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Daniel Lorenzini-Gutierrez
Mechanical Engineering Department,
Rochester Institute of Technology,
Rochester, NY 14623
e-mail: [email protected]
Satish G. Kandlikar1
Mechanical Engineering Department,
Rochester Institute of Technology,
Rochester, NY 14623
e-mail: [email protected]
Variable Fin Density Flow
Channels for Effective
Cooling and Mitigation
of Temperature Nonuniformity
in Three-Dimensional Integrated
Circuits
The surface temperature of integrated circuit (IC) chips cooled with a single-phase liquid
flow increases along the flow direction following the increase in the liquid temperature.
Increasing the heat transfer coefficient along the flow direction is an effective way to
enhance the cooling performance while mitigating the temperature nonuniformity and
high pressure drop concerns. This investigation evaluates numerically the cooling performance of different flow channel designs suitable in 3D IC applications with channel
heights restricted to 100 lm. Internal configurations featuring offset strip fins with variable fin density and variable spacing ribs were studied in an effort to minimize the temperature nonuniformity while maintaining a relatively low pressure drop. The
performance of 13 different designs for the variable-fin-density configuration and three
different rib configurations have been evaluated and compared with two baseline cases,
corresponding to a smooth flow channel and a flow channel with continuous fins. All of
the analyzed internal configurations are contained within a flow channel of 100 lm height
and 910 lm width. A coolant chip formed by nine flow channels for the dissipation of
200 W of a 3D IC with a surface area of 1 cm2 is the base for this investigation. The best
performing configuration resulted in a temperature variation of less than 30 K with a
pressure drop of 34 kPa as compared to a temperature variation of 38 K and a pressure
drop of 144 kPa with continuous fins and 51 K and 21 kPa for a smooth flow channel.
[DOI: 10.1115/1.4027091]
Keywords: 3D IC, electronics cooling, numerical simulation, temperature nonuniformity,
pressure drop
1
Introduction
High heat flux removal from evolving IC chips requires cooling
techniques that result in a lower overall temperature difference.
Microchannels provide a very high heat transfer coefficient and a
small flow passage volume. They have been identified as an effective technique in electronics cooling [1–4]. Colgan et al. [5]
demonstrated a liquid cooler using offset strip fins in microchannels to dissipate large heat fluxes approaching 1 kW/cm2. Steinke
and Kandlikar [6] measured the heat transfer coefficients with the
offset strip fin geometry investigated by Colgan et al. to be above
500,000 W/m2 K.
Kosar and Peles [7,8] investigated the pin fin geometry in
microchannels and found that the heat transfer is significantly
enhanced. The accompanying pressure drop was also seen to be
quite large. The geometry employed by Colgan et al. [5] had multiple short paths that reduced the pressure drop significantly.
Kosar and Peles [9] studied various fin shapes and their application in a MEMS-based heat sink.
Escher et al. [10] proposed an optimized manifold configuration
for a microchannel heat sink for cooling a 2 2 cm2 chip with a
heat flux of up to 750 W/cm2 and a temperature difference
1
Corresponding author.
Contributed by the Electronic and Photonic Packaging Division of ASME for
publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received July 30,
2013; final manuscript received February 25, 2014; published online April 29, 2014.
Assoc. Editor: Gongnan Xie.
Journal of Electronic Packaging
between fluid inlet and chip surface temperature of 65 K. The
calculated thermal resistance for this design was 0.087 cm2 K/W
for operating conditions corresponding to flow rates lower than
1 l/min and remarkably low pressure drops (less than 10 kPa).
More recently, Zhang et al. [11] proposed a 3D IC system with
on-demand microfluidic cooling technology in order to expand the
lateral scalability of such devices. The microfluidic heat sink featured micropin-fin structures with circular cross section of 150 lm
diameter and 200 lm height in a staggered array. Experimental
results demonstrated that this design is capable of maintaining
the stack temperature below 50 C for a power dissipation of
200 W/cm2. As a continuation of the previous investigation, the
same micropin-fin design and array were implemented by Zhang
and Bakir [12] for the independent tier cooling of a two-processor
stack with different heat fluxes (100 and 55 W/cm2), demonstrating the reduction in junction temperature of approximately 25 C
when compared to an air-cooled heat sink. The pressure drop
associated with the operation of the microfluidic heat sinks proposed in Refs. [11] and [12] was not reported. Additional recent
publications regarding the numerical study and optimization of
micropin-fin geometries and layouts can be found in the literature
[13–16].
The single-phase cooling of IC chips utilizing a uniform geometry flow passage with enhancement structures, such as fins, yields
a constant value of high heat transfer coefficient throughout the
flow length. As the liquid picks up heat, its temperature rises, and
the wall surface temperature also rises. This results in a
C 2014 by ASME
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nonuniform temperature of the channel walls on which IC devices
are located. Rubio-Jimenez et al. [17,18] suggested a variable fin
density configuration in which the fin density increases along the
flow length from inlet to exit. The higher heat transfer coefficient
offsets the lower available temperature difference toward the exit,
resulting in a more uniform temperature distribution. The sparse
placement of fins near the entrance reduces the pressure drop
without adversely affecting the heat transfer. Different pin fin
cross sections (circular, square, elliptical, and rectangular with
rounded sides) were numerically investigated in Ref. [17] for variable fin lengths (75, 100, and 150 lm) and fin heights (100, 200,
and 300 lm) for in-line pin fin distributions. The best performing
configuration found in the aforementioned investigation was further analyzed in Ref. [18] for the case of offset configurations,
reporting a further reduction in the wall temperature and temperature gradient when compared to the in-line configurations.
