IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 2, NO. 5, MAY 2012
825
Numerical Analysis of Novel Micro Pin Fin
Heat Sink With Variable Fin Density
Carlos A. Rubio-Jimenez, Satish G. Kandlikar, and Abel Hernandez-Guerrero
Abstract— Numerical analyses to characterize and design
micro pin fin heat sinks for cooling the 2016s IC chip heat
generation are carried out in this paper. A novel design with
variable fin density is proposed to generate a more uniform
temperature of the IC chip junctions. The variable-density
feature allows the gradual increase of the heat transfer area
as coolant passes through the system. Single-phase water in the
laminar regime is employed. Four different fin shapes (circle,
square, elliptical, and flat with two redounded sides) are analyzed.
The junction temperature and pressure drop variations in the
heat sink generated by these shapes are presented. The effects
of varying the fin length and height are also studied. The best
heat sink configuration has a thermal resistance ranging from
0.14 to 0.25 K/W with a pressure drop lower than 90 kPa and
a junction temperature ∼314 K under the conditions studied.
The temperature gradient at the bottom wall of the heat sink
is considered as a parameter for comparing various heat sink
designs. The novel cooling device has an overall temperature
gradient lower than 2 °C/mm, which is significantly lower than
the temperature gradients in other schemes reported in literature.
Index Terms— Micro pin fin heat sink, single-phase flow,
uniform junction temperature, variable fin density.
I. I NTRODUCTION
C
URRENTLY, electronic devices have revolutionalized
industrial processes and the entertainment technology
sector. IC chips are the key components in these devices. The
new generation of electronic devices has a higher capacity to
process information and is smaller in size than its predecessor.
This development has been possible because every component
is now highly reliable, smaller, lighter, and cheaper with short
design cycles. Several technological challenges have helped to
achieve this status, such as new materials and manufacturing
techniques, novel electronic designs, better handling of high
heat fluxes, and so on. In the heat dissipation field, according
to The International Technology Roadmap for Semiconductors,
the challenge is transcendental. The 2016s 22-nm complementary metal–oxide–semiconductor devices are expected to
Manuscript received September 1, 2011; accepted February 17, 2012. Date
of publication April 10, 2012; date of current version May 3, 2012. This work
was supported in part by CONACYT-Mexico. Recommended for publication
by Associate Editor D. Agonafer upon evaluation of reviewers’ comments.
C. A. Rubio-Jimenez was with the University of Guanajuato, Salamanca
36885, Mexico. He is now with the Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY 14623 USA (e-mail:
caalruji@yahoo.com.mx).
S. G. Kandlikar is with the Department of Mechanical Engineering,
Rochester Institute of Technology, Rochester, NY 14623 USA (e-mail:
sgkeme@rit.edu).
A. Hernandez-Guerrero is with the Department of Mechanical Engineering,
University of Guanajuato, Salamanca 36885, Mexico (e-mail: abel@ugto.mx).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TCPMT.2012.2189925
generate up to 288 W of heat, while limiting the maximum
design temperature to <85 °C [1]. Therefore, the new cooling
systems to be used in these electronic devices should have a
thermal resistance ranging from 0.14 to 0.25 °C/W, with higher
reliability and smaller size than the current cooling systems
(air-cooling technologies) which are reaching their maximum
performance limit.
One alternative for cooling electronic devices emerged with
the pioneering work of Tuckerman and Pease [2] three decades
ago. Their experiments, based on internal flow, demonstrated
that the heat transfer coefficient increases as the hydraulic
diameter is reduced to microscale. Their results showed that a
microchannel heat sink can achieve a thermal resistance of
0.09 K/W and is capable of dissipating up to 790 W/cm2
with a temperature rise of 71 °C. Although these results
indicate that this cooling system dissipates the heat fluxes
that are expected in the near future, there are some important
technical drawbacks: 1) the fluid pressure drop is very large
(>200 kPa); and 2) the junction temperature of the heat sink
and the chip is highly nonuniform along the flow direction
(∼70 °C of temperature difference in only 10 mm). These
drawbacks make the cooling system unreliable and seriously
affect the performance and lifetime of the IC chips [3], [4].
Severe damage, such as cumulative failure, fatigue per cycle in
some materials, acceleration of chemical reactions, metal and
electronic migration, and so on, may result on chips when
the heat removal is handled inappropriately. Moreover, the
temperature variation causes clock skew [5].
