluid impact on ribs and grooves [35]. As the flow rate increases, the impact effect becomes
the central region. This allows the cooler fluid at the center and the hotter fluid near the
stronger, and the pressure drop loss increases.
microchannel wall to fully mix, promoting temperature uniformity [34]. The combination
Figure
of ribs7. and
Flow grooves
velocity and streamline
causes distribution
periodic figures for and
interruption different channels: (a)
generation of the
thechannel
boundary layer,
inlet for v  1m / s ; (b) z = 6.4–11.8 mm (y = 0.5 mm), v  1m / s ; (c) z = 6.4–11.8 mm (y = 0.5 mm),
significantly enhancing the heat transfer effect. And as the inlet velocity increases, it
v  0.6m / s .
significantly leads to stronger flow mixing.
Figure 8
Figure 8 shows shows thethe variation
variation of pressure
of pressure dropflow
drop with withrateflow ratetypes
for two for two types of radiators
of radiators
when
when P
P =
=19 19
W . It can be seen that the pressure drop of the two types of radiators increases increases
W. It can be seen that the pressure drop of the two types of radiators
with the increase inin
with the increase flow flow rate,
rate, andandthe the pressure
pressure drop drop
of theof the TFMCHS
TFMCHS is greater is greater
than thatthan that of
of the RMCHS. This because the pressure drop in a straight channel is mainlymainly
the RMCHS. This is because the pressure drop in a straight channel is caused caused by
friction
by frictionloss
lossonon the innerwall
the inner wall of the
of the channel,
channel, and
and the thepressure
static static pressure
graduallygradually
decreases decreases
along
alongthe theflowflow direction.
direction. For For
complex channels,
complex a pressure
channels, drop notdrop
a pressure only not
includes
onlyfriction
includes friction
loss along the inner wall of the channel but also includes
loss along the inner wall of the channel but also includes pressure loss pressure loss caused bycaused
direct by direct
fluid impact on ribs and grooves [35]. As the flow rate increases, the impact
fluid impact on ribs and grooves [35]. As the flow rate increases, the impact effect becomes effect becomes
stronger, and the pressure drop loss increases.
stronger, and the pressure drop loss increases.

Figure 8. Variation in pressure drops with flow rate for two heat sinks, P=19 W .

4.4. Heat Transfer Characteristics of Heat Sinks

For chip cooling, the highest and average temperatures on the surface of the heat sink
are of utmost concern, as the uniformity of temperature distribution directly affects the
reliability, efficiency, and service life of microchips. Figures 9 and 10 show the average
temperature and maximum temperature of two heat sinks measured under four different

Variation
Figure8.8.Variation
Figure in pressure
in pressure drops
drops with with flow
flow rate forrate
twofor two
heat heatP=19
sinks, W .P= 19 W.
sinks,

4.4. Heat Transfer Characteristics of Heat Sinks

For chip cooling, the highest and average temperatures on the surface of the heat sink
are of utmost concern, as the uniformity of temperature distribution directly affects the
reliability, efficiency, and service life of microchips. Figures 9 and 10 show the average
Micromachines 2024, 15, 713 11 of 15

power levels as a change in flow rate. Five thermocouple test points were set up on the
Micromachines 2024, 15, 713 bo om surface of the heat sink using a multichannel thermometer. The average 10 and
of 14
maximum temperatures of five data points were obtained. The test results indicate that
the average and maximum temperatures of both types of radiators decrease with
increasing flow rates.
4.4. Heat Transfer As the flow
Characteristics rate
of Heat increases, the trend of decreasing average and
Sinks
maximum temperatures decreases, indicating that increasing the flow rate to lower the
For chip cooling, the highest and average temperatures on the surface of the heat sink
bo om temperature after reaching a certain value is not an effective method. From the
are of utmost concern, as the uniformity of temperature distribution directly affects the
figure, it can be seen that the heat dissipation capacity of TFMCHSs is significantly higher
reliability, efficiency, and service life of microchips. Figures 9 and 10 show the average
than that of RMCHSs, and as the power increases from 12 W to 33 W, the heat dissipation
temperature and maximum temperature of two heat sinks measured under four different
performance P=33 W , compared with
power levels of as TFMCHSs
a change inbecomes
flow rate. be Fiveer and be er. Whentest
thermocouple points were set up on
RMCHSs, the average and maximum temperatures
the bottom surface of the heat sink using a multichannel thermometer.of TFMCHSs decreased by The 6.8average
°C and
9.7
and°C, respectively.
maximum This is of of
temperatures great
fivesignificance
data pointsfor improving
were obtained. theThe
reliability of chips
test results and
indicate
extending their lifespan.
that the average and maximum temperatures of both types of radiators decrease with
It can be
increasing explained
flow rates. Asas the
follows:
flow theratecombination
increases, the of trend
groovesof and ribs is beneficial
decreasing average and for
enhancing heat transfer, mainly due to the interruption and redevelopment
maximum temperatures decreases, indicating that increasing the flow rate to lower the of the velocity
boundary layer and thermal
bottom temperature boundary
after reaching layer,value
a certain strong fluidandisturbance,
is not and the
effective method. mixing
From the
effect
figure,of internal
it can be seeneddies. The
that the trapezoidal
heat dissipationrib changes
capacity of the mainstream
TFMCHSs flow direction,
is significantly higher
weakening the vortexand
than that of RMCHSs, zone inside
as the power theincreases
cavity, from
impacting
12 W tothe boundary
33 W, layer, and
the heat dissipation
enhancing
performance theof heat transfer
TFMCHSs effect. better
becomes Meanwhile, due to
and better. the presence
When P= 33 W, of grooves,with
compared the
convective heat transfer area inside the channel increases.
RMCHSs, the average and maximum temperatures of TFMCHSs decreased by 6.8 C and Compared with ◦
straight
9.7 ◦ C, respectively.
channels, the microchannel
This is of proposed in this for
great significance article has a lower
improving and more
the reliability uniform
of chips and
temperature
extending their andlifespan.
a more significant heat dissipation effect.