The concept of variable fin density is further investigated in the
present work focusing on the 3D IC architecture. The flow channel height needs to be lower in this application because of the
presence of through silicon vias (TSVs). Since longer TSVs
adversely affect the electrical performance of the chip, shorter
TSVs, and hence smaller channel heights are desired. A channel
height of 100 lm has been suggested for such applications in an
accompanying article being published in this issue by Kandlikar
[19]; reducing the channel height to the specified value implies a
significantly higher flow restriction when compared to earlier
investigations [17,18]. Various fin density scenarios are considered in this study to dissipate 200 W (100 W on each top and bottom chip surfaces) in the channel over a flow length of 10 mm
under a relatively low pressure drop of approximately 30 kPa.
Alfieri et al. [20] demonstrated water cooling of a stack of four
3D IC chips. The height of the channel was 100 lm with a TSV
length of 150 lm. The entire microchannel height was filled with
full-height pin fins of 50 lm diameter placed at a pitch of 100 lm.
They dissipated 125 W/cm2 using a water flow rate of 122 ml/min.
The pressure drop was rather high at 110 kPa due to the closely
spaced fins.
This investigation reports the assessment of the cooling performance by means of varying the internal configuration and
geometric parameters within the flow channels. In an alternative
proposal to the pin fin designs and arrangements reported in
Refs. [17] and [18], the present investigation is focused on flow
channel rib structures and offset strip fins with variable density
along the flow direction, subjected to the specified TSV height
restriction. The objective is to design a configuration capable of
dissipating high heat fluxes with a low pressure drop, while maintaining the surface temperature uniform and below the limits for
IC chips. Results from this investigation demonstrate the ability of
a 100 lm thick coolant layer to provide cooling of a 3D IC stack
for power dissipation of up to 200 W with relatively low pressure
drops. The issue related to bring water in close proximity to
electronic devices remains an outstanding concern.
2 Description of the Coolant Layer and Flow
Channels
Figure 1 depicts the base for designing a coolant layer with
flow channels of variable internal configurations. The coolant
layer with dimensions L L is subjected to a uniform heat flux q00
at both bottom and top surfaces and is cooled by nine flow channels of rectangular cross section W H separated by a wall of
width tw. Values of these dimensions are summarized in Table 1
and Fig. 1 depicts a schematic view of the coolant layer for a 3D
IC area of 1 cm2.
Four internal channel configurations were analyzed:
(1) Smooth channel—flow channel formed by flat walls.
(2) Continuous-fins channel—flow channel formed by continuous fins along its length, with cross section a b and
placed at both top and bottom surfaces with a separation
distance c.
021007-2 / Vol. 136, JUNE 2014
Fig. 1 Schematic view to scale of the coolant layer for a 3D IC
area of 10 mm 3 10 mm heated at both bottom and top surfaces
(3) Cross-ribs channel—the channel length L was divided into
four sections of length Lcr; the first section is smooth, while
the remaining sections contain semicylindrical ribs perpendicular to the flow direction and with radius Ri, which is
different in each section. The number of ribs is the same
for every section, separated one from each other by a
distance d.
(4) Variable-fin-density channel—the channel length L was divided into different sections according to the number of
finned regions for each case: after a smooth entrance region
of length Le, an increasing number of equally spaced rectangular fins of cross section e f and length Lf are
introduced streamwise.
All of the internal configurations and their geometric parameters are depicted in detail in Fig. 2, while the different values of
these parameters are summarized in Table 1.
Two baseline cases were defined in this investigation: (1) the
smooth flow channel where the heat transfer area is the lowest of
all the analyzed cases; (2) the continuous-fins channel where the
heat transfer area is the highest. In order to obtain an internal
channel configuration capable of achieving the desired performance, the effects of geometric parameters were assessed in the
cross-ribs and variable-fin-density channels by analyzing different
fin density combinations. Three cross-ribs configurations with
constant repeat distances of 25, 50, and 100 lm for each case
were analyzed and designated as CR-XX, where XX indicates the
value of the repeat distance in lm. These values were selected in
order to assess their effect on surface temperature and pressure
drop as the density of cross-ribs increases along with the heat
transfer area and flow restriction. The rib radius is also varying
along the flow direction in order to increase the heat transfer coefficient in downstream locations. A total of 13 chosen configurations for the variable-fin-density channel are reported in this
investigation and are designated as VFD-Y, where Y indicates the
type of configuration according to Fig. 3, which illustrates the top
view and dimensions to scale of these internal configurations, in
compliance with the values listed in Table 1. The cross section
dimensions of the fins are indicated in Fig. 3 for each configuration as (width height) in lm. For example, configuration VFD-I
contains offset strip fins with 20 lm width, 40 lm height, and
1.6305 mm long, separated by 0.3 mm gaps.
3 Comparison Parameters of Cooling Performance
of the Different Fin Configurations
The cooling performance will be evaluated by comparing the temperature distribution on the heating surfaces and its uniformity while
inspecting the pressure drop along the flow channel; these indicators
are significantly affected by the internal configuration adopted and
will be examined in the Results and Discussion section.
The thermal resistance is a common indicator of cooling performance, which relates the temperature rise of the surface above
the input coolant temperature with the dissipated power
R¼
Ts;ave Tf;in
q00 As
(1)
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Fig. 2 Schematics of the different internal configurations analyzed: (a) smooth channel, (b) continuous-fins channel, (c) crossribs channel, and (d) variable-fin-density channel. Not to scale—for illustrative purposes only.
Enhanced heat transfer results in lower average surface
temperatures and therefore lower thermal resistance. The compactness ratio c is also considered as a parameter of comparison,
defined as the ratio of heat transfer area to the coolant layer
volume
c¼
Aht
Vcl
(2)
The maximum temperature difference on the heating surface is
utilized to give a measure of the temperature nonuniformity
DTs ¼ Ts;max Ts;min
(3)
Another important indicator of heat sink performance is the pumping power required to circulate the coolant through the flow channels. The required pumping power is obtained as
W_ p ¼ DPV_
Journal of Electronic Packaging
(4)
where DP is the pressure drop of the coolant along the flow channels and V_ is the volumetric flow rate of coolant.
