Microchannels and Minichannels - 2004
June 17-19, 2004, Rochester, New York, USA
Copyright © 2004 by ASME
ICMM2004 – xxxx
OPTIMIZATION OF MICROCHANNEL GEOMETRY FOR DIRECT CHIP COOLING
USING SINGLE PHASE HEAT TRANSFER
Harshal R. Upadhye1 and Satish G. Kandlikar2
Thermal Analysis and Microfluidics Laboratory,
Mechanical Engineering Department,
Rochester Institute of Technology, Rochester NY 14623.
1
[email protected]
2
[email protected]
ABSTRACT
Direct cooling of an electronic chip of 25mm x 25mm
in size is analyzed as a function of channel geometry for
single-phase flow of water through small hydraulic
diameters. Fully developed laminar flow is considered with
both constant wall temperature and constant channel wall
heat flux boundary conditions. The effect of channel
dimensions on the pressure drop, the outlet temperature of
the cooling fluid and the heat transfer rate are presented.
The results indicate that a narrow and deep channel results
in improved heat transfer performance for a given pressure
drop constraint.
INTRODUCTION
One of the most important parameters affecting the
performance of silicon integrated circuits is the circuit
temperature. Maintaining the circuit temperature below
certain limit of about 850 C is very important. Air cooling
has been the most commonly used cooling method for
majority of chips used in computer applications. Current
trends indicate that as the fabrication technology improves,
silicon chips with millions of devices can be fabricated.
These trends point to very high heat fluxes in chip modules.
To maintain temperature of the circuit in such a scenario is a
daunting task and fabrication of such devices might be
limited by their cooling capability.
Direct Chip cooling with microchannels or
minichannels is a good solution for cooling of such devices.
These chips have machined microchannels through which
cooling liquid such as water is circulated. The cooling
water removes heat by single-phase forced convection. The
cooling passages within these chips can be fabricated along
with the circuit components, or as a follow-on process.
Liquid cooling, especially with water, will give additional
benefits of superior thermal properties.
The design and optimization of such microchannel
passages in a direct heat sink is important from an
operational standpoint. Pressure drop considerations will
further determine the pumping power required and the
operating pressure to which the chips will be subjected. The
microchannels must be optimized using the range of flow
channel dimensions that can be fabricated. Fabrication
methods will also play a major role in the overall design of
the direct heat sink. The current work consists of studying
the effects of varying channel dimensions on pressure drop
and the heat transfer characteristics of such a chip for a
given heat duty. Basic equations are presented and the
performance characteristics are obtained for a specific chip
size of 25mm x 25mm as an example.
Traditionally, air has been the preferred fluid for
cooling electronic components, either a single chip or an
entire printed circuit board consisting of numerous chips.
With heat fluxes going beyond 100W/cm2, air cooling may
no longer be possible. The low heat transfer coefficient
coupled with a low specific heat makes air as a poor choice
in microchannel flow passages. Liquids, especially water,
as compared to air or gases, offer a very good alternative
due to their higher heat transfer coefficient, higher specific
heat and lower specific volume compared to air. Water in
particular is highly desirable because of its thermal
properties as well as other characteristics such as low cost
and extensive experience in other systems.
Figure 1 shows a schematic of the microchannel
geometry investigated in the present study. Microchannels
are machined or etched in silicon substrate and closed by a
cover plate on top to form flow passages. Cooling liquid
flows through these channels. As is shown later, such a
configuration is capable dissipating heat fluxes in excess of
100W/cm2. The microchannel flow geometry offers large
surface area for heat transfer and a high convective heat
transfer coefficient. But the small channel dimensions result
in a very high pressure drop. The objective of this study is
to investigate the thermal and pressure drop characteristics
of these passages in an attempt toward obtaining optimized
channel dimensions to match the given heat transfer and
pressure drop requirement.
important parameter dictating the performance of a
microchannel heat sink.
Knight et al. (1992) presented the governing equations
for fluid dynamics and heat transfer in the heat sink in a
dimensionless form and then presented a scheme for solving
these equations. Solution procedure for both laminar flow
and turbulent flow through the channels was presented.
