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Extending the Heat Flux Limit with Enhanced Microchannels in
Direct Single Phase Cooling of Computer Chips
Satish G. Kandlikar1 and Harshal R. Upadhye
Thermal Analysis and Microfluidics Laboratory,
Mechanical Engineering Department,
Rochester Institute of Technology, Rochester, NY 14623
1
[email protected]
Abstract
The high heat transfer coefficients in microchannels are
attractive for direct cooling of computer chips requiring high
heat-flux removal. However, the high heat removal capability
of microchannels is associated with a severe pressure drop
penalty.
Channel size optimization therefore becomes
necessary in selecting an appropriate channel geometry
configuration. As the heat flux increases beyond about 2
MW/m2, the heat transfer and pressure drop characteristics of
the plain channels dictate the use of turbulent flow through the
channels, which suffers from an excessive pressure drop
penalty.
It therefore becomes essential to incorporate
enhancement features in the microchannels and multiple
passes with shorter flow lengths to provide the desired
solution. Results obtained from a theoretical analysis are
presented as parametric plots for the heat transfer and pressure
drop performance of a 10×10-3 m × 10×10-3 m (10 mm x 10
mm) silicon chip incorporating plain microchannels. The
enhanced microchannels with offset strip fins in single-pass
and split-flow arrangements are also investigated. The results
show that the enhanced structures are capable of dissipating
heat fluxes extending beyond 3 MW/m2 using water as the
coolant in a split-flow arrangement with a core pressure drop
of around 35 kPa.
Keywords
Microchannels, Electronics Cooling, Channel Geometry,
Pressure Drop, Optimization.
Nomenclature
Ac
cross-sectional area of fin, m2
Adiv
area offered by each division for heat transfer, m2
effective channel area for heat transfer considering
Aw
the fin efficiency effects, m2
a
channel width, m
b
channel depth, m
Cp
specific heat at constant pressure, J/kg-°C
d
hydraulic diameter of the channels, m
apparent friction factor
fapp
gc
acceleration due to gravity, m/s2
h
heat transfer coefficient, W/m2-°C
k
thermal conductivity of water, W/m-°C
kf
thermal conductivity of the fin material (silicon),
W/m-°C
L
channel length, m
m
fin efficiency constant defined by Eq. (6)
•
mc
n
mass flow rate through a single channel, kg/s
number of parallel microchannels
0-7803-8985-9/05/$20.00 ©2005 IEEE-
Nu
P
Pr
Q
Qdiv
q”
Re
s
Tb
Tout
Tin
Ts
um
W
x
Nusselt number
perimeter of channel, m
Prandtl number
heat rate, W
heat dissipated per element, W
heat flux based on the base area, W/m2
Reynolds number
thickness of the fin, m
Fluid bulk temperature, °C
temperature at the outlet of the microchannels, °C
temperature at inlet of the microchannels, °C
surface temperature at the base of the heat sink, °C
mean fluid velocity through the microchannel, m/s
width of the chip area being cooled, m
axial distance from the entrance of the channel, m
x+
x*
hydrodynamic entry length
thermal entry length
Greek Symbols
αc
channel aspect ratio, a/b
αf
fin aspect ratio, s/b
∆p
core frictional pressure
microchannel, Pa
ηf
fin efficiency
µ
dynamic viscosity, N-s/m2
ρ
drop
across
the
density, kg/m3
1. Introduction
Thermal management of electronic devices is one of the
important aspects of electronics packaging. Air has been the
fluid of choice in such cooling applications. With the rapid
advances in microelectronics technology, the volume
occupied by the devices has reduced considerably. But with
increasing demand for faster and more efficient processors,
the number of circuits and the power dissipation per unit
volume has also increased. The combined effect of this has
lead to an increase in the heat flux that needs to be removed
from the chip surfaces. There is also a desire to reduce the
junction temperature, as the increased temperature adversely
affects the electrical performance of the devices and reduces
their reliability. Possible damage involves junction fatigue,
changes in electrical parameters and thermal runaway.
Direct cooling of chips offers a practical solution to the
heat dissipation problem. In such systems, water (with
possible addition of antifreeze to allow cold weather
shipments) is circulated in microchannels fabricated on the
chip substrate. Such systems need to be carefully designed to
meet the cooling requirements under the operational
constraints. Pressure drop is an important parameter which
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governs the pump selection, required pumping power, and the
maximum pressure to which the chip is subjected. In the
present work, an analysis is carried out to optimize the
channel configuration that yields a minimum pressure drop for
a given heat load. The constraints for the optimization are the
maximum allowable chip temperature, heat dissipated,
pressure drop for the fluid stream flowing through the
channels, and the manufacturing constraints.