9. Average
Figure 9. Averagetemperature
temperature figures of the
figures bottom
of the bo surfaces of twoofchannels
om surfaces under different
two channels heating
under different
heating
powers:powers:
(a) 12 W.(a)
(b)1219W.
W.(b)
(c)19
15W.
W.(c)
(d)1533W.
W.(d) 33 W.

It can be explained as follows: the combination of grooves and ribs is beneficial for
enhancing heat transfer, mainly due to the interruption and redevelopment of the velocity
boundary layer and thermal boundary layer, strong fluid disturbance, and the mixing effect
of internal eddies. The trapezoidal rib changes the mainstream flow direction, weakening
the vortex zone inside the cavity, impacting the boundary layer, and enhancing the heat
transfer effect. Meanwhile, due to the presence of grooves, the convective heat transfer
area inside the channel increases. Compared with straight channels, the microchannel
proposed in this article has a lower and more uniform temperature and a more significant
heat dissipation effect.
Micromachines 2024, 15, 713 12 of 15
Micromachines 2024, 15, 713 11 of 14

The temperature cloud maps of the bottom surfaces of the two radiators when
QV = 30 mL/min and P= 19 W are shown in Figure 11. From the figure, due to the al-
most absence of fluid mixing in the straight passage, the temperature of the RMCHS is
significantly higher than that of the TFMCHS. This is mainly because the flow inside the
channel is laminar, and in the absence of external interference, there is basically only heat
transfer inside the fluid, and thermal convection can be ignored. The closer the fluid is to
the wall, the greater the influence of the boundary layer and the worse the heat transfer
Micromachines 2024, 15, 713
effect. Compared with the RMCHS, the TFMCHS has a much smaller temperature gradient 12 of 15
and a more uniform temperature distribution. This indicates that ribs and grooves have a
significant impact on the temperature field [36].

Figure 10. Maximum temperature figures of the bo om surfaces of two channels under different
heating powers: (a) 12 W. (b) 19 W. (c) 15 W. (d) 33 W.

The temperature cloud maps of the bo om surfaces of the two radiators when
QV =30 mL/min and P=19 W are shown in Figure 11. From the figure, due to the
almost absence of fluid mixing in the straight passage, the temperature of the RMCHS is
significantly higher than that of the TFMCHS. This is mainly because the flow inside the
channel is laminar, and in the absence of external interference, there is basically only heat
transfer inside the fluid, and thermal convection can be ignored. The closer the fluid is to
the wall, the greater the influence of the boundary layer and the worse the heat transfer
effect. Compared with the RMCHS, the TFMCHS has a much smaller temperature
gradient and a more
Maximum uniform figures
temperature temperature
of the distribution.
the bottom This
surfaces of
of twoindicates under
that ribs and
Figure
Figure 10.
10. Maximum temperature figures of bo om surfaces two channels
channels under different
different
groovespowers:
heating have a(a)
significant impact
12 W. (b) 19 W. (c)on
W. (c) 15 the
15 W.
W.(d)temperature
(d) 33
33W.
W. field [36].