In a refrigeration system, the coefficient of performance (COP)
is defined as the heat removed by the cycle divided by the work
done in the cycle. In order to relate different performance parameters in a single quantity, a modified coefficient of performance
(COPm) was defined as follows:
COPm ¼
q00 As
DTs W_ p
(5)
This parameter gives a ratio of the dissipated power by the heat
sink and the required power to pump the coolant from inlet to outlet, being inversely proportional to the maximum temperature difference on the heating surface. One of the design objectives is to
have a COPm as high as possible, identifying a configuration capable of dissipating large heat fluxes with a reduced pressure drop,
while maintaining a uniform surface temperature. The units of
this proposed parameter (1/K) do not hold a physical significance
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Table 1 Geometric dimensions of the flow channel and the different internal configurations analyzed
Parameter
Symbol
Value
Flow channel
Channel width (lm)
Channel height (lm)
Channel length (mm)
Wall thickness (lm)
Substrate thickness (lm)
W
H
L
tw
tsi
910
100
10
215
50
Continuous-fins channel
Fin height (lm)
Fin width (lm)
Fin spacing (lm)
a
b
c
20
20
20
Cross-ribs channel
Section length (mm)
Repeat distancea (lm)
Rib radius 1 (lm)
Rib radius 2 (lm)
Rib radius 3 (lm)
Lcr
d
R1
R2
R3
2.5
25, 50, 100
5
10
15
Variable-fin-density channel
Smooth entrance lengtha (mm)
Fin widtha (lm)
Fin heighta (lm)
Fin lengtha (mm)
Le
e
f
Lf
2.578, 4.0
20, 50, 100
20, 40, 50
0.75, 0.96, 0.987,
1.275, 1.6305, 2.274
0.3
Gap spacing (mm)
a
Lgap
It is important to point out that other fluid thermophysical properties such as density, thermal conductivity, and specific heat may
be regarded as constant, since their variation for the fluid temperature range of the present investigation (303–323 K) is 0.8%, 4%,
and 0.05%, respectively, based on the water properties reported in
Ref. [22]. In contrast, the variation of water dynamic viscosity
over the specified range is over 30%, where the assumption of a
constant value for this parameter may result in a significant
overestimation of the pressure drop. In regards to the solid domain
(silicon), its thermophysical properties vary less than 13% over a
temperature range from 300 to 360 K [23,24]. These assumptions
are validated in the Validation of the Numerical Model section.
4.2 Governing Equations and Boundary Conditions. Based
on the prevalent assumptions, the conservation equations for mass
and momentum of fluid in the Cartesian coordinate system are
@u @v @w
þ þ
¼0
@x @y @z
@u
@u
@u
@p
qf u þ v þ w
¼ þ lr2 u
@x
@y
@z
@x
@v
@v
@v
@p
qf u þ v þ w
¼ þ lr2 v
@x
@y
@z
@y
@w
@w
@w
@p
þv
þw
¼ þ lr2 w
qf u
@x
@y
@z
@z
(7)
(8)
(9)
(10)
The geometric parameter was varied according to the specified values.
and, therefore, just a numerical value is mentioned in the Results
and Discussion section.
4
The energy conservation equation for the fluid domain is
@T
@T
@T
qf cpf u
þv
þw
¼ kf r2 T
@x
@y
@z
(11)
Computational Model
4.1 Model Assumptions. The numerical model employed to
compute the temperature distribution and flow field of the present
investigation relies on the following assumptions:
(1) Steady state, laminar, and incompressible flow.
(2) Constant and uniform heat flux applied on the substrate
surface.
(3) Radiation heat transfer effects are negligible.
(4) Constant fluid and solid thermophysical properties except
fluid dynamic viscosity, which tends to decrease as fluid
temperature increases and can be predicted with accuracy
to within 2.5% from 0 C to 370 C with the following
expression [21]:
l ¼ 2:414 105 10247:8=ðT140Þ Pa s
(6)
In regards to the solid regions, the energy equation reduces to the
Laplace equation under the assumptions of isotropic and constant
thermal properties. The coolant fluid used for all the simulations
is water, while the solid domain is silicon; the value of these properties is listed in Table 2.
The boundary conditions are set according to the fluid–solid
interactions in the computational domain. A constant volumetric
flow rate of 16.17 ml/min is considered at the fluid inlet for each
channel (145.53 ml/min coolant layer total) with an inlet fluid
temperature of 303 K. This volumetric flow rate corresponds to a
temperature rise of the fluid from inlet to outlet of 20 K, chosen as
the base for comparison of the different configurations analyzed.
A mass conservation condition ðm_ in ¼ m_ out Þ is specified at the
flow outlet. Due to the geometry of the flow channel, symmetry
boundary conditions are used in order to reduce the computational
domain to one fourth of the flow channel for all of the configurations illustrated in Fig. 2. The walls where the fluid and solid
Fig. 3 Different internal configurations (to scale) analyzed for the variable-fin-density channel. Dimensions are in millimeters.
021007-4 / Vol. 136, JUNE 2014
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Table 2 Properties of water and silicon
Property
3
Density (kg/m )
Thermal conductivity (W/m K)
Specific heat (J/kg K)
Dynamic viscosity (Pa s)
Symbol
Silicon
Water
qsi, qf
ksi, kf
c, cpf
l
2330
148
700
—
998
0.6
4182
Given by Eq. (6)
domains meet are set as interfaces while the walls adjacent to both
inlet and outlet are considered as adiabatic. A constant and uniform heat flux is specified at both top and bottom surfaces of the
heat sink, as depicted in Fig. 1, with a value of q00 ¼ 100 W/cm2.