ANALYSIS
A chip with 25mm × 25mm active cooling surface area
covered with microchannels machined on one side and heat
dissipating devices on the other side, as shown in Fig. 1, is
considered.
Cover plate
b
LITERATURE REVIEW
L
a
W
Figure 1 Microchannel’s machined in Silicon.
The dimensions of the microchannels, width a and
depth b are the main parameters of interest. The length of
the channels L is fixed by the geometry of the chip for
which the cooling passages are designed. The channel
width a will decide how many channels can be fitted. The
wall thickness s is assumed to be 35µm, which represents
the minimum thickness that can be easily manufactured with
current fabrication technology.
1
0.95
Fin Efficiency
Microchannel heat sink concept was first introduced by
Tuckerman and Pease (1981).
The heat sink they
manufactured was able to dissipate 790W/cm2. Phillips,
(1987) presented a detailed analysis of the forced
convection, liquid cooled microchannel heat sinks. Recent
work includes work by Bergles et al. (2003), Qu and
Mudawar (2002) and by Ryu et al.(2002).
Bergles et al. (2003) discussed the design
considerations for small diameter internal flow channels. A
design problem with given heat rate and chip dimensions
was studied in detail, the main focus being on pumping
power and material thickness required. They concluded that
cooling systems having smaller diameter channels result in a
compact system and generally does not impose a larger
pumping power requirement. Fin effects were found to be
significant in designs where thin solid sections were
utilized.
Qu and Mudawar (2002) tested microchannel heat sink
1cm wide and 4.8cm long. The microchannels machined in
the heat sink were 231µm wide and 712µm deep. Apart
from this they also presented numerical analysis for a unit
cell containing a single microchannel and surrounding solid.
The measured pressure drop across the channels and
temperature distribution showed good agreement with the
numerical results. They concluded that the conventional
Navier-Stokes and energy equations remain valid for
predicting fluid flow and heat transfer characteristics in
microchannels.
Ryu et al. (2002) performed numerical optimization of
thermal performance of microchannel heat sinks. The
objective of the optimization was to minimize thermal
resistance. They varied the channel width, channel depth
and the fin thickness to come up with an optimized solution.
Their observation was that the channel width is the most
s
0.9
0.85
0.8
0.75
0.7
0
20
40
60
Fin Thickness (microns)
80
Figure 2 Fin efficiency for various fin thickness for a
channel depth of 300µm.
The number of channels that can be accommodated in given
width is given by
W
n=
a+s
h = Nu
(1)
From Eq. (1) we can see that the number of channels that
can be fitted in a given width is dependent on channel width
a and the spacing s. The spacing s is fixed to 35µm, as a
result the channel width is the deciding factor for number of
channels that can be fixed in the given width W.
Figure 2 shows the fin efficiency as a function of the fin
thickness for a maximum fin height (channel depth) of 300
µm. A thick fin will have a better fin efficiency, but the
number of channels decreases with an increase in the fin
thickness, and the area available for heat transfer also
decreases. With a fin thickness of 35 µm, the fin efficiency
is above 90 percent. Although including fin thickness as a
variable would lead to further refinements, the fabrication
limit is believed to be the limiting factor.
The analysis is done considering two boundary
conditions – (i) constant channel wall temperature and (ii) a
constant heat flux boundary condition. In both cases heat
transfer from the top cover plate is neglected. The flow
through the channel is assumed to be laminar and fully
developed. Water is used as a coolant having constant
properties and the heat sink material is silicon. The
hydraulic diameter is calculated from the channel
dimensions:
4ab
d=
2( a + b )
From the definition of Nusselt number
(2)
b
a
ηf =
Constant Channel Wall Temperature Case
The constant temperature Ts of the channel walls is
assumed to be the design temperature that should not be
exceeded in the unit. In case of electronic circuits it can be
the maximum allowable temperature in the circuit. In this
study we have assumed it to be 358 K. As a result the
maximum water temperature at the outlet theoretically
possible will be 358K. Water temperature at the inlet Tin is
300K.