The temperature cloud maps of the bo om surfaces of the two radiators when
QV =30 mL/min and P=19 W are shown in Figure 11. From the figure, due to the
almost absence of fluid mixing in the straight passage, the temperature of the RMCHS is
significantly higher than that of the TFMCHS. This is mainly because the flow inside the
channel is laminar, and in the absence of external interference, there is basically only heat
transfer inside the fluid, and thermal convection can be ignored. The closer the fluid is to
the wall, the greater the influence of the boundary layer and the worse the heat transfer
effect. Compared with the RMCHS, the TFMCHS has a much smaller temperature
gradient Temperature
Figure 11. and contours
uniformofoftemperature
a morecontours
Figure 11. Temperature
the heater surface for two heat sinks,
distribution.
the heater surface for two heatThis V = 30
QVQ=30
sinks,indicates
mL/min
that and
ribs and
mL/min and
P = 19
groovesW.have a significant impact on the temperature field [36].
P=19 W .
4.5. Performance Evaluation
4.5. Performance
The TFMCHS Evaluation
has good heat transfer characteristics and a more uniform temperature
distribution, but the
The TFMCHS has pressure
good drop also increases.
heat transfer Therefore,
characteristics andwea use
morea thermal
uniformenhancement
temperature
factor
distribution, but the pressure drop also increases. Therefore, we useThe
to evaluate the comprehensive performance of flow and heat transfer. a compar-
thermal
ison of the Nusselt number ( Nu/Nu ) and
enhancement factor to evaluate the comprehensive
0 apparent friction coefficient
performance of flow and heat( f / f are two
0 ) transfer.
parameters used to identify heat dissipation Nu /performance and pressure drop performance.
The comparison of the Nusselt number 
Nu0 
and apparent friction coefficient 
f / f0 
From Figure 12, it can be seen that both Nu/Nu0 and f / f 0 increase with the increase in

Figure 11. Temperature contours of the heater surface for two heat sinks, QV =30 mL/min and
P=19 W .
Micromachines 2024, 15, 713 13 of 15

Micromachines 2024, 15, 713 13 of 15

are two parameters used to identify heat dissipation performance and pressure drop
Micromachines 2024, 15, 713 12 of 14
are two parameters used to Nu / Nu0 and andf / f0 pressure drop
performance. From Figure 12,identify
it can beheat
seendissipation
that both performance increase with
the increase inFrom
inlet flow rate. f / f
performance. Figure 12,This indicates
it can be seenthat
thatthe TFMCHS0has
both Nu / Nu andgood heat dissipation
0 increase with
performance,
the
inletincrease but
flow rate. the
in This rib structure
inlet indicates
flow rate.that
This leads to significant
theindicates
TFMCHS that
hasthe friction
TFMCHS
good losses [37].
has goodperformance,
heat dissipation heat dissipation
but
performance, butleads
the rib structure the rib
to structure
significantleads to significant
friction losses [37].friction losses [37].

Figure 12. The variation of Nu / Nu0 and

f / f0 Q
with V in microchannel heat sinks.
Figure 12. The variation of Nu/Nu 0 and f / f with
f / 0f0 Q VQin microchannel heat sinks.
Figure 12. The variation of Nu / Nu0 and with V in microchannel heat sinks.
The relationship between the thermal enhancement factor and flow rate when
The relationship between the thermal enhancement factor and flow rate when P= 19 W
P=19The
W relationship
is shownisin shown
Figure in
13.Figure
between
From 13. the
the From the
thermal
graph, graph,
it can it can
thatbe
enhancement
be seen seen
thefactor that
andthe
enhancement flow enhancement
rate when
coefficient is
coefficient
P=19 W is always
is shown
always greater thaningreater
Figure
1 and than 1 and
13. From
increases increases
withthethe graph,with the
increaseitincan increase
beflow
inlet in
seenrate. inlet
thatThis flow
themeans rate.
thatThis
enhancementthe
means thatisthe
coefficient
comprehensive comprehensive
always
performance ofperformance
greater than 1 and
the TFMCHS ofhas
increases the
withTFMCHS
been the has been
increase
improved. in improved.
inlet
When flow
the When
rate.
flow This
rate is
the flow
means rate
that is
the 32.5 mL/min,
comprehensive the thermal
performance enhancement
of the TFMCHS factor can
has reach
been
32.5 mL/min, the thermal enhancement factor can reach 1.26. Therefore, for chip cooling, 1.26. Therefore,
improved. When
for
the chip
flowcooling,
TFMCHS the TFMCHS
rate is more
32.5 mL/min,
economicalis more
the economical
thermal
and and effective.
enhancement
effective. factor can reach 1.26. Therefore,
for chip cooling, the TFMCHS is more economical and effective.