Zero mass flux and no-slip boundary conditions were prescribed
at the channel internal walls (fluid–solid interface).
4.3 Numerical Procedure. The computational fluid dynamics (CFD) software ANSYSV FLUENTV 14.0 was used to solve
numerically the governing equations through the finite volume
method. The solution was initially approached using the firstorder upwind scheme for discretizing the momentum equation
and, after a certain level of convergence was attained, the solution
was refined by using the second-order upwind scheme. The SIMPLE
algorithm was employed for the coupling of velocity and pressure.
Convergence was attained when the residuals of the mass,
momentum, and energy equations reached a value of 1 105.
Calculations were performed with variations in the number of
mesh elements in order to ensure that the solution was grid
independent. The grid independence was achieved by successive
mesh refinements, approximately doubling the number of nodes
from one mesh to another until the criterion j(Nj Njþ1)
=Njj<1 103 was attained. In this criterion, Nj represents the
computed value for the parameter of comparison and Njþ1 is the
value obtained with the next mesh. The pressure drop and the average temperature of the heating surface at the exit (x ¼ L) were
used as the parameters of comparison. Table 3 shows how grid independence was achieved for the different internal configurations,
and therefore, the results of this investigation are those based on
the mesh sizes corresponding to model No. 2.
R
5
R
Results and Discussion
The numerical results were obtained for the temperature and
pressure fields in the computational domain. The average values
for temperature and pressure were calculated with a numerical
surface integration for both flow inlet and outlet in order to obtain
the fluid temperature rise and pressure drop, respectively. The numerical values of DTf were compared with the results from the
energy balance
q00 As
(12)
DTf ¼
_ p
mc
The error in numerical and energy balance values for DTf was
lower than 0.02% for all of the simulated cases in this
investigation.
5.1 Validation of the Numerical Model. The numerical
method and procedure employed for this investigation have been
validated in the author’s previous work [25], in which CFD results
showed a good agreement with experimental data for the assessment of the effect of structured roughness on heat transfer in
microchannels. Further validation of the present numerical model
was done with the experimental results of Tuckerman and Pease
[26] for silicon microchannels with rectangular cross sections,
where the dimensions of the continuous-fin design can be adapted
to reproduce the analyzed geometries by Ref. [26] if just the lower
part of Fig. 2(b) is considered and the channel height (H) is modified to match the fin height (a) with an adiabatic top wall and
heated bottom wall, while the channel length is kept at 10 mm
(heated area of 1 cm2). Table 4 presents the geometric features of
the microchannels and the operating conditions employed in order
to compare the maximum thermal resistance (obtained by replacing Ts,ave with Ts,max in Eq. (1)) reported in the cited experimental
study and the predicted value with the present model. The
obtained results indicate that there is a reasonable agreement with
the experimental results. Experimental analysis will be conducted
in the future for the best-performing internal configurations of this
investigation.
5.2 Performance Assessment of the Baseline and CrossRibs Configurations. Figure 4 presents the temperature variation
of the heating surfaces along the flow direction for the internal
configurations corresponding to the baseline designs (smooth and
continuous-fins) and cross-ribs (CR-25, CR-50, and CR-100), in
which the marker symbols are used to indicate the characteristic
regions depicted in Fig. 2(b). For the baseline cases, the lowest
surface temperature is found at the inlet section and increases
almost linearly after the entrance region due to the thermal development of the flow, reaching the highest temperature at the outlet
section. The overall performance of these internal configurations
is summarized in Table 5. The results indicate that the heat dissipation is significantly improved when the compactness ratio is
increased. For example, the increase in c from the smooth channel
to the continuous-fins is 83%, while the maximum temperature
difference is reduced by 12.97 K. However, the increase in the
heat transfer area within the flow channel results in an increased
pressure drop.
Figure 5 shows the variation of pressure drop along the flow
direction for the baseline and cross-ribs configurations. The pressure drop variation for the baseline configurations is linear after
the curvature observed at the inlet section due to the hydrodynamic development effects, while for the cross-ribs configurations
Table 3 Grid independency study
Internal configuration
Mesh model
Smooth
Continuous-fins
Cross-ribs (CR-25)
Variable-fin-density (VFD-A)
Journal of Electronic Packaging
1
2
3
1
2
3
1
2
3
1
2
3
Mesh elements
210,000
420,000
750,000
2,875,950
4,108,500
5,478,000
3,170,367
4,013,123
5,884,164
1,890,788
2,853,200
4,025,865
DP (kPa)
17.55
20.82
20.83
127.23
144.42
144.38
26.60
29.29
29.27
20.56
22.92
22.92
j
DP DPjþ1 DPj
1
1.863 10
4.803 104
—
1.351 101
2.769 104
—
1.011 101
6.828 104
—
1.148 101
2.181 104
—
T z¼L (K)
370.71
368.87
368.55
349.18
347.49
347.48
362.12
360.75
360.63
360.67
359.59
359.59
j
jþ1 T
z¼L T z¼L j
T
z¼L
4.963 103
8.675 104
—
4.839 103
2.888 105
—
3.783 103
3.326 104
2.994 103
1.390 105
—
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Table 4
Case
1
2
3
Numerical validation of the maximum thermal resistance with experimental data [26]
c (lm)
b (lm)
H ¼ a (lm)
tsi (lm)
q00 (W/cm2)
3
_
V(cm
/s)
Rmax (K/W) Exp. [26]
Rmax (K/W) Num.