In the last few years, numerous studies have been carried
out considering microchannels in order to understand
the microscale phenomena [6]–[8] and generate reliable
cooling systems [9]–[11]. In a similar way, nonconventional
microcooling systems based on different techniques have been
proposed every year [12]–[14]. However, only a few works
have shown good performance. Peles et al. [15] proposed
a micro pin fin heat sink as an alternative for cooling IC
chips. Their analytical–experimental study was based on
correlations developed for coolant flow through a bank of
tubes at macroscale. Their results showed that this arrangement
dissipates up to 790 W/cm2 with a temperature rise of 30.7 °C;
this means that the system achieves a thermal resistance of
0.039 K/W. Unfortunately, the pressure drop was larger than
200 kPa. Colgan et al. [16], [17] proposed a nonconventional
heat sink formed by two layers using water and a fluorinated
hydrocarbon fluid as coolants. Several staggered fins and
multiple inlet/outlet sections were manufactured on the first
and second layers, respectively. Their results showed that
this system, using water, dissipates up to 500 W/cm2 and
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IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 2, NO. 5, MAY 2012
achieves a thermal resistance as low as 12 mm2 °C/W with a
maximum pressure drop of 65 kPa. Stenike and Kandlikar [18]
experimentally determined the heat transfer coefficient with
the silicon offset strip fin arrangement to be in excess of
500 000 W/m2 °C using single-phase flow of water. Recently,
Wälchli et al. [19] proposed a heat sink configuration formed
by three interconnected layers. Water flowing through the
system experiences several direction changes due to the
horizontal and vertical channel interconnections. This results
in an increase in the heat transfer coefficient and, thus, a
reduction in the thermal resistance. Their experimental results
showed that this system yields a thermal resistance of around
0.08 K/W with a pressure drop of 40 kPa. Following the
same research theme, Escher et al. [20] proposed a novel
heat sink configuration based on manifold channels. Their
numerical results showed that this heat sink dissipates up to
750 W/cm2 with a temperature difference between the fluid
inlet and the chip of 65 K and a pressure drop lower than
10 kPa. A thermal resistance of 0.087 cm2 K/W was reported.
The heat sink by Escher et al. [20] is able to dissipate the
same heat flux as reported by Tuckerman and Pease [2], but
with a pressure drop that is 10 times lower. Clearly, these
recent studies provide a promising path for meeting the heat
dissipation requirements for the 2016s IC chips. Moreover,
the technical literature shows that the uniformity of the chip
temperature has not been considered as a design parameter
in cooling devices employing single-phase flow in laminar
region. Microchannel heat sinks using two-phase flow or boiling have been studied as an alternative for providing uniform
chip temperature [21]; however, they require the usage of water
at subatmospheric pressures due to the IC chip temperature
limit of around 80 °C. The usage of a refrigerant adversely
affects the performance and increases the cost of the system.
In this paper, a novel micro pin fin heat sink configuration
with variable fin density is proposed and analyzed. This configuration offers a reliable cooling system capable of dissipating
high heat fluxes at a low pressure drop while maintaining
uniform junction temperature.
II. U NIFORM T EMPERATURE D ISTRIBUTION C ONCEPT
A large part of the liquid-cooling technologies is based on
forced convection mechanism in internal flow. According to
the theory, the temperature difference between the coolant and
channel wall remains constant along the flow length when
fully developed condition and constant properties are assumed
under a constant heat flux boundary condition. The coolant
temperature rises along the flow length [Tfluid = Tfluid (z)]
and, therefore, the channel wall temperature increases accordingly. Assuming that the temperature difference between the
heat sink and the junction remains constant, the junction
temperature will then vary in a similar manner as the fluid
temperature along the flow direction [TIC = TIC (z)]. Based on
the conservation of thermal energy, the temperature difference
between coolant and channel wall is determined by the heat
flux and the convective thermal resistance (Fig. 1). Thus, if the
thermal resistance is constant, it would result in a temperature
Fig. 1. Sketch of temperature variation in internal flow systems subject to
constant heat flux and thermal resistance.
Fig. 2. Sketch of temperature variation in an internal flow system subject
to constant heat flux, uniform wall temperature, and variable total thermal
resistance.
variation as shown in Fig. 1 and described by Eq. (1)
Tbottom (z) − Tfluid (z) = q Rtotal .
(1)
According to (1), and considering a constant heat flux, a
constant junction temperature is achieved when the thermal
resistance reduces along the flow length as indicated in Fig. 2.
Since the thermal resistance varies inversely with the product
h A, this product should increase linearly along the flow length
to achieve a uniform surface temperature.
Microchannels technical literature indicates that the heat
transfer coefficient increases when: 1) the channel hydraulic
diameter decreases; or 2) the channel aspect ratio decreases.
Although these options improve the heat dissipation in conventional microchannel heat sinks, the pressure drop goes up in an
inverse cubic proportion to the hydraulic diameter. Moreover,
a single microchannel should be divided into a number of
sections along the flow length in order to gradually increase
the heat transfer coefficient and generate uniform junction
temperature. This clearly affects the complexity and cost of
the cooling device. On the other hand, using variable density
pin fins provides a simple way to enhance heat transfer rate
while maintaining a uniform surface temperature.