The
manufacturing constraints are not addressed in the present
work. The analysis is extended to an enhanced microchannel
incorporating offset strip-fin configuration in single-pass and
split-flow arrangements.
2. Literature Review
Microchannel heat sink concept was first introduced by
Tuckerman and Pease [1]. The heat sink they manufactured
was able to dissipate 7.9 MW/m2 with a maximum substrate
temperature rise of 71 °C and a pressure drop of 186 kPa.
Phillips [2] presented a detailed analysis of the forced
convection liquid cooled microchannel heat sinks. Recent
investigations include the work by Upadhye and Kandlikar
[3], Kandlikar and Grande [4], Steinke and Kandlikar [5],
Bergles et al. [6], Qu and Mudawar [7], and Ryu et al. [8].
Upadhye and Kandlikar [3] presented an analysis for
optimizing the microchannel geometry for direct chip cooling
using single-phase heat transfer with water as the working
fluid. A chip with an active cooling area of 25.4×10-3 m ×
25.4×10-3 m (25.4 mm × 25.4 mm) was analyzed. A fully
developed laminar flow with constant channel wall
temperature or constant heat flux condition was considered.
The analysis showed that a narrow and deep channel is better
than having a wide and shallow channel from the heat transfer
and pressure drop perspectives. For the chip size considered,
and with a heat load of 1 MW/m2, a channel width between
150×10-6 m (150 µm) and 250×10-6 m (250 µm) was found to
result in the lowest pressure drop for a channel depth of
250×10-6 m (250 µm).
Kandlikar and Grande [4] discussed the cooling limits of
the plain rectangular microchannels with water cooling for
high heat flux dissipation and illustrated the need for
enhanced microchannels. Steinke and Kandlikar [5] carried
out an extensive review of conventional single-phase heat
transfer enhancement techniques. Several passive and active
enhancement techniques for minichannels and microchannels
were discussed. Some of their proposed enhancement
techniques include fluid additives, secondary flows,
vibrations, and flow pulsations.
Bergles et al. [6] discussed the design considerations for
small diameter internal flow channels. A design problem with
a given heat rate and chip dimensions was studied in detail,
the main focus being on pumping power and material
thickness requirement. They concluded that cooling systems
having smaller diameter channels result in a compact system
and generally not impose a larger pumping power
requirement.
Qu and Mudawar [7] tested microchannel heat sinks
10×10-3 m (10 mm) in width and 48×10-3 m (48 mm) long.
The microchannels machined in the heat sink were 231×10-6
m (231 µm) wide and 712×10-6 m (712 µm) deep. They also
presented a numerical analysis for a unit cell containing a
Kandlikar,et.al, Extending the Heat Flux Limit with …..
single microchannel and the surrounding heat sink material.
The measured pressure drop across the channels and the
temperature distribution showed good agreement with their
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. [8] performed a numerical optimization of
thermal performance of microchannel heat sinks. The
objective of the optimization was to minimize the convective
thermal resistance of the fluid. They varied the channel
width, channel depth, and fin thickness to arrive at an
optimized solution. They observed that the channel width is
the most important parameter governing the performance of a
microchannel heat sink.
Knight et al. [9] derived the governing equations for fluid
flow and heat transfer in a microchannel heat sink in a
dimensionless form and presented a scheme for solving these
equations. Solution procedures for both laminar flow and
turbulent flow were presented.
3. Objectives of the Present Work
The objectives of the present work are:
1. Develop an algorithm to analyze the heat transfer and
pressure drop characteristics of a given chip cooled with plain
and enhanced microchannels by incorporating the developing
flow effects.
2. Present the results in a parametric form to identify the
optimum geometrical configuration that meets the cooling
requirements and results in the lowest core frictional pressure
drop.
3. Study the effects of enhanced microchannels
incorporating the offset strip-fins.
4. Study the effects on incorporating a split-flow
arrangement with enhanced microchannels.
4. Assumptions
The heat transfer and pressure drop analysis are developed
under the following major assumptions
1.
2.
3.
4.
5.