56
55
50
44
45
50
320
287
302
213
143
156
181
277
790
4.7
6.5
8.6
0.110
0.113
0.090
0.115
0.114
0.094
Table 5 Cooling performance for the smooth, cross-ribs, and continuous-fin configurations operating with a flow rate of
145.53 ml/min
Internal configuration
Smooth
CR-100
CR-50
CR-25
Continuous-fins
Ts,ave (K)
DTs (K)
R (K/W)
DP (kPa)
W_ p (mW)
c (mm2/mm3)
COPm
351.45
351.06
348.66
347.76
333.99
51.15
49.18
46.02
42.93
38.18
0.2423
0.2403
0.2283
0.2238
0.1550
20.82
22.22
24.91
29.29
144.42
50.50
53.90
60.42
71.04
350.36
8.98
9.31
9.65
10.31
16.44
77.42
75.45
71.93
65.58
14.95
Fig. 4 Variation of the surface temperature along the flow
direction for the baseline and cross-ribs configurations operating with a flow rate of 145.53 ml/min and 200 W dissipation
it can be inferred that the fully developed flow conditions are disrupted at the beginning of every section of transversal ribs,
increasing the slope of the pressure curve. The current geometry
of cross-ribs used is semicylindrical. Further heat transfer performance enhancement and reduction in pressure drop are
expected with the use of smoothly varying sinusoidal geometry as
analyzed by Dharaiya and Kandlikar [25]. Further optimization of
this geometry is recommended in the future work.
The heat transfer performance of the continuous-fin configuration is the best of the analyzed configurations so far due to its
increased compactness ratio in comparison with the other configurations. However, the pressure drop caused by this internal configuration is approximately seven times higher than that of the
smooth channel and further improvements should be made in
order to address this issue by increasing the heat transfer area for
selected regions while reducing the flow restriction. When compared using the modified coefficient of performance, the smooth
channel results in a value of COPm approximately three times
higher than the continuous-fins channel, where the computed
value of the latter is significantly affected by the high pumping
power required for this configuration despite its significant thermal advantage.
It should be noted that significant nonuniformity in surface temperature is introduced near the inlet due to entrance region effect.
It is not possible to provide such high heat transfer coefficients,
even with the highest density fins, downstream in the channel. A
practical way to overcome this problem is to place high heat flux
generating devices near the entrance. This will enable dissipating
larger heat fluxes in these devices, while simultaneously achieving
a higher degree of temperature uniformity over the chip surface.
The increase in c caused by introducing transversal ribs into the
flow channel results in lower surface temperatures and
021007-6 / Vol. 136, JUNE 2014
Fig. 5 Variation of the pressure drop along the flow direction
for the baseline and cross-ribs configurations operating with a
flow rate of 145.53 ml/min and 200 W dissipation
temperature gradients when compared to the smooth channel,
with a slight increase in the pressure drop. Configuration CR-25
reduces the maximum temperature difference and average surface
temperature by 8.22 K and 3.69 K, respectively, with a pressure
drop increase of 8.47 kPa when compared to the smooth channel.
Amongst the results presented so far, the configuration CR-25
seems to represent the most balanced one in terms of heat transfer
and pressure drop by qualitative comparison in Figs. 4 and 5.
However, when using the quantitative COPm indicator, it turns out
that the computed value for the cross-ribs configurations falls
below that of the smooth channel and decreases as a result of the
increased pressure drop associated with the increase in cross-ribs
density. Although thermal performance is improved with the
cross-ribs channels, this crucial parameter is limited by the low
flow velocities near the walls and ribs while the flow restriction is
significant and limits the overall performance. Therefore, a configuration capable of providing increased surface with fins exposed
to higher velocities and thereby higher heat transfer coefficients
must be sought.
5.3.1 Performance Assessment of the Variable-Fin-Density
Configurations—Effect of the Fin Cross Section. In order to further increase the heat transfer coefficient along the flow direction,
the concept of introducing offset strip fins with variable density
was investigated. The first configurations analyzed are the VFD-A
to VFD-G channels, which share the same offset configuration divided into three sections after the smooth entrance while the fin
width and height are varied according to the specified values in
Fig. 3.
Figure 6 presents the temperature variation of the heating surfaces along the flow direction for the configurations VFD-A to
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Fig. 6 Variation of the surface temperature along the flow
direction for the baseline, variable-fin-density (VFD-A to VFD-G)
and CR-25 configurations operating with a flow rate of
145.53 ml/min and 200 W dissipation
VFD-G and their comparison with the baseline cases. The use of
markers for the variable-fin-density configurations allows identifying the location of the finned sections and gaps, in accordance
to Fig. 3. Results from Fig. 6 indicate that increasing the fin height
results into lower surface temperatures; this is due to the increase
in heat transfer coefficient on the finned regions, which are
exposed to higher flow velocities near the centerline when compared to the cross-ribs configurations. The best-performing case
(in terms of heat transfer) of the cross-ribs configurations (CR-25)
was included in Fig. 6 for comparison purposes, where it can be
noted that its surface temperature is higher than all of the variable-fin-density configurations due to the aforementioned reasons.
These comments are quantitatively reinforced by comparing the
COPm values listed in Table 6 between the cross-ribs and variable-fin-density channels where, in general, the latter configuration exhibits higher values of combined performance, arising from
its outstanding heat transfer performance without excessive pumping requirements. Based on these results, special attention was
given to the analysis and improvement of the latter configuration.
The peak-valley behavior near the transition zones for the variable-fin-density configurations is a result of the increase in heat
transfer area and thermal development effects. The inlet section of
all of the VFD configurations is smooth, which allows similar
thermal and hydraulic development than that of the smooth channel case in this region. However, these developed conditions are
disrupted by the internal channel structures, which increase the
heat transfer coefficient and decrease the temperature around the
fins. This effect is more pronounced on the transition gaps, after
which the flow continues to develop thermally and hydraulically.
