86 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 3, NO. 1, JANUARY 2013
Abstract— A comparison of the performances of online and offset micro pin-fin heat sinks with variable fin density is given in this paper. The cooling systems generate uniform junction temperatures, which improves the integrated circuit (IC) chip’s performance. Water is used as a coolant in the single phase and laminar regime. 4748 micro flat fins with rounded sides, which are distributed in three different sections along the flow length, are used in these configurations. The bottom wall temperature profile along the flow length, overall thermal resistances, pressure drops, and pumping powers for both configurations are presented. The results indicate that the offset micro pin-fin heat sink is a good alternative for cooling the IC chips of 2016. The cooling system using this fin configuration is capable of achieving a thermal resistance as low as 0.1 K/W with a pumping power requirement of 0.45 W. Comparisons with other cooling devices reported in the technical literature are presented.
Index Terms— Micro pin-fin heat sink, online and offset fin configurations, uniform junction temperature, variable fin density.
I. I NTRODUCTION
E LECTRONIC devices are the keystone in a large part of industrial processes and entertainment. The main component of these devices is the integrated circuit (IC) chip. In the past decades, these microelectronic systems have shown extraordinary growth. Currently, high-tech electronic devices (e.g.,
Intel and Xeon processors) have achieved processing speeds of 6.4 GT/s (3.2 GHz) in multicore packages [1]. This high performance comes from deep studies upon each component, making each single electronic device highly reliable, smaller, lighter, and cheaper. This trend in miniaturization generates important technological challenges: research of new materials and manufacturing techniques, appropriate heat dissipation, and packaging system, etc.
Manuscript received March 3, 2012; revised August 29, 2012; accepted
September 14, 2012. Date of publication December 11, 2012; date of current version January 4, 2013. This work was supported by the Consejo Nacional de Ciencia y Tecnología (CONACYT), Mexico. This work was conducted at the Thermal Analysis, Microfluidics and Fuel Cell Laboratory, Rochester
Institute of Technology. Recommended for publication by Associate Editor P.
Dutta 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, Universidad de 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.2012.2225143
In 2006, the international technology roadmap for semiconductors (ITRS) forecast the scenario for the generation of
9-nm CMOS devices for 2016 [2]. According to this roadmap, the next generation of IC chips is going to be designed with the current maximum design temperature (
<
85 °C), but the thermal energy generated by them should be up to 288
W. This implies that the new generation of cooling systems should have a thermal resistance ranging from 0.14 °C/W to
0.25 °C/W with high reliability and adequate size. Currently,
IC chip cooling systems are based on air-cooling technologies.
The total heat transfer surface required by these heat sinks is directly proportional to the total thermal energy to be dissipated. Clearly, this is an important drawback for future applications since their size and weight are limiting factors.
Liquid cooling technologies have emerged as a viable alternative for cooling electronic devices. Tuckerman and
Pease [3] showed that it is possible to substantially increase the heat transfer coefficient when a fluid is passing through microchannels. Heat sinks based on these channel dimensions were analyzed experimentally. Their results showed that this kind of cooling systems can achieve a thermal resistance of 0.09 K/W, and dissipate up to 790 W/cm
2 with a water temperature rise of 71 °C. Although these results indicate that this kind of cooling systems can be perfectly used in the near future in IC chip packaging, there are important drawbacks that limit their application. First, the fluid pressure drop is very large ( > 200 kPa), affecting directly the energy required by the system. Second, the temperature at the bottom wall of the heat sink along the flow length is highly nonuniform ( T ∼ 70 °C in 10 mm), reducing seriously the chip’s performance and lifetime [4], [5] and causing clock skew on the system [6].
Numerous studies on micro phenomena [7]–[9] and designs of reliable microchannel heat sinks [10]–[12] can be found in the literature. Some nonconventional techniques and methodologies have been used to design this kind of microcooling systems [13]–[15]; however, only a few works have shown outstanding performance that suit future needs. Among the most outstanding works is the research of Peles et al. [16].
They proposed a micro pin-fin heat sink with constant fin density as an alternative cooling system for IC chips. They used the correlations provided previously in a bank of tube analyses at the macroscale. Their experimental results showed that this configuration was capable of dissipating up to
790 W/cm
2 with a temperature rise of 30.7 °C. Thus, the system thermal resistance is 0.039 K/W. The major drawback of this heat sink was the large pressure drop generated in the system (
>
200 kPa). Colgan et al. [17], [18] proposed a nonconventional heat sink formed by two layers. Several
2156–3950/$31.00 © 2012 IEEE

RUBIO-JIMENEZ et al.: PERFORMANCE OF ONLINE AND OFFSET MICRO PIN-FIN HEAT SINKS 87 stages of fins were manufactured on the first layer. Inlet/outlet zigzagged sections were incorporated on the second layer.