Constant heat flux on the channel walls – The boundary
condition on the microchannel walls is assumed to be
axially constant wall heat flux with circumferentially
constant wall temperature. The heat flux along the length
of the channel is constant, while the wall temperature
varies along the channel length in the flow direction.
Heat losses from the cover plate are neglected – The
cover plate on the microchannels is assumed to be
insulated and hence the fin tip can be considered to be
under adiabatic tip boundary condition. The solution
obtained will be on the conservative side by neglecting the
heat losses from the cover plate.
The coolant flow is steady and incompressible – Since the
working fluid is water and the maximum pressure drop is
generally less than 100 kPa, the incompressible flow
assumption should be valid.
Uniform heat flux over the active chip surface area is
assumed with no local hotspots.
Constant properties are assumed for both the cooling
fluid (water) and the wall material (silicon).
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6.
A single-pass arrangement with plain microchannels is
considered. The analysis is later modified to analyze
enhanced microchannels and the split-flow arrangement.
5. Analysis
A chip with L=10×10-3 m (10 mm) and W=10×10-3 m (10
mm) active cooling surface area and a microchannel depth b =
200×10-6 m (200 µm) is considered as shown in Fig. 1.
Microchannels are fabricated on one side and the heat
dissipating devices are placed on the other side of the chip.
The maximum temperature of the channel walls is to be
maintained below 360 K with an inlet water temperature of
300 K. The analysis uses the specified channel depth (as
governed by the manufacturing constraints) and does not
include the silicon thermal resistance between the channel
bottom wall and the chip surface receiving heat. The analysis
can however be extended to include this resistance if desired.
Similarly, other chip geometries, channel depths, and fluid
inlet temperatures can be readily handled.
Cover plate
The fin aspect ratio
αf =
L
W
Fig. 1 Microchannel geometry
The dimensions of the microchannels, width a and fin
thickness s, are the main parameters of interest. The length of
the channels L is fixed by the prescribed geometry of the chip
for which the cooling passages are designed. The channel
depth b is assumed to be known. This is due to the fact that
the channel depth is governed by the manufacturing process
and the chip configuration. The channel width a and the fin
thickness s together will determine the number of parallel
channels that can be accommodated. The wall thickness s has
a lower limit of 30×10-6 m (30 µm), which represents the
minimum thickness that can be readily manufactured with the
current microfabrication technology.
In an effort to arrive at a common terminology in the
microchannel heat sink application, three non-dimensional
parameters – channel aspect ratio, fin aspect ratio and fin
spacing ratio – are defined and described below.
The channel aspect ratio
αc
is defined as the ratio of the
a
b
from 0 to 1 ( 0 < α c ≤ 1 and 0 < α f ≤ 1 ).
(1)
αc
αf
Although α c
and
is
>1
can be employed, this configuration is of little practical
interest as narrow and deep channels (with α c <1) were
shown to be more desirable for high heat flux dissipation,
Upadhye and Kandlikar [3]. They also showed that the fin
aspect ratio of α f >1 does not yield any benefits with the
silicon substrate from fin efficiency considerations.
The ratio of the fin aspect ratio to the channel aspect ratio
plays an important role in the heat transfer analysis. It is
defined as the fin spacing ratio β and is given by:
αf s
=
αc a
(3)
The practical range for the fin spacing ratio is also β <1
because utilizing channels that are smaller than the fin
thickness is not desirable from overall heat transfer and
pressure drop considerations, and due to the danger of
potential blockage of the channels with particulates.
The channel width, chip width, number of channels, and
the fin aspect ratio are related by the following equation.
a=
W
n + (n + 1) β
The channel aspect ratio
(4)
αc
is an important parameter
because the friction factor and the Nusselt number in the
laminar flow region are both dependent on this ratio. The
Nusselt number and friction factor information is derived
from Kakac et al. [10]. For a particular Re and α c , the fappRe
values are obtained from the appropriate charts.
The constant heat flux (approximation, due to fin effects)
on the channel walls is found by dividing the total design heat
load by the available wall surface area. The effective channel
wall heat transfer surface area, considering the fin efficiency
effects, is given by:
where
ηf
(5)
is the fin efficiency.
The fin efficiency for a
rectangular, constant cross-sectional area fin under adiabatic
fin tip boundary condition is given by:
ηf =
Kandlikar,et.al, Extending the Heat Flux Limit with …..