The observed behaviors for the variable-fin-density configurations
help to homogenize the temperature distribution, which is a
desired feature for the thermal management of 3D ICs. The objective of analyzing these designs is to find a balanced configuration
in terms of heat transfer and pressure drop.
The effect of varying the fin height to 20, 40, and 50 lm for a
fixed fin width of 20 lm was assessed for the configurations VFDA, VFD-B, and VFD-C, respectively. Results available in Figs. 6,
7, and Table 6 suggest the use of the cross section of the VFD-B
channel due to an increased heat transfer performance (decrease
of the maximum temperature difference of 13.46 K and 4.41 K
when compared to the smooth and VFD-A configurations, respectively) with a relatively low increase in pressure drop (increase of
4.65 kPa and 2.55 kPa when compared to the smooth and VFD-A
configurations, respectively). The computed COPm value for the
VFD-B configuration indicates a clear thermal advantage over
pumping power while providing a reduced maximum temperature
difference when compared to the baseline and cross-ribs configurations. It is important to note that increasing the fin height from
40 to 50 lm does not significantly affect the heat transfer
performance due to the similar heat transfer area between both
Journal of Electronic Packaging
cases (c 9.95 mm2/mm3). However, the connection between the
top and bottom fins for the 50 lm case (VFD-C) introduces a higher
flow restriction to the system and an increase in pressure drop, thus
reducing the COPm value with respect to the VFD-B case.
The effect of varying the fin width to 50 and 100 lm along with
fin heights of 20 and 40 lm was assessed for the configurations
VFD-D to VFD-G. A fin height of 40 lm is preferred due to the
previously mentioned improvements in heat transfer; however,
when combined with wider fins, the flow restriction is increased
significantly (e.g., the pressure drop of the VFD-G configuration
is 115% higher than that of the VFD-B configuration). Although
higher heat transfer coefficients are obtained for wider fins (due to
the increase in area subjected to higher velocities through the fin
top wall), the concept of achieving uniform temperature is contrasted by the presence of relatively large temperature gradients
between the finned sections, as can be readily noticed in Fig. 6
where the amplitude of the peak-valley behavior is notorious
when compared to the cases of 20 lm fin width. These statements
are reinforced by analyzing the temperature contours reported in
Fig. 10, which allow the visual detection of temperature nonuniformities associated with wider fins. Using the COPm indicator, it
is found that the combined performance of wider fins (VFD-D to
VFD-G) is highly affected by the flow restriction, where all of the
computed values are lower than that of the VFD-B configuration.
Due to the thermal and hydraulic drawbacks associated with the
use of wider fins, the configuration VFD-B is chosen as the balance between performance indicators, which lie between the baseline cases. Despite these achievements and discussion, the effect
of increasing the number of finned regions with the objective of
achieving better performance needs to be assessed.
5.3.2 Performance Assessment of the Variable-Fin-Density
Configurations—Effect of the Fin Distributions. Once the fin
cross section of the configuration VFD-B was proven to achieve a
balanced performance in terms of heat transfer and pressure drop
when compared to its counterparts, the effect of strategically modifying the fin distribution using the concept of increased heat
transfer area along the flow direction was investigated for the configurations VFD-H to VFD-M. These configurations present different fin lengths and densities with the objective of achieving
lower surface temperatures and reduced temperatures gradients
with small pressure drop penalties.
Configurations VFD-H and VFD-I were designed in order to
reduce the surface temperature and temperature gradients by
means of introducing one more section of increased fins (four offset strip fins). The results plotted in Figs. 8 and 9 (summarized in
Table 6) indicate that a remarkable increase in thermal performance is obtained when higher fin densities are employed, as a
result of the following: (1) the thermal development is affected by
the downstream geometry in which the heat transfer area is
increasing, resulting in lower surface temperatures; (2) the strategically inserted fin regions help to reduce temperature gradients,
resulting in lower peak-valley effects. Although the pressure drop
for these configurations is increased approximately 30% when
compared to the VFD-B channel, these values may be acceptable
since the thermal performance can be compared now with that of
the continuous-fins (i.e., the maximum surface temperature values
observed in these configurations are similar to those of the
continuous-fins, while the temperature uniformity is improved).
The value of the COPm indicator decreased 16.5% for the VFD-H
channel and 12.3% for the VFD-I when compared to the value of
the VFD-B configuration because of the stronger effect of the
pumping power on this fabricated parameter. However, the aforementioned positive effects on temperature uniformity balance the
hydraulic concerns associated to these designs, where it can be
observed in Fig. 8 that the temperature fluctuations past the
smooth entrance of the channel are remarkably stabilized when
compared to the baseline cases.
Although the performance objectives of uniform temperature
distributions and relatively low pressure drop can be achieved to a
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Table 6 Cooling performance for the variable-fin-density configurations operating with a flow rate of 145.53 ml/min
Internal configuration
VFD-A
VFD-B
VFD-C
VFD-D
VFD-E
VFD-F
VFD-G
VFD-H
VFD-I
VFD-J
VFD-K
VFD-L
VFD-M
Ts,ave (K)
DTs (K)
R (K/W)
DP (kPa)
W_ p (mW)
c (mm2/mm3)
COPm
345.56
343.57
343.53
346.50
341.94
345.29
339.47
342.62
342.06
342.76
342.11
342.69
340.93
42.45
38.04
38.52
42.19
34.96
39.67
32.81
33.68
32.41
32.58
30.28
32.84
28.62
0.2128
0.2028
0.2026
0.2175
0.1947
0.2114
0.1823
0.1961
0.1953
0.1988
0.1955
0.1984
0.1896
22.92
25.47
26.86
27.21
41.07
31.49
54.80
34.48
34.07
33.91
34.14
33.08
37.41
55.61
61.79
65.17
66.01
99.64
76.39
132.95
83.64
82.66
82.27
82.81
80.26
90.77
9.50
9.95
9.95
9.47
9.96
9.48
9.98
9.97
10.15
9.89
10.02
9.99
10.12
84.72
85.09
79.67
71.81
57.41
65.99
45.85
70.99
74.65
74.62
79.76
75.88
76.99
Fig. 7 Variation of the pressure drop along the flow direction
for the baseline, variable-fin-density (VFD-A to VFD-G) and CR25 configurations operating with a flow rate of 145.53 ml/min
and 200 W dissipation
certain level with the VFD-H and VFD-I designs, further improvement in pressure drop was sought by means of increasing the
smooth entrance length from 2.578 to 4 mm; configurations J and
K were designed for this increased length with four and five strip
fin regions, respectively.