The entrance region effects are neglected and the
Nusselt number is assumed to be constant (single-phase
laminar flow). The value of Nusselt number is obtained
from Kakac et al. (1987). The Nusselt number is for
circumferentially and axially constant wall temperature at
all four walls of a rectangular channel.
Nu = 7.541(1 − 2.610α + 4.970α 2
− 5.119α 3 + 2.702α 4 − 0.548α 5 )
tanh( mb)
mb
(4)
(6)
where
m=
hP
k f Ac
(7)
The perimeter of the rectangular fin is assumed to be twice
the passage length.
P = 2L
(8)
The cross section area of the fin is
(9)
Ac = Ls
Substituting Eqs. (8) and (9) into the expression for m in Eq.
(7),
m=
(3)
(5)
where k is the thermal conductivity of the fluid. The walls
separating the channels can be treated as rectangular fins of
uniform cross-section. From Incropera and DeWitt (2002)
the fin efficiency is given as
The channel aspect ratio is given by
α =
k
d
2h
kf s
(10)
An iterative technique is followed to calculate the mass flow
rate and the water outlet temperature.
The initial
assumption is made that the liquid enters the microchannels
at temperature Tin and leaves the microchannels at a
temperature Tout =Ts. With this assumption and knowing the
heat rate, mass flow rate required can be found out.
•
m=
Q
(11)
C p (Tout − Tin )
& can now be used to calculate Tout by rearranging the
This m
logarithmic mean temperature difference equation.
− hAn
•
Tout = Ts − (Ts − Tout )e
mCp
(12)
where the product hA is
hA = haL + 2 Lbhη f
(13)
The Tout obtained from Eq.(12) is compared with the
assumed Tout and then the Tout is adjusted. The process is
iterated until Tout value is converged. Knowing Tout the mass
flow rate required is calculated from Eq.(11). The mass
in Eq.(5) the value of convective heat transfer coefficient h
can be found out. The maximum allowable surface
temperature is again a constraint here.
The outlet
temperature of the fluid is given by
•
flow rate per channel
m c is found by the total mass flow
Tout = Ts −
•
m by the number of channels n. The velocity of fluid
through each channel is
•
V=
mc
ρab
(14)
and the Reynolds number for the flow is
Re =
Vd
ν
2CLρV 2
Re d
(15)
(16)
where
C = f Re
(17)
The value of C from Kakac et al. (1987) is
C = 24(1 − 1.3553α + 1.9467α 2
− 1.7012α 3 + 0.9564α 4 − 0.2537α 5 )
(22)
Once the outlet temperature is known we can easily find out
the mass flow rate required from Eq. (11). Equations (14)(16) give us the flow velocity, the Reynolds number and the
pressure drop through the channels.
RESULTS AND DISCUSSION
The pressure drop across the channels is given by the
following equation –
∆p =
q"
h
(18)
The fluid outlet temperature, flow Reynolds number,
the mass flow rate and the pressure drop in a direct heat sink
for a given heat rate are calculated for various channel
dimensions. The effect of geometrical parameters on the
channel heat transfer and pressure drop performance is
discussed in the following sections.
Constant Channel Wall Temperature
As the channel width changes for a given thickness, the
aspect ratio also changes. This affects the Nusselt number,
as seen from Eq. (4). Figure 3 shows the variation of
Nusselt number with channel aspect ratio for both constant
heat flux and constant channel wall temperature boundary
conditions. At aspect ratio of 1 (i.e. a square channel) the
Nu is lowest. As the channel gets more skewed, Nu
increases.
8
Constant Heat Flux Case
7
In constant heat flux condition the wall heat flux is
found by dividing the channel wall area by the desired heat
rate.
Q
Aw
(19)
2
(20)
− 2.4765α 3 + 1.0578α 4 − 0.1861α 5 )
1
0
The Nusselt number from Kakac et al (1987) is
Nu = 8.235(1 − 2.0421α + 3.0853α 2
4
3
The area of wall Aw is
Aw = (2η f b + a ) L.n
5
Nu
q" =
Constant heat flux
Constant channel wall temperature
6
0
0.25
0.5
0.75
1
Aspect Ratio
(21)
The Nusselt number given by the above equation is valid for
circumferentially constant wall temperature and axially
constant wall heat flux for channels with rectangular
geometry. From the definition of the Nusselt number given
Figure 3 Variation of Nusselt number with aspect ratio.