(2)
Aw = (2η f b + a ) Ln
channel width to the channel depth. It is given by:
αc =
s
b
The practical range of interest for both
b
a
is defined as the ratio of the fin
thickness to the fin height. It is given by:
β=
s
αf
tanh mb
mb
(6)
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The fin parameter m is given by:
x+ =
hP
k f Ac
m=
(7)
where h is the heat transfer coefficient, P is the perimeter, and
Ac is the fin cross-sectional area. The perimeter of the fin in
contact with the fluid is given by:
P = 2L
(8)
The cross-sectional area of the fin
Ac = sL
(9)
Substituting the perimeter and the cross-sectional area from
Eqs. (7) and (8) into Eq. (6), m reduces to
2h
kfs
m=
(10)
The heat transfer coefficient h is calculated from the Nusselt
number.
h = Nu
k
d
(14)
where x is the axial distance from the entrance along the
channel length.
Similarly, the local Nusselt numbers for thermally
developing flows are obtained from Kakac et al. [10]. The
data is presented in a tabular form for various values channel
aspect ratio α c and x* given by:
x* =
Ac is given by:
xd
Re
xd
Re Pr
(15)
7. Solution Procedure
As mentioned in Section 5, the channel depth is decided
by the manufacturing process. For the results presented in
this paper, a channel depth of 200×10-6 m (200 µm) is
considered. The minimum fin thickness is assumed to be
30×10-6 m (30 µm). The channel length is 10×10-3 m (10
mm). Since the non-dimensional lengths x+ and x* are
functions of the axial distance from the entrance, the channel
is divided into smaller divisions. The axial distance of each
division from the channel entrance is the distance of the center
of that particular division from the entrance. This is shown in
Fig. 2.
(11)
where h is the heat transfer coefficient, and d is the hydraulic
diameter given by the following equation for the rectangular
microchannel shown in Fig. 1:
d=
4ab
2(a + b )
(12)
The Nusselt number and friction factor information is
obtained from the literature in the developing flow region.
Using this information, the microchannels are analyzed as
heat exchangers. The details of the heat transfer and pressure
drop calculations and the heat exchanger analysis are
described in the following sections.
6. Nusselt Number and Friction Factor in the Laminar
Developing Region
Several investigators have studied the laminar developing
flow in rectangular ducts. The developing flow effects are
represented by an apparent friction factor between the inlet to
a duct and the location of interest. The frictional pressure
drop for fluid flow through a channel of length L is given by:
∆p =
2( f app Re )µu m L
d2
(13)
where fapp is the apparent friction factor that includes the
effect of the developing flow. The apparent friction factors
from Kakac et al. [10] for fappRe are presented as a function
the channel aspect ratio α c and x+ given by:
Kandlikar,et.al, Extending the Heat Flux Limit with …..
Fig. 2 Channel divided into smaller number of divisions
along its length.
The numbers indicate the division numbers and x indicates
the distance of a particular division from the entrance. This x
is used in Eq. (14) and Eq. (15) to get x+ and x* for the
division.
The results obtained from the analysis are plotted in the
form of an operating envelope. The heat load and the channel
depth are assumed to be known in this envelope. The
important parameters to be determined are the channel width,
the fin thickness, and the required mass flow rate. Once these
parameters are known, the pressure drop can be calculated
using Eq. (13). The objective in finding these parameters is to
have the lowest value of the pressure drop under the given
constraints. To solve this problem, the following algorithm is
developed.
1. The number of channels, n, is assumed to be 50 in the
beginning. If the number of channels is less than 50, it
was found that the channels become too wide and require
an excessive fluid flow rate with a high pressure drop to
dissipate a given heat load.
2. The fin spacing ratio β is used as a parameter in plotting
the results. Knowing the number of channels n and the fin
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3.
4.
5.
6.
spacing ratio β , the channel width a, and the fin thickness
s are calculated from Eqs. (1) to (4).
The channel depth is assumed to be known. The
hydraulic diameter is calculated from the known channel
dimensions.
The channel length is divided into a certain number of
equal divisions, tentatively set as 10.
A low starting value of the inlet Reynolds number is
assumed (tentatively set as Re=50). Knowing Re, x* is
calculated at the center of each division. Knowing this x*,
Nu and h at each division is found from the look-up tables
and charts [10]. This approach allows the use of variable
fluid properties along the flow length.
For a particular division, the energy balance equation is
applied and outlet temperature of the coolant at that
division is calculated.