Results shown graphically in Figs. 8 and 9 (summarized in
Table 6) indicate a significant improvement in overall performance of the VFD-K configuration when compared to all of the previously discussed cases. Temperature uniformity is a remarkable
feature of the VFD-J and VFD-K configurations, since the maximum temperature difference is reduced by 5.6 K and 7.9 K,
respectively, when compared to the continuous-fin configuration,
and Fig. 10 shows this uniformity through the surface temperature
contours. For these cases, the pressure drop is very similar
(34 kPa) and represents only 23% of the pressure drop calculated for the continuous-fin configuration. When comparing configurations VFD-J and VFD-K, the latter is chosen because of its
higher temperature uniformity (maximum temperature difference
reduced by 2.3 K with respect to VFD-J), while the pressure drop
is increased in just 0.23 kPa. As a consequence of the aforementioned results, the COPm indicator of the VFD-K channel is 7%
higher than that of the VFD-J configuration. Although the COPm
value for the VFD-B case is slightly higher than that of the VFDK channel due to its reduced flow restriction, the latter configuration offers an outstanding temperature uniformity (observed in the
temperature stabilization after the smooth entrance region) without an excessive pumping power demand.
At this point, the configuration VFD-K has shown to provide
the best heat transfer and pressure drop performance of the analyzed cases so far. In order to further reduce the associated pressure drop with this design, the configurations VFD-J and VFD-K
021007-8 / Vol. 136, JUNE 2014
Fig. 8 Variation of the surface temperature along the flow
direction for the baseline and variable-fin-density configurations (VFD-H to VFD-M) operating with a flow rate of 145.53
ml/min and 200 W dissipation
Fig. 9 Variation of the pressure drop along the flow direction
for the baseline and variable-fin-density configurations (VFD-H
to VFD-M) operating with a flow rate of 145.53 ml/min and 200 W
dissipation
were used as a reference to propose a new configuration capable
of achieving this objective while retaining the heat transfer performance. The configuration VFD-L was designed as follows: the
fin sections with three and four offset strip fins of the configuration VFD-J were elongated from 1.275 to 1.59 mm in length,
while the fin sections with one and two offset strip fins were shortened from 1.275 to 0.96 mm in length. Although the results indicate a reduction in pressure drop of 0.83 kPa when compared to
VFD-J channel and 1.06 kPa when compared to VFD-K channel,
the latter configuration is still preferred due to its superior temperature uniformity (maximum temperature difference reduced by
2.56 K respect to the VFD-L case) and a COPm 5% higher than
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Fig. 10 Temperature contours (K) on the heat sink surface for all the analyzed
configurations operating with a flow rate of 145.53 ml/min and 200 W dissipation
Fig. 11 Streamlines over a velocity magnitude contour (m/s)
for the VFD-K configuration operating with a flow rate of
145.53 ml/min. Image scaled by a factor of 0.5 in the z direction
for illustrative purposes.
Fig. 13 Variation of the pressure drop along the flow direction
for the baseline and the best-performing configurations operating with a flow rate of 291.06 ml/min and 200 W dissipation
Fig. 12 Variation of the surface temperature along the flow
direction for the baseline and the best-performing configurations operating with a flow rate of 291.06 ml/min and 200 W
dissipation
that of the VFD-L channel. This is due to the increased number of
finned sections of the VFD-K channel over the VFD-L configuration (five and four, respectively), which help to further stabilize
the temperature fluctuations past the entrance region.
As a last effort to further increase the thermal performance of
the VFD-K configuration and assess the pressure drop increase
associated, the configuration VFD-M was designed with an
increase from five to six finned sections, resulting in a fin length
of 0.75 mm, as depicted in Fig. 3. The results indicate that the
maximum temperature difference is further reduced in 1.66 K
when compared to the VFD-K configuration, while the pressure
drop is increased in 3.27 kPa. Nevertheless, the computed value of
the COPm for this last design is 3.4% lower than that of the VFDK channel due to the stronger influence of the pumping power on
Journal of Electronic Packaging
this parameter. Visual inspection of the temperature contours for
the VFD-K and VFD-M configurations depicted in Fig. 10 indicates the superiority of these designs in terms of surface temperature reduction and uniformity with respect to all of the analyzed
configurations in this investigation. The main design targets of
achieving low surface temperatures and temperature uniformity
while maintaining a reduced pressure in comparison to the baseline cases are fulfilled by configurations VFD-K and VFD-M.
Figure 11 depicts the streamlines over a velocity contour
located at the midsection of the fin height for the VFD-K configuration, where it can be observed that the flow trajectory is not significantly distorted by the implementation of these fin structures,
thus allowing the attainment of a high combined performance
(COPm).