The effect of channel width on heat transfer coefficient
is result of the changing Nusselt number with channel width
as well the change in the hydraulic diameter. The combined
effect of these two parameters on h is plotted in Figure 4. It
is seen that the heat transfer coefficient goes through a
1
0.8
0.6
T*
minimum at a channel width somewhat larger than that
corresponding to an aspect ratio of 1. The heat transfer
coefficient decreases with the channel width up to this
minimum value, before rising slowly for larger channel
widths. For the deepest channel of 300 µm plotted in Fig. 4,
a channel width below about 100 µm results in a significant
improvement in the heat transfer coefficient. However, the
heat transfer performance needs to be considered in
conjunction with the associated pressure drop. The effect of
channel width on the outlet water temperature is considered
next.
0.4
Channel Depth (microns)
50
100
150
200
250
300
0.2
40000
Channel Depth (microns)
50
100
150
200
250
300
30000
2
h (W/m K)
35000
0
25000
100
200
300
Channel Width (microns)
400
Figure 5 Dimensionless Coolant Outlet Temperatures
(Constant Channel Wall Temperature, Chip heat flux
100W/cm2)
20000
15000
10000
100
200
300
Channel Width (microns)
400
Figure 4 Variation of h with channel width for various
channel Depths. (Constant Surface Temperature)
Figure 5 shows the variation of T* as a function of
channel width, for various channel depths. The
dimensionless temperature is defined as
T* =
Tout − Tin
Ts − Tin
As seen from Fig. 6, the pressure drop for a very narrow
channel is high, but it decreases with increasing depth. Still
there exist some better solutions to the problem. A slightly
wider channel and a deeper channel offer less pressure drop.
For example – in Fig. 6, at a channel width of 60 µm and
depth of 150 µm the pressure drop is 62100 Pa. An increase
in width to about 120 µm results in pressure drop of 21100
Pa for the same depth. Increase in depth also lowers the
pressure drop. At 120 µm channel width and channel depth
of 300 µm the pressure drop is 6500 Pa.
As the chip heat flux is increased, the mass flow rate
required for taking out the heat increases. As a result the
(23)
300000
Channel Depth (microns)
50
100
150
200
250
300
2
The outlet temperature is very close to the surface
temperature for a narrow and deeper channel. As the
channel becomes wide, the outlet temperature decreases.
The wider channel therefore causes two problems. As the
outlet temperature decreases the mass flow rate required to
carry away the specified amount of heat, increases. Another
factor is the number of channels. Since the width of each
channel is large, the total number of channels that can be
fitted decreases. As a result the mass flow through each
channel increases. Therefore pressure drop increases.
Figure 6 shows the pressure drop values for various channel
dimensions for a constant channel wall temperature case
with a chip heat flux of 100 W/cm2. Only the frictional
pressure drop considering fully developed flow is
considered here. The entrance region effect and the inlet
and outlet losses will affect the pressure drop characteristics
somewhat, but their effect is expected to be relatively small
compared to the frictional pressure drop in the channel.
Pressure Drop (N/m )
250000
200000
150000
100000
50000
0
100
200
300
Channel Width (microns)
400
Figure 6 Pressure Drop for Constant Channel Wall
Temperature
Reynolds number and the pressure drop also increase. In
Fig. 7, pressure drop is plotted against channel width for a
chip heat flux of 200 W/cm2. The pressure drop has
increased for all the channel configurations considered.
300000
Channel Depth (microns)
50
100
150
200
250
300
Pressure Drop (N/m2)
250000
predicted by using constant temperature boundary condition.
Figure 9 shows the variation of pressure drop as a function
of channel geometry for a constant heat flux condition. The
pressure drop for a 50 µm deep channel, from Fig. 9, is far
more as compared to deeper channels for the same width.