Tout =
Qdiv
+ Tin
m c C p
(16)
are needed to dissipate higher heat fluxes, Kandlikar and
Grande [4]. Therefore an offset strip-fin construction is
analyzed for dissipating heat fluxes above 3 MW/m2. In this
type of construction, the continuous fin in the microchannels
is broken down into several smaller fins that are placed offset
to each other in the flow direction as shown in Fig. 3. In the
fin arrangement analyzed, there is no gap or overlap with the
downstream fins.
The analysis of the strip-fin arrangement is carried out in a
different manner than that described earlier for plain
microchannels. In this arrangement, the fin length (i.e. length
in the flow direction) is small and the heat transfer coefficient
h is high over the fin (being in the initial developing region).
The pressure drop is calculated using the fappRe over the fin
length without breaking it down further into subdivisions.
The values of h and fappRe are calculated in a similar fashion
as explained previously. As a result significantly higher heat
transfer coefficients are obtained, but with an increase in the
pressure drop as well.
where Qdiv is heat input per channel per division. This
approach will allow extension of the analysis to non-uniform
heat load conditions in the future work. The calculated Tout
from Eq. (15) becomes Tin for the next division. The bulk
temperature Tb for the division is the average of Tin and Tout.
The fluid properties are calculated at this mean temperature.
The Tin for the first division is the fluid inlet temperature and
is assumed to be 300K. The process is repeated until the
channel outlet is reached. The surface temperature at the exit
of the channel is then given by:
Ts =
Qdiv
+ Tb
hAdiv
(17)
Fig. 3 Offset strip-fins shown in the top view, with
individual fin length l along the fin length.
This temperature is compared to the maximum allowable
surface temperature, assumed to be 360 K. If the exit surface
temperature is above this allowable maximum temperature,
the assumed value of Re is increased by a small increment
(tentatively set at an increment of 5) and the calculations are
repeated. Further refinements are made as the solution begins
to converge. The calculations are stopped once the outlet
surface temperature reaches a temperature within a certain
limit below the maximum allowable temperature.
1. For the converged value of Re, the corresponding values
of mass flow rate and pressure drop are calculated. The
pressure drop is the summation of the pressure drops
calculated in each division.
2. The entire procedure is repeated for different number of
channels and different fin spacing ratios.
3. The results are plotted as parametric plots depicting
number of channels versus fin spacing ratio, with channel
frictional pressure drop, total fluid mass flow rate, and fin
thickness as parameters. The plots are used to identify the
desirable region from pressure drop considerations.
9. Split-flow Arrangement
Another possible modification to the system is to reduce
the fluid flow length in the microchannels. In the single-pass
arrangement, fluid enters the microchannels at one end of the
chip and exits on the other end as shown in Fig. 4. In the
split-flow arrangement, also shown in Fig. 4, the fluid is
introduced at the center and exits on the two sides. The inlet
and exit locations could be interchanged if desired.
8. Enhanced Microchannels
Although the heat transfer coefficients are very high with
water flow in microchannels, higher heat transfer coefficients
Fig. 4
Schematics of single-pass and split flow
arrangements showing fluid flow through microchannels.
Kandlikar,et.al, Extending the Heat Flux Limit with …..
(a) Single-pass
arrangement
(b) Split-flow
arrangement
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The split-flow arrangement is advantageous over the
single-pass arrangement in two ways: (i) the flow length of
the fluid stream in the microchannels is reduced by half, and
(ii) the fluid flow rate through the microchannels is also
halved. Both these factors contribute to reducing the pressure
drop. Furthermore, the reduction in the flow rate does not
lower the heat transfer coefficient significantly (being in the
laminar region); some reduction in h however is expected as
the enhancement due to the developing flow is lower for the
lower Reynolds number in the split-flow arrangement. The
analysis is also carried out to investigate the combined effects
of enhanced microchannels and the split-flow arrangement.
The area reduction due to the central inlet manifold is
however neglected.
10. Results and Discussion
A chip with a cooling area of 10×10-3 m × 10×10-3 m
(10mm × 10mm) is considered with a heat load of 300 W.