It is important to mention that the channel height restriction
imposed by the TSVs (100 lm) plays an important role for the
selection of enhanced fin structures, since the pressure drop is significantly increased when compared to the values reported in the
literature for channels with lower aspect ratios. For example, the
best configuration reported by Ref. [17] indicated that channel
with a height of 200 lm with variable density micropin fins is capable to dissipate 230 W/cm2 with a pressure drop of 29.5 kPa. On
the other hand, the design of equally distributed circular micropin
fins investigated in Ref. [20] with the same channel height as the
present work (100 lm) resulted in design capable of handling a
heat flux of 125 W/cm2 with an associated pressure drop as high
as 110 kPa. When comparing these results with the VFD-K
configuration, the clear advantage of heat transfer (heat flux of
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Table 7
Cooling performance for selected configurations operating with a flow rate of 291.06 ml/min
Internal configuration
Ts,ave (K)
DTs (K)
R (K/W)
Smooth
VFD-K
VFD-M
Continuous-fins
340.24
331.52
330.49
325.83
40.53
22.78
22.11
28.10
0.1862
0.1426
0.1375
0.1142
DP (kPa)
W_ p (mW)
c (mm2/mm3)
COPm
51.88
92.23
101.68
314.52
251.74
447.51
493.35
1526.02
8.98
10.02
10.12
16.44
19.60
19.62
18.34
4.66
Fig. 14 Temperature contours (K) on the heat sink surface for the baseline and the bestperforming configurations operating with a flow rate of 291.06 ml/min and 200 W dissipation
200 W/cm2) and pressure drop (34 kPa) indicates the direction
of this work toward a design of more efficient and balanced configuration for the thermal management of high-power electronic
devices.
6 Effect of Flow Rate on the Best-Performing
Configurations
As mentioned in Sec. 4.2, all of the analyzed cases in this investigation were compared for a heat flux of 100 W/cm2 on each bottom and top surfaces (total power dissipation of 200 W) and a heat
sink flow rate of 145.53 ml/min corresponding to a fluid temperature increase of 20 K. In order to assess the thermal and hydraulic
behavior at higher flow rates, the best performing and baseline
configurations were analyzed for a heat sink flow rate of
291.06 ml/min and fluid temperature rise of 10 K. The temperature
variation curves shown in Fig. 12 indicate the superior temperature uniformity of the VFD-K and VFD-M configurations over the
baseline configurations. Overall performance results summarized
in Table 7 along with pressure curves of Fig. 13 suggest configuration VFD-K as the best design since the pressure drop associated
with this design is 9.45 kPa lower than that of VFD-M configuration with a more stable temperature uniformity as shown in the
temperature contours of Fig. 14, in which it can be observed that
the highest temperatures are located at the midsection of the channel for the variable-fin-density configurations and the VFD-K
design is capable of maintaining a uniform temperature distribution even at higher flow rates. The VFD-K configuration presents
the highest COPm of the cases listed in Table 7, which reinforces
the previous claims regarding the superior thermal and hydraulic
capabilities associated to this design.
7
Conclusions
A coolant layer with flow channels of variable fin density was
numerically investigated with the objective of designing an internal configuration capable of dissipating high heat fluxes with a
low pressure drop, while reducing the surface temperature nonuniformity and keeping the maximum temperatures below the limits
for IC chips. The results from this investigation indicate that
increasing the heat transfer area along the flow direction with offset strip fins is an effective way for the effective cooling of these
devices. Although the cooling performance of the cross-rib
021007-10 / Vol. 136, JUNE 2014
geometries is better than that of a smooth channel, further study
and optimization using smoothly varying sinusoidal profiles is
recommended. The configuration VFD-K was proven to accomplish the targets sought in this investigation, dissipating a total
power of 200 W (100 W/cm2 on each bottom and top surfaces) of
a 3D IC of 10 mm 10 mm, with a pressure drop of 34 kPa
(pumping power of 83 mW) as compared to a pressure drop of
144 kPa (pumping power of 351 mW) for the continuous-fin
design. The temperature uniformity is a remarkable feature of this
design, in which the maximum temperature variation is less than
30 K as compared to a temperature variation of 38 K and 51 K
for the continuous-fins and smooth flow channel configurations. A
coolant layer formed by nine flow channels with the internal configuration VFD-K is suggested as an effective option for the thermal management of 3D ICs, with a low channel height of 100 lm
in order to comply with the thermal silicon vias constraint associated to these devices.
The low temperatures near the entrance region lead to large
temperature nonuniformities in all of the geometries investigated.
Placing higher heat flux devices in this region will extend the high
heat flux removal capability of the cooler, while significantly
reducing the temperature nonuniformity.
As a final note, the modified coefficient of performance parameter used in this study places equal weight on the pumping power
and temperature nonuniformity. Selection of this parameter is
rather arbitrary, and another suitable performance matrix may be
used for comparison depending on the importance of specific
attributes in the cooling system design.
Nomenclature
A¼
c,cp ¼
COP ¼
k¼
m_ ¼
P¼
q00 ¼
R¼
T¼
u, v, w ¼
V¼
heat transfer area (m2)
specific heat (J kg1 K1)
coefficient of performance
thermal conductivity (W m1 K1)
mass flow rate (kg s1)
pressure (Pa)
heat flux (W m2)
thermal resistance (K W1)
temperature (K)
velocity components (m s1)
volume (m3)
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V_ ¼ volumetric flow rate (m3 s1)
W_ ¼ power (W)
Greek Symbols
compactness ratio (mm2 mm3)
pressure drop (Pa)
temperature rise of the coolant (K)
maximum temperature difference on the heating surface
(K)
l ¼ dynamic viscosity (kg m1 s1)
q ¼ density (kg m3)
c¼
DP ¼
DTf ¼
DTs ¼
Subscripts
ave ¼
cl ¼
f¼
ht ¼
in ¼
m¼
max ¼
min ¼
p¼
s¼
si ¼
average
cooling layer
fluid
heat transfer
inlet
modified
maximum
minimum
pump
heating surface
silicon substrate
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