Pin configuration has been analyzed by a few investigators
[15], [22], but with constant fin density. Section III presents
the design of the fin arrangements with variable fin density
for the heat sinks proposed in this paper.
RUBIO-JIMENEZ et al.: NUMERICAL ANALYSIS OF NOVEL MICRO PIN FIN HEAT SINK
SL,I
SL,III
ST,I
Flow direction
ST,III
ST,II
SL,II
827
...
...
SI
Fig. 3.
SII
SN
SIII
Sketch of sections marked on the square heat sink. The transversal and longitudinal rows, ST and S L dimensions, and fin places are shown.
TABLE I
H EAT S INK PARAMETERS FOR THE T HREE C ONFIGURATIONS
50 µ m
Parameter
Flow
direction
25 µm
Fin length
Fig. 4.
Fin length
Pin fin shapes and dimensions considered in the analyses.
III. M ODEL D EFINITION
A 10-mm × 10-mm IC chip surface is considered as the
base for designing and building the novel micro pin fin heat
sinks with variable fin density. The cooling system is formed
by fins placed on a 200-μm-thick silicon substrate. In order to
generate the variable fin density, sections (SI, SII, … SN) are
marked parallel to the flow direction on this surface (Fig. 3).
A number of transversal and longitudinal rows separated by
ST and SL , respectively, are marked at each section. One pin
fin is placed at each intersection. Three overall configurations
are developed.
1) Configuration I: micro pin fin heat sinks formed by
990 fins placed on four sections. The fin height is
200 μm. Four fin shapes are considered (circle, square,
ellipse, and flat with two rounded sides as shown in
Fig. 4). The fin length is varied (75, 100, and 150 μm).
2) Configuration II: micro pin fin heat sinks formed by
3696 fins placed on four sections. The fin height is varied
(100, 200, and 300 μm). Flat-shaped fins are used.
3) Configuration III: micro pin fin heat sinks formed by
4748 fins placed on three sections. The fin height is
200 μm. Flat-shaped fins are considered.
Table I shows the geometrical parameters for these configurations. Additionally, the following two configurations are also
analyzed for comparison.
1) Microchannel heat sink formed by 33 rectangular channels with 200-μm height, channel aspect ratio of 1.0 and
space between the channels of 100 μm.
Length (mm)
No. of pin fins
No. of
longitudinal rows
No. of transversal
rows
S L (μm)
ST (μm)
ρ pin fin (no. of
pin fins/mm3 )
Section I
Section II Section III Section IV
Configuration I
1.4
2.8
4.2
1.6
0
231
462
297
0
7
7
3
0
33
66
99
0
0
400
300
600
150
600
100
0
41.66
55.55
93.75
4.2
1848
1.8
1188
Length (mm)
No. of pin fins
No. of
longitudinal rows
No. of transversal
rows
S L (μm)
ST (μm)
ρ pin fin (no. of
pin fins/mm3 )
1.0
0
Length (mm)
No. of pin fins
No. of
longitudinal rows
No. of transversal
rows
S L (μm)
ST (μm)
ρ pin fin (no. of
pin fins/mm3 )
1.5
330
Configuration II
3.0
660
0
20
28
12
0
33
66
99
0
0
150
300
150
150
150
100
0
111.11
222.22
333.33
3.3
2178
–
–
Configuration III
5.2
2240
10
34
22
–
33
66
99
–
150
300
150
150
150
100
–
–
111.11
217.94
333.33
–
2) Heat sink formed by a single large channel of 200-μm
height and 9.9-mm width. This model is called non-pin
fin heat sink.
The thickness of the silicon substrate under the channels
for all models is 200 μm. Due to the symmetry that the heat
sinks present, only 1/66 part of the heat sink was modeled. The
effects of the external walls in the large channel are considered
negligible.
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IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 2, NO. 5, MAY 2012
Symmetries
Flat-shaped fins
the assumptions and boundary conditions mentioned previously. The finite-volume vertex-centered code was used for
getting the initial approach. A second-order upwind scheme
was used for discretizing the momentum equation, whereas a
SIMPLE algorithm was used for the pressure–velocity coupling [25]. Convergence criterion was set to 1 × 10−6 for
residuals
∇U = 0
ρ (U · ∇U ) + P − = 0
U · ∇T = 0
ρ c p (U · ∇T ) − k f ∇ 2 T = 0
Fluid
flow
Silicon substrate
Fig. 5. Mesh generated in the MF-50 × 100 ×200-66 model formed by
>500 000 hexahedral elements.