The channel depth is 200×10-6 m (200 µm). The analysis is
carried out for developing a design envelope. The resulting
envelope for the above conditions is presented in Fig. 5. The
x-axis represents the number of channels and the y-axis
represents the fin spacing ratio. The contour plot shows the
pressure drop in kPa (dash-dot lines). The solid lines indicate
the fin thickness in µm. Since the minimum thickness that
can be fabricated for a fin is 30×10-6 m (30 µm), the
configurations represented by the region below 30×10-6 m (30
µm) are not feasible. For the region above the 30×10-6 m (30
µm) line, a pressure drop of less than 25 kPa can be obtained
with the number of channels between 72 and 96. The
resulting fin spacing ratio is between 0.25 and 0.4. All the
configurations in between these numbers will yield a lower
pressure drop than any other configuration under the given
design constraints. Once the fin spacing ratio and the number
of channels are selected, the actual channel width and the fin
thickness can be calculated from Eqs. (1) to (4).
As an example, select 80 channels (n=80) and a fin
spacing ratio of 0.35 (β=0.35) with a pressure drop of 25 kPa
from Fig. 5. Substituting these values in Eqs. (1) to (4), we
get a channel width of 92 µm and a fin thickness of 32×10-6 m
(32 µm).
A similar contour plot developed for water flow rate is
shown in Fig. 6 for the same heat flux of 3 MW/m2 and a
channel depth of 200×10-6 m (200 µm).
The dash-dot lines in Fig. 6 show contours for mass flow
rates in 10-3 kg/s. The solid lines indicate the fin thickness.
For the design point considered earlier, with n=80, β =0.35,
a=92×10-6 m (92 µm), b=32 ×10-6 m (32 µm), the flow rate is
seen to be 1.6x10-3 kg/s.
Kandlikar,et.al, Extending the Heat Flux Limit with …..
Fig. 5 Contour plot of fin spacing ratio β vs. number of
channels with pressure drop (dash-dot lines) and fin thickness
in µm (solid lines) as parameters for water flow in plain
rectangular microchannels in single-pass arrangement at a
heat flux of 3MW/m2.
Fig. 6 Contour plot of fin spacing ratio β vs. number of
channels with water flow rate in 10-3 kg/s (dash-dot lines) and
fin thickness in µm (solid lines) as parameters for water flow
in plain rectangular microchannels in single-pass arrangement
at a heat flux of 3MW/m2.
A similar contour plot for pumping power is shown in Fig.
7 with contour lines for pumping power shown in mW. The
pumping power plot shown in Fig. 7 completes the design
solution as now we have all the information needed to define
the microchannel cooling system that will satisfy the specified
constraints with a minimum pressure drop. Similar plots can
be constructed for any other heat load, channel depth, or
overall chip size.
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pressure drop remains almost the same in both configurations
because the reduction in the mass flow rate is countered by an
increase in the friction factor for the enhanced geometry. The
reduced mass flow rate and pressure drop lead to a reduced
pumping power requirement for the enhanced microchannel
configuration as compared to the plain microchannels.
The enhanced microcrochannels are analyzed next in the
split flow arrangement shown in Fig. 4b. Figure 10 shows the
pressure drop comparison between the single-pass and splitflow arrangements for the enhanced microchannels. The
split-flow arrangement yields a significantly lower pressure
drop as compared to the single-pass arrangement for the same
heat load. In the split-flow arrangement, the pressure drop is
reduced significantly because of the reduction in the flow
length as well as a reduction in the mass flow rate.
Fig. 7 Contour plot of fin spacing ratio β vs. number of
channels with pumping power in mW (dash-dot lines) and fin
thickness in µm (solid lines) as parameters for water flow in
plain rectangular microchannels in single-pass arrangement at
a heat flux of 3MW/m2.
For the enhanced microchannel configuration, the offset
strip-fin arrangement shown in Fig. 3 is used with a channel
width of 200×10-6 m ( 200 µm) and a channel depth of
200×10-6 m (200 µm). A fin thickness of 100×10-6 m (100
µm) is employed. A higher fin thickness is used as the fins in
this configuration may not be as strong as the long continuous
fins. With this configuration, 33 channels can be constructed
in 10×10-3 m (10 mm) width. The fin length in the flow
direction is l=0.5×10-3 m (0.5 mm), see Fig. 3.
Fig. 9 Heat load versus mass flow rate, in 10-3 kg/s, for
plain (l=10 mm) and enhanced offset strip-fin microchannels
(l=0.5 mm) in single-pass arrangement on a 10 mm × 10 mm
chip.