300000
250000
Pressure Drop (N/m2 )
200000
200000
150000
Channel Depth (microns)
150000
100000
50
100
150
200
250
300
100000
50000
0
50
75
100
125
150
Channel Width (microns)
50000
0
Figure 7 Pressure Drop for Constant Channel Wall
Temperature
For an assumed maximum allowable pressure drop of
30000 Pa, a 50 µm deep channel does not provide us with an
acceptable solution. Also channels having width beyond
125 µm do not offer practical solution because of the high
pressure drop except for channels with 250 µm and 300 µm
width.
Constant Heat Flux
For the constant heat flux boundary condition, h values
are shown in Fig. 8. The values are slightly higher than the h
values for constant surface temperature boundary condition.
100
200
300
Channel Width (microns)
400
Figure 9 Pressure Drop for Constant Heat Flux. (Chip heat
flux 100W/cm2)
As in the constant surface temperature case, a deeper
channel offers a lesser pressure drop. Hence deeper
channels should be employed. The width of the channel has
significant effect on the pressure drop. A very narrow
channel offers a relatively higher pressure drop than a wider
channel. But beyond a certain critical value, which depends
on the chip heat flux and the channel depth, the pressure
drop increases.
CONCLUSIONS
1.
45000
40000
Channel Width (microns)
50
100
150
200
250
300
30000
2
h (W/m K)
35000
2.
25000
20000
3.
15000
10000
5000
0
4.
100
200
300
Channel Width (microns)
400
5.
Figure 8 Variation of h with channel width for various
channel Depths. (Constant Heat Flux)
The predicted pressure drop for the constant heat flux
boundary condition is slightly higher than the pressure drop
Heat transfer and pressure drop characteristics for
single phase flow in direct heat sinks are analyzed.
The results are presented for a chip with an active
cooling area of 25mm x 25mm.
The fin effect of channel walls separating adjacent
flow channels was analyzed. A wall thickness of
35 µm resulted in fin efficiencies above 90 percent.
This wall thickness was the minimum that is
recommended from fabrication point of view.
Pressure drop, an important parameter for
microchannel heat sink design is a strong function
of the channel geometry.
From both heat transfer and pressure drop
perspectives, a narrow and a deep channel is better
than having a wide and shallow channel.
For a constant wall temperature case and for a chip
heat flux of 100W/cm2 we can definitely narrow
down on particular channel dimensions which will
give a lower pressure drop. Channel width in
between 150µm and 250µm definitely seems to be
a better choice with channel depth of 250µm.
6.
Channel width larger or smaller than this range
increases the pressure drop. Increasing the channel
depth any further does not substantially reduce the
pressure drop. The constant heat flux condition
also indicates towards a similar trend with a slight
difference in pressure drop values.
From the above analysis we can identify a region
of possible channel configurations that can help in
designing microchannels. The current work only
considers a chip of 25mm × 25mm.
The
methodology and equations presented here can be
applied to other chip sizes in arriving at the
desirable channel configurations.
Future work is planned to include the effects of entrance
region and entry and exit losses on pressure drop.
ACKNOWLEDGEMENTS
The work was carried out at the Thermal Analysis and
Microfluidics Laboratory at RIT.
NOMENCLATURE
Ac
Aw
a
b
C
Cp
d
f
h
k
kf
L
m
cross sectional area of fin
area offered by the channel walls for heat transfer
channel width
channel depth
constant defined by Eq. 17
specific heat at constant pressure
hydraulic diameter of the channel
fully developed fanning friction factor
heat transfer coefficient
thermal conductivity of water
thermal conductivity of fin material (silicon)
channel length
fin efficiency constant defined by Eq. 10
•
m
mass flow rate
•
mc
n
Nu
P
Q
q”
Re
s
mass flow rate through single channel
number of channels that can be fitted in heat sink
Nusselt number
perimeter of channel
heat rate
heat flux
Reynolds number
thickness of the fin
T*
Tout
Tin
Ts
V
W
dimensionless temperature
temperature at the outlet of the microchannels
temperature at inlet of the microchannels
surface temperature of the heat sink
fluid velocity through the microchannel
width of the chip to be cooled
Greek Symbols
α
ηf
ρ
ν
channel aspect ratio
fin efficiency
density
kinematic viscosity
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