IV. N UMERICAL A NALYSIS
A. Assumptions
The following assumptions are made in the numerical
modeling:
1) steady state;
2) water enters the heat transfer area with uniform velocity
at ambient temperature (293 K);
3) constant fluid and solid thermal properties (except fluid
viscosity, given by (2) [23], [24]);
4) constant and uniform heat flux from the substrate;
5) negligible radiation effects
(2)
μ = 2.414 × 10−5 10247.8/(T −140) .
B. Mesh Generation and Boundary Conditions
The mesh generated for each model is formed by approximately half million hexahedral elements distributed uniformly,
except in the section near fin walls where a cell ratio of 1.025
is set. This mesh is adapted to the fin shape. Fig. 5 shows
a part of the solid domain and its mesh. A mesh sensitivity
analysis was performed to reach the appropriate number of
elements for achieving convergence.
The boundary conditions for the models are adjusted according to the fluid-surrounding interactions. A constant mass flow
rate is considered at the fluid inlet section of the model. A
constant heat flux is set at the bottom wall of the solid domain.
A mass conservation condition was adjusted at the fluid outlet
section. Symmetry conditions for both domains are considered
at the symmetry walls. The walls which interact between both
domains are set as interface conditions. The upper wall of the
channel and the fins are considered adiabatic.
C. Numerical Model and Validation
Commercial CFD software was used for numerically solving
the governing equations (3)–(6) for both domains considering
(3)
(4)
for solid
(5)
for fluid.
(6)
Results are generated for the flow and temperature fields,
and pressure domain in both domains. In order to validate
the numerical results, the fluid temperature difference in a
micro pin fin heat sink model and the pressure drop in the
microchannel heat sink model were determined and compared
with the analytical results. The average temperature and
pressure values at the fluid inlet and outlet sections are calculated using numerical surface integration using (7) and (8),
respectively. Equations (9) and (10) were used to determine
analytically the fluid temperature and pressure difference. For
the pin fin heat sink geometry with 1 mL/s of water and a
heat flux of 100 W/cm2 , the numerical and analytical fluid
temperature differences are 24.07 and 23.91 K, respectively.
The error is lower than 0.7%. For the microchannel heat sink
geometry with 1 mL/s of water and the same heat flux, the
numerical and analytical pressure drop are 1.65 and 1.70 kPa,
respectively. Overall, the agreement with the numerical results
and theoretical predictions is seen to be reasonable
1
Tx,y d Ac out −
Tx,y d Ac in
(7)
T =
A c Ac
A
c
1
P =
(8)
Px,y d Ac out −
Px,y d Ac in
A c Ac
Ac
q As
T =
(9)
ṁcp
2Poμu L
ρu 2
P =
.
(10)
+
K
Dh 2
2
V. R ESULTS
A. Effects of Pin Fin Shapes
Fig. 6 shows the junction temperature variation of the micro
pin fin heat sink based on Configuration I with different fin
shapes along the dimensionless flow direction (z ∗ = z/L). The
operating conditions are: flow rate of 1 mL/s and heat flux of
100 W/cm2 . For simplification, the heat sinks are called as
MA-50 × LLL × HHH-NN, where:
1) A indicates the fin shape (C-circle, S-square, E-ellipse,
and F-flat);
2) LLL indicates the fin length (μm);
3) HHH indicates the fin height (μm);
4) NN indicates the number of longitudinal rows that forms
the arrangement.
The temperature variations for microchannel and non-pin fin
heat sink are studied as well. Although these last two models
RUBIO-JIMENEZ et al.: NUMERICAL ANALYSIS OF NOVEL MICRO PIN FIN HEAT SINK
Fig. 6. Variation of the junction temperature along the dimensionless flow
length for the (a) microchannel heat sink, (b) non-pin fin heat sink, and
(c)–(f) micro pin fin heat sinks based on Configuration I with different fin
shapes (Table II). q = 100 W/cm2 and flow rate = 1 mL/s.
TABLE II
OVERALL P ERFORMANCE OF M ICROCHANNEL , N ON -P IN F IN ,
AND M ICRO P IN F IN H EAT S INK B ASED ON C ONFIGURATION I
W ITH D IFFERENT F IN S HAPES
Heat sink
a) Microchannel
b) Non-pin fins
c) MC50 × 50 ×
200-17
d) MS-50 × 50 ×
200-17
e) ME-50 × 75 ×
200-17
f) MF-50 × 75 ×
200-17
342.75
389.16
349.06
41.31
68.28
14.72
5.80
1.61
4.63
Pumping
γ
R
Power
(K/W)
(mm2 /mm3 )
(W)
0.498 0.194
15.00
0.962 0.053
5.20
0.561 0.152
6.91
344.02
12.06
5.76
0.510
0.190
7.40
344.30
10.06
5.01
0.513
0.166
7.42
342.46
8.47
5.61
0.495
0.185
7.47
Tbottom,avg Tbottom
(K)
(K)
P
(kPa)
have different temperature magnitudes caused mainly by the
increase in the heat transfer coefficient when microchannels
are used, the paths are similar. The lowest temperature is found
at the fluid inlet section as expected and increases almost
linearly. The largest temperature is found at z ∗ = 1.0. The
temperature differences between the bottom wall and the fluid
at the outlet are ∼41 and ∼68 K for microchannel and non-pin
fin heat sinks, respectively. Moreover, the temperature profiles
generated by the proposed micro pin fin heat sinks at this wall
are more uniform because of the fin density variation. These
temperature curves show four slight peaks/valleys near the
transition zones among fin sections (Fig. 3). These variations
are caused by three factors: 1) increase in the heat transfer area
from one section to the next; 2) increase in the heat transfer
coefficient with the increase in fin density; and 3) the entrance
region effect.