Fig. 8 Heat load versus pressure drop for plain (l=10 mm)
and enhanced offset-strip fin microchannels (l=0.5 mm) in
single-pass arrangement on a 10 mm × 10 mm chip.
Figures 8 and 9 show a comparison between the enhanced
offset strip-fin microchannels (fin length 0.5 mm) and the
plain microchannels (fin length 10 mm) with a channel width
of 200×10-6 m (200 µm) and a depth of 200×10-6 m (200 µm).
Figure 8 shows the pressure drop as a function of the heat
load, while Fig. 9 depicts the mass flow rate as a function of
the heat load.
The pressure drop for the enhanced
microchannels is slightly lower than the plain microchannels
for the same heat load, while the mass flow rate is seen to be
considerably lower for the enhanced microchannels. The
Kandlikar,et.al, Extending the Heat Flux Limit with …..
Fig. 10 Comparison of pressure drops for the enhanced
microchannels with offset strip-fins (l=0.5 mm) in single-pass
and split-flow arrangements on a 10 mm × 10 mm chip.
The split-flow arrangement yields a definite improvement
over the single-pass arrangement. The heat dissipation
capacity for a specified pressure drop is significantly higher
than the single-pass arrangement for the enhanced
microchannels as seen from Fig. 10. This improvement can
be attributed to the increased heat transfer coefficient leading
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to a reduced mass flow rate, and the reduced fluid flow length
for each fluid stream. The header arrangement however may
become somewhat more complex.
11. Additional Considerations
i. The results are presented for a temperature difference of
60 °C between the maximum allowable chip temperature
and the inlet water temperature. The corresponding fluid
thermal resistance can be readily calculated and applied
to other temperature difference conditions (a slight error
will result due to differences in the water properties at the
different operating temperatures).
ii. The results are expected to be different for different
working fluids, such as antifreeze mixtures or with
mineral oils. Similar analysis is recommended with the
actual properties of the fluid used. Similarly, slight
differences are expected to result when these results are
applied to copper heat sinks.
iii. The results presented in this paper consider the frictional
pressure drop in the microchannel core only. The
pressure drops due to the entrance and exit area changes
between the header and the microchannels, and the
pressure drops in the headers are not included in the
analysis.
iv. More aggressive strip-fin designs could be implemented
with shorter fin lengths and shorter microchannel widths
for dissipating higher heat fluxes. Both the heat transfer
coefficient and the friction factor will increase
accordingly. Multiple inlet and outlet manifolds will be
beneficial with such aggressive designs to reduce the
pressure drops by limiting each individual fluid stream
length through the microchannel passages.
v. Another consideration that plays a major role is the
pressure drop introduced by the filtering system. As the
microchannel dimensions become smaller, the filters will
be required to remove smaller particles from the fluid
stream to avoid blockage of the microchannel flow
passages. This will further increase the pressure drop
with narrower microchannels due to finer filters
employed.
12. Conclusions
• An analysis is presented for evaluating the
thermohydraulic performance of microchannels in direct
chip cooling application by considering the developing
flow effects. The analysis includes only the core
frictional pressure drop and does not include the entrance
and exit contraction and expansion losses.
• The results are presented as parametric plots to identify
the desired channel width, fin thickness, and mass flow
rate for a given heat load and channel depth using water
as the cooling fluid.
• Plain rectangular microchannels and enhanced
microchannels with offset strip-fins are considered. The
enhanced microchannel configuration is further evaluated
under single-pass and split-flow arrangements.
• Direct cooling of chips with water in microchannels
offers a viable solution from a thermohydraulic
viewpoint. Plain microchannels of 200×10-6 m (200 µm)
depth and between 100×10-6 m (100 µm) and 200×10-6 m
(200 µm) width are able to dissipate heat fluxes of up to 3
Kandlikar,et.al, Extending the Heat Flux Limit with …..
•
•
MW/m2 with a frictional pressure drop of under 35 kPa in
the core.
For higher heat fluxes beyond 3 MW/m2, plain
microchannels require excessive water flow rates that
impose higher pressure drop penalties.
Providing
enhanced offset-strip fins with a split-flow arrangement
enables accommodating such high heat fluxes with a core
pressure drop of around 35 kPa.
Enhanced offset strip-fin configuration in a split-flow
arrangement provides an attractive option for extending
the heat flux limit in direct chip cooling application.
Further splitting the flow into multiple inlets and outlets
may be considered, along with more aggressive split-fin
designs.
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