Figure
Figure 13. Relationship
Relationship between
between thermal
thermal enhancement
enhancement factor and flow
flow rate for TFMCHS.
Figure 13. Relationship between thermal enhancement factor and flow rate for TFMCHS.
5. Conclusions
5. Conclusions
The heat
The heat transfer
5. Conclusions transfer characteristics
characteristics of of TFMCHSs
TFMCHSs were were studied
studied through
through experiments
experiments andand
numerical
numerical simulations,
simulations, and the fluid
and the fluid flow characteristics
flow characteristics of RMCHSs were
of through
RMCHSs studied through
were studied
The heat transfer characteristics of TFMCHSs were studied experiments and
numerical
through simulations.
numerical The conclusions
simulations. The are as follows:
conclusions are as follows:
numerical simulations, and the fluid flow characteristics of RMCHSs were studied
1.
1. Thenumerical
The
through average and
average and maximumThe
maximum
simulations. temperatures
temperatures
conclusions ofare
of theas
the bottom
bo surfaces of
om surfaces
follows: of two
two types
types of
of heat
heat
sink at different power levels were experimentally measured. The temperature of
1. sink
The at different
average
TFMCHSs isand
power levels
maximum
significantly lower
were experimentally
temperatures
than thatofofthe bo om
RMCHSs.
measured.
surfaces
And as the
The
of twotemperature
powertypes of
of heat
increases,
TFMCHSs
sink is significantly
at different power lowerwere
levels thanexperimentally
that of RMCHSs. And as the
measured. Thepower increases,
temperature of
the heat dissipation effect of TFMCHSs becomes stronger.
the heat dissipation
TFMCHSs is effect of
significantly TFMCHSs
lower than becomes
that of stronger.
RMCHSs. And as the power increases,
2. Compared to RMCHSs, TFMCHSs have the highest friction loss, mainly due to the
2. Compared
the heat to RMCHSs,
dissipation TFMCHSs have the highest friction loss, mainly due to the
direct impact of fluideffect
on the ofribTFMCHSs
structure.becomes stronger.
The increase in flow area caused by grooves
direct
2. Compared impact of fluid
to RMCHSs, on the rib
TFMCHSs structure. The increase
have the highest frictionin flow loss,
area caused
mainlyby duegrooves
to the
has little effect on friction loss.
has li
direct le effect
impact ofon friction
fluid on loss.
the rib structure. The increase in flow area caused by grooves
3. The combination of grooves and ribs is beneficial for enhancing heat transfer, mainly
3. The
has combination onoffriction
grooves and ribs is beneficial for enhancing heat transfer, mainly
duelito letheeffect
interruption andloss.
redevelopment of the velocity boundary layer and thermal
due
3. The to the
combination interruption
of grooves and redevelopment of for
theenhancing
velocity boundary layer and
boundary layer, strong fluid and ribs is beneficial
disturbance, and the mixing effect ofheat transfer,
internal mainly
eddies. The
due to the interruption
trapezoidal rib causes theand redevelopment
mainstream to flow of theS-shape,
in an velocitythereby
boundary layer and
impacting the
upper and lower wall boundary layers and enhancing heat transfer. The fan-shaped
groove increases the contact area between fluid and solid in the microchannel while
Micromachines 2024, 15, 713 13 of 14

creating a vortex zone that weakens heat conduction within the fluid but enhances
convective heat transfer. This enables sufficient mixing of fluids in the channel.
4. The comprehensive performance can be evaluated using the thermal enhancement
coefficient. When the inlet flow rate is 32.5 mL/min, the thermal enhancement
factor reaches 1.26. Therefore, for chip cooling, the TFMCHS is more effective
and economical.

Author Contributions: Conceptualization, L.J. and J.W.; data curation, L.J., X.H., Y.C. and G.Y.;
writing—original draft preparation, L.J. and J.W.; writing, L.J.; supervision, Z.Z. and J.Q.; project
administration, C.C., X.P. and M.C. All authors have read and agreed to the published version of
the manuscript.
Funding: This work is supported by the Zhejiang Provincial Natural Science Foundation of China
(LTGG23F010001) and the Key Scientific and Technological Projects of Wenzhou City (ZG2022013).
Data Availability Statement: The original contributions presented in the study are included in the
article, further inquiries can be directed to the corresponding authors.
Conflicts of Interest: Author Lufan Jin was employed by the company Penta Laser (Zhejiang) Co.,
Ltd. The remaining authors declare that the research was conducted in the absence of any commercial
or financial relationships that could be construed as a potential conflict of interest.

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