In the temperature curves for the variable fins (C-E), it
is observed that the circular pin fin (C) presents the highest junction temperature as well as the largest temperature
difference between maximal and minimal points. The flatshaped fin improves the heat dissipation since it has the
lowest junction temperature as well as the lowest temperature
difference. The overall performance of these configurations
is shown in Table II. The heat transfer area to fluid volume
829
Fig. 7. Variation of the pressure drop along the dimensionless flow length
for the (a) microchannel heat sink, (b) non-pin fin heat sink, and (c)–(f) micro
pin fin heat sinks based on Configuration I with different fin shapes (Table II).
q = 100 W/cm2 and flow rate of 1 mL/s.
ratio γ is considered as a parameter for comparison. The
results show that the heat dissipation is improved when γ
is slightly increased (e.g., the increase in γ between circleand flat-shaped fin configurations is ∼1.1%) and the overall
temperature difference is reduced by 6.25 K. The square (D)
and the elliptical (E) fin configurations present similar temperature results with minimal differences at the inlet section.
One important observation is that the fin shape does not
affect the heat dissipation since it is possible to achieve a
similar temperature profile with square- or ellipse-shaped fin
configurations because γ is almost the same in both cases.
Fig. 7 shows the pressure drop variation of micro pin
fin heat sink configurations with 17 rows and different fin
shapes. Microchannel and non-pin fin heat sinks pressure drop
variations along the flow direction are shown as well. For these
last two cases, the pressure drop variation is linear with slight
curvature at the fluid inlet section due to the hydrodynamic
development effects. There is a difference of ∼4 kPa between
the two heat sinks due to the decrease of the channel hydraulic
diameter when microchannels are used. Moreover, the pressure
curves of pin fin heat sink models show several waves along
the flow length. The increase/decrease of the fluid velocity
across the fin arrangement and the stagnation points near the
fin walls cause these paths. Overall, the results show that the
pressure drop increases when the transversal pitch is reduced,
for a given longitudinal pitch in the section. Also, it is observed
that the fin shape plays a very important role in the energy
lost by friction effects. Analyzing the results for these four
configurations, it is observed that the lowest pressure drop is
generated when circular fins are used (4.6 kPa). Moreover, the
largest pressure drop is found in square- and flat-shaped fin
configurations (∼5.7 kPa), although there is a 50% difference
of fin length between the two geometries. Thus, it is possible to
highlight that the frictional losses are greatly reduced when the
fin walls perpendicular to the flow direction are redounded, and
rise slightly when the fin length increases. These effects are
more complex when ellipse- and flat-shaped fins are compared.
Although they have the same fin length, the pressure drop is
lower in the former (∼12% lower), because it has a larger wall
curvature than the latter. According to these results, the usage
of ellipse- and flat-shaped fin arrangements formed by 17 rows
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IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 2, NO. 5, MAY 2012
Fig. 8. Overall junction temperature and pressure drop for pin fin heat sinks
with ellipse- and flat-shaped fins based on Configuration I and different fin
lengths. q = 100 W/cm2 and flow rate = 1 mL/s.
Fig. 9. Variation of the junction temperature along the flow length in the
heat sinks based on Configuration II with different fin heights and flow rates.
q = 100 W/cm2 .
TABLE III
OVERALL P ERFORMANCE OF M ICROCHANNEL , N ON -P IN F IN , AND
M ICRO P IN F IN H EAT S INK BASED ON C ONFIGURATION I W ITH
E LLIPSE - AND F LAT-S HAPED F INS S UBJECT TO D IFFERENT F IN L ENGTHS
Heat sink
g) ME-50 × 75 ×
200-17
h) ME-50 × 100 ×
200-17
i) ME-50 × 150 ×
200-17
j) MF-50 × 75 ×
200-17
k) MF-50 × 100 ×
200-17
l) MF-50 × 150 ×
200-17
Tbottom,avg Tbottom
(K)
(K)
γ
344.30
10.06
P
(kPa)
5.01
340.73
8.50
5.39
0.477
8.00
335.83
4.31
5.74
0.428
9.26
342.46
8.47
5.61
0.495
7.47
339.13
4.19
6.17
0.461
8.14
335.33
5.15
7.46
0.423
9.96
R
(K/W)
0.513
(mm2 /mm3 )
7.42
produces better performing heat sinks. However, the thermal
resistance is larger than the value required by 2016s IC chips.
B. Effects of Fin Length
Fig. 8 shows the junction temperature and pressure drop
of the heat sink with ellipse- and flat-shaped fins for three
different fin lengths (75, 100, and 150 μm). The heat
dissipation is improved when the fin length is increased
because of the increase of γ (Table III). The average
bottom temperature is reduced 2.5 and 2.1% for ellipse- and
flat-shaped fins, respectively, when the fin length is varied
from 75 to 150 μm. Moreover, the pressure drop is larger
when flat-shaped fins are used due to the increased area of
the surface walls parallel to the flow direction. The results
indicate that, although the ellipse-shaped fin heat sink has the
largest improvement in the heat dissipation with the increase
in the fin length, the lowest IC chip temperature is achieved
using flat fins. Thus, it is highly recommended to use the
latter fin shape in this kind of micro heat sink.
C. Effects of Fin Height and Flow Rate
Fig. 9 shows the junction temperature variation along the
flow length for micro heat sinks based on Configuration II with
different fin heights and flow rates. Clearly, the heat dissipation
Fig. 10. Thermal resistance variation for different flow rates and fin heights
(h f ) based on Configuration II. q = 100 W/cm2 .
is improved when the amount of coolant increases; however,
the junction temperature variation loses uniformity. Two different effects in the two adjacent sections cause this uniformity
loss. First, the heat sink works as a single channel in the first
section (SI) whereby the heat dissipation is improved when the
fin height (channel height) decreases and vice versa (e.g., the
bottom temperature at z ∗ = 0.1 is 321.5 and 331.46 K when
the fin height is 100 and 300 μm, respectively). Second, the
increase in the fin height improves the heat dissipation at the
subsequent sections (SII–SIV) because the heat transfer area
increases (e.g., the bottom temperature at z ∗ = 0.8 is 328.06
and 324.2 K when the fin height is 100 and 300 μm, respectively). The variation in the fin height positively affects the heat
dissipation of the system at one section, and negatively affects
at another section at the same time, thus seriously affecting
the temperature uniformity. Therefore, it is recommended to
avoid sections without fins in this kind of micro heat sink.
Fig. 10 presents the overall thermal resistance variation in
the heat sinks based on Configuration II for different flow rates
and fin heights. The thermal resistance is almost the same
for the three fin height cases when the flow rate is below
1.5 mL/s. For flow rates higher than 1.5 mL/s, the effects
of increasing the heat transfer area becomes more important
for the heat dissipation. These results show that the 60-rows
heat sink configuration requires a higher flow rate of water
for getting thermal resistance values around 0.1 K/W since
this curve decreases slightly after 2 mL/s.
RUBIO-JIMENEZ et al.: NUMERICAL ANALYSIS OF NOVEL MICRO PIN FIN HEAT SINK
Fig. 11. Pressure drop variation for different flow rates and fin heights based
on Configuration II. q = 100 W/cm2 .
TABLE IV
831
Fig. 12. Variation of fluid temperature and junction temperature along the
flow direction for (a) conventional microchannel heat sink, (b) non-pin fin
heat sink, and (c) conventional pin fin heat sink with constant fin density
based on Configuration III.
OVERALL P ERFORMANCE OF M ICRO P IN F IN H EAT S INK BASED ON
C ONFIGURATION II W ITH D IFFERENT F IN H EIGHTS AND F LOW R ATES
Tbottom
(K)
R
(K/W)
Mass flow
rate (mL/s)
Tbottom,avg
(K)
1
326.09
10.68
44.13
0.339
2
316.15
6.32
98.80
0.232
3
311.88
7.72
163.04
0.189
P(kPa)
m) MF-50100 × 100-60
n) MF-50 × 100 × 200-60
1
326.47
10.30
13.87
0.335
2
3
316.92
312.78
10.50
9.01
30.04
49.50
0.239
0.198
1
326.55
11.90
7.99
0.336
2
317.24
12.32
17.30
0.242
3
313.41
11.57
27.68
0.204
o) MF-50 × 100 × 300-60
Fig. 11 shows the pressure drop variation when the fin
height is varied for different flow rates. The pressure rises
when the flow rate increases; however, the friction losses are
larger for fin heights lower than 200 μm. The effects of the
single channel at SI and the decrease of the gap between fins
(“apparent channels”) in the subsequent sections cause this
large pressure drop. The fin height effects are minimal after
this point for fin heights larger than 250 μm.
Table IV presents the overall performance of Configuration I
subject to different fin heights and flow rates. These results
show that the usage of fins with 200-μm height generates
good results. The heat sink could achieve thermal resistance
values around 0.2 K/W.
D. Performance of MF-50×100×200-66 Heat Sink
Fig. 12 shows the junction temperature profile of the micro
pin fin heat sink based on Configuration III. The temperature
profiles generated with microchannel heat sink and non-pin
fin heat sink models are added for comparison. Fig. 13 shows
that this heat sink configuration reaches a comparably lowaverage bottom temperature with a uniform temperature profile
(Tbot,ave = 39.9 °C, T = 5.7 °C) as compared to the
Fig. 13. Thermal resistance and pressure drop variation for different flow
rates in MF-50×100×200-66 heat sink.
microchannel heat sink (Tbot,ave = 57 °C, T = 38 °C) and
the non-pin fin heat sink (Tbot,ave > 100 °C, T = 68 °C).
In this paper, the temperature gradient along the flow length
is used as a parameter for comparison. Thus, according to the
temperature differences shown above, the microchannel heat
sink, the non-pin fin heat sink, and the MF-50×100×200-66
heat sink have temperature gradients of 6.83 °C/mm,
3.75 °C/mm, and only 1.63 °C/mm, respectively. Since the
lower temperature gradients reduce thermal stresses and other
adverse effects, the proposed heat sink is expected to increase
the lifetime of the IC chips.
Revisiting Fig. 12, there are two drastic zones found in the
temperature curves of the MF-50 × 100 × 200-66 heat sink at
the positions where changes of section take place. Considering
the maximal and minimal points at the vicinity of these zones,
the temperature gradient is ∼2.7 °C/mm. Although this value
is larger than the overall temperature gradient of the device, it
remains below the gradient values found in the microchannel
heat sink and non-pin fin heat sink. It is possible to redesign
the local fin configuration in this zone to reduce this effect.
Fig. 13 shows the thermal resistance and pressure drop
variation of the MF-50 × 100 × 200-66 heat sink for different
flow rates. These results show that this proposed heat sink is
attractive since it is capable of achieving the thermal resistance
832
IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 2, NO. 5, MAY 2012
TABLE V
P ERFORMANCE OF S EVERAL H EAT S INKS I NTO THE L IQUID -C OOLING
T ECHNOLOGIES AND THE MF-50 × 100 × 200-66 H EAT S INK
Author
Description
Tuckerman
and Pease
(1981) [2]
Knight et al.
(1992) [9]
Rectangular
microchannel heat
sink
Rectangular
microchannel heat
sink using
turbulent flow
Rectangular
microchannel heat
sink for multichip
modules
Micro heat sink
with circular
staggered pin fins
Micro heat sink
with semielliptical
staggered pin fins
Optimized
microchannel heat
sink
Radial heat sink
with boiling fluid
Gillot et al.
(2000) [10]
Peles et al.
(2005) [15]
Colgan et al.
(2007) [17]
Husain and
Kim
(2008) [11]
DaguenetFrick et al.
(2010) [26]
Escher et al.
(2010) [20]
This paper
(2011)
Heat sink formed
by manifold
channels
MF-50 × 100 ×
200-66
P
(kPa)
R
(K/W)
207
0.090
Pump
q ∗
Power max 2
(W/cm )
(W)
2.3
>650
207
0.056
>10.0 >1000
180
0.092
∼47.0 >650
203
0.039
–
>1500
<35
0.105
<0.9
>500
–
0.081
–
>700
–
0.080
0.05
750
<10
0.087
∼0.15 >680
29.5
0.207
0.04
230
∗ Considering 1 × 1-cm IC chip with maximum design temperature of
85 °C and ambient temperature of 25 °C.
needed by 2016s IC chips [1] (0.14–0.25 °C/W) with a reasonable pressure drop penalty (28–90 kPa). Also, the pumping
power required in the systems is ranging from 0.02 to 0.34 W
which is at least 10 times lower than microchannel heat sinks.
Table V presents the overall performance of different micro
heat sink systems studied in the literature. The MF-50×
100×200-66 performance is also shown for comparison. The
results show that the proposed heat sink has a pressure drop
considerably lower than other microchannel heat sinks [2], [9],
[10] and the pin fin heat sinks proposed by Peles et al. [15].
The cooling device proposed by Escher et al. [20] is seen
to have a lower resistance value due to multiple manifolds.
However, the low flow rate required by MF-50×100×200-66
makes it more reliable than Escher et al.’s device [20] and
microchannel heat sinks [2] because the pumping power is
only 0.04 W (∼4 times lower than the Escher et al.’s heat
sink and ∼50 times lower than Tuckerman and Pease’s heat
sink). Only the boiling system proposed by Daguenet-Frick et
al. [26] presents similar pumping power value. Although this
proposed cooling system has the largest thermal resistance of
all devices, it could effectively dissipate the maximum heat
generation rate of 288 W expected in 2016 IC chips while
maintaining the surface temperature within allowable limit and
presenting the lowest temperature gradients among the systems
analyzed in this paper.
VI. F UTURE W ORK
The analysis presented in this paper clearly identifies the
benefits of using variable-density fins in 3-D IC packaging
for achieving uniform junction temperature along the flow
length. Efforts are being continued at Rochester Institute of
Technology to experimentally validate these findings.
VII. C ONCLUSION
Micro pin fin heat sinks with variable fin density were
analyzed numerically in order to dissipate the high heat fluxes
expected from the 2016s IC chips with low pressure drops and
uniform junction temperatures. The results showed that the fin
shape plays an important role in the pressure drop rather than
the heat dissipation which was mainly affected by the heat
transfer area to fluid volume ratio γ . The best performance
was obtained when flat-shaped fins were used. The 100-μm
fin length made the system more desirable (good heat
dissipation with a reasonable pressure drop). Moreover, the
results generated with the fin height variation were interesting
since two different effects were found. According to these
observations, it was recommended to avoid the usage of
sections without fins in this kind of micro heat sink systems.
The MF-50 × 100 ×200-66 heat sink presents better performance compared to previous microcooling devices reported
in literature. This proposed device can dissipate the heat
flux expected by the 2016s IC chips with a pressure drop
around 20 kPa and a pumping power as low as 0.04 W.
Further, the system keeps the junction temperature uniform
within 6 °C. Considering the temperature gradient as a parameter for comparison, this cooling system has an overall
value of 1.63 °C/mm which was four times lower than the
temperature gradient generated in rectangular microchannel
heat sinks subject to similar sizes and operating conditions.
ACKNOWLEDGMENT
This paper was conducted in the Thermal Analysis,
Microfluidics, and Fuel Cell Laboratory at Rochester Institute
of Technology (RIT), Rochester, NY. The authors would like
to thank D. Kudithipudi in the Department of Computer
Engineering, RIT, for his support and insightful discussions.
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833
Carlos A. Rubio-Jimenez received the B.S. and
M.S. degrees in mechanical engineering from the
University of Guanajuato, Salamanca, Mexico, in
2007 and 2008, respectively, where he is currently
pursuing the Ph.D. degree in mechanical
engineering.
He is involved in designing reliable micro heat
sinks for cooling high-tech electronic devices.
He has published a few conference and journal
papers. He is a CONACYT Scholar and received a
Fulbright Garcia-Robles Scholarship for developing
the experimental work of his Ph.D. project with the Rochester Institute of
Technology, Rochester, NY.
Satish G. Kandlikar received the Ph.D. degree from
the Indian Institute of Technology, Mumbai, India,
in 1975.
He is a Gleason Professor of mechanical engineering with the Rochester Institute of Technology
(RIT), Rochester, NY. He was a Faculty Member at the Indian Institute of Technology, Bombay,
before joining RIT in 1980. His research is concerned with heat transfer and fluid flow phenomena
in microchannels and minichannels, and with
advanced single-phase and two-phase heat exchangers incorporating smooth, rough, and enhanced microchannels. He has published more than 180 journal and conference papers.
Dr. Kandlikar is a fellow of the American Society of Mechanical Engineers
(ASME), an Associate Editor of a number of journals including the ASME
Journal of Heat Transfer, and an Executive Editor of the Heat Exchanger
Design Handbook published by Begell House. He received the RIT’s Eisenhart
Outstanding Teaching Award in 1997 and the Trustees Outstanding Scholarship Award in 2006. Currently, he is involved in a project on fuel cell water
management under freezing conditions, sponsored by the U.S. Department of
Energy.
Abel Hernandez-Guerrero received the B.S. degree
from the University of Guanajuato, Salamanca, Mexico, and the Ph.D. and M.S. degrees from Oregon
State University, Corvallis.
He has published more than 220 scientific papers
in journals and international energy conferences.
Dr. Hernandez-Guerrero was the President of the
Mexican Society of Mechanical Engineering from
2000 to 2002 and the Chair of the American Society
of Mechanical Engineers (ASME) Student Sections
Committee from 2006 to 2010 and the ASME
Advanced Energy Systems Division from 2007 to 2008. He has been a
member of the Mexican System of Researchers (National Top Honors Society)
since 1992. He received the ASME Student Section Advisor Award in 2001
and the ASME Johnson & Johnson Medal in 2006. He was an Associate
Editor of the ASME International Journal of Fuel Cell Technology, and a
member of the Editorial Board of the International Journal of Exergy, the
International Journal of Energy Research, and the International Journal of
Thermodynamics. He is a fellow of ASME.