Then, both layers were bonded face to face. The results showed that this system could achieve a thermal resistance as low as 12 mm
2
°C/W and dissipate a heat flux of 50 W/cm
2 when water is flowing through the arrangement. The maximum pressure drop was reported as 65 kPa. In the same way,
Wälchli et al. [19] analyzed a heat sink configuration formed by three interconnected layers. Flowing water was used as the coolant. The change of direction caused by the horizontal and vertical channel interconnections increased strongly the heat transfer coefficient. Their results showed that this configuration was capable of reaching thermal resistance values as low as
0.08 K/W with a pressure drop of only 40 kPa. Recently,
Escher et al. [20] proposed a novel cooling system based on the results of Wälchli et al. [19]. Their system was formed by manifold channels that were placed perpendicularly. Numerical analysis showed that this kind of arrangement dissipates up to 750 W/cm
2 with a temperature difference of 65 °C and a pressure drop of lower than 10 kPa. The thermal resistance of this device was around 0.08 m
2
K/W. These results show an improvement in the reliability of microcooling systems because this heat sink can dissipate the same heat flux as the microchannel heat sink proposed in [3] but with 10 times lower pressure drop. Although these results are very encouraging for near-future applications, further studies are needed in order to reduce the large temperature variation that these devices generate in the IC chip. Moreover, several investigations are aimed at the design of 3-D IC chip packaging. Clearly, an appropriate thermal management is extremely required. Thus, new designs of microcooling systems have to consider easy stack integration.
An alternative for reducing the temperature variation on the IC chips is the use of flow boiling [21]. However, water at subatmospheric conditions or a refrigerant is required, resulting in significant increase in the cost of the system.
Recently, Rubio-Jimenez et al. [22] proposed a micro pinfin heat sink with variable fin density as an alternative for cooling the next generation of IC chips. The design of these systems considers the reduction of the temperature variation on the IC chip. Their numerical results show that a micro pin-fin heat sink with 4748 flat fins placed in an online fin configuration can achieve thermal resistance values ranging from 0.14 to 0.25 K/W with pressure drops lower than
100 kPa. The temperature gradient at the junction wall between the heat sink and the IC chip was proposed as a parameter of comparison. Temperature gradients lower than 2 °C/mm were observed.
On the other hand, Steinke and Kandlikar [23] have proposed and studied some passive enhancement techniques for microchannels and mini-channels. Their discussion indicates that the inclusion of some flow disruptions can serve to trip the boundary layer and, importantly, increase the heat dissipation. Offset strip fins were proposed as an alternative for microchannel heat sinks. Carefully constructed geometries were suggested.
Steinke and Kandlikar [24] and Steinke et al. [25] carried out experimental analyses in enhanced microchannel heat
Fig. 1.
Sketch of micro pin-fin heat sink with variable fin density for both online and offset fin configurations.
sinks formed by offset strip fins with 250–500-
μ m length and
50-
μ m channel width. Their results showed that this device could achieve a thermal resistance as low as 0.1 K/W and dissipate up to 1000 W/cm
2
. However, the pressure drop was still in the range of 150–180 kPa.
Taking into account the conclusions of [23], this paper analyzes the overall performance of micro heat sinks when offset fin configurations with variable fin density are used as the base for designing microcooling systems. Therefore, the online fin configuration analyzed in [22] is used as the starting point (MF-50
×
100
×
200
−
66). Then, the thermal and hydrodynamic performances of both online and offset configurations are compared. Furthermore, a comparison of these heat sinks with other microcooling systems found in the literature is provided.
II. M ODEL D EFINITION
In this paper, a 10 × 10 mm IC chip is considered as the base for designing and building the offset micro pin-fin heat sinks with variable fin density. The cooling system is formed by 4748 flat fins placed on a 200-
μ m-thick silicon substrate. The fin width, length, and height are 50, 100, and
200
μ m, respectively. The rounded sides have a radius of
25
μ m. The heat sink is divided longitudinally in three sections
(SI, SII, and SIII). Fig. 1 shows a sketch of these sections for both online and offset fin configurations. Table I shows the parameters for each section.
For comparison, a microchannel heat sink formed by
33 rectangular channels with 200
μ m height, channel aspect ratio 1.0, space between channels 100
μ m, and substrate silicon thickness 200
μ m is analyzed. Only 1/66 of the heat sinks were modeled because of their symmetry.

88 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 3, NO. 1, JANUARY 2013
TABLE I
H EAT S INK P ARAMETERS FOR B OTH M ICRO P IN -F IN H EAT S INKS
Section I Section II Section III
1.5
5.2
3.3
330
10
33
150
300
111.11
2240
34
66
150
150
217.94
2178
22
99
150
100
333.33
Symmetries
Parameter
Length (mm)
No of pin fins
No. of longitudinal rows
No. of transversal rows
S
L
(
μ m)
S
T
(
μ m)
ρ pin fin
(No. of pin fins/mm
3 )
Flat-shaped fins
III. N UMERICAL A NALYSIS
A. Assumptions
The numerical analysis is based on the following assumptions.
1) The system is in the steady state.
2) Water in single phase and laminar regime enters the system at ambient temperature (25 °C) under nondeveloped conditions.
3) The fluid and solid thermal properties remain constant, except fluid viscosity, which is given by (1). The justification to this assumption can be found in [26] and
[27].
4) The heat flux is constant and uniform.
5) Radiation effects can be neglected
μ =
2
.
414
×
10
−
5
10
247 .
8
T − 140
.
(1)
B. Mesh Generation and Boundary Conditions
The mesh generated in the model is formed by approximately half a million hexahedral elements distributed uniformly, except in the section near the fin walls where a cell ratio of 1.025 is set. This mesh is adapted to the fin shape. Fig. 2 shows a part of the solid domain and its mesh.
A mesh sensibility analysis was done in order to arrive at the appropriate number of elements for achieving satisfactory results.
The boundary conditions for the models are adjusted according to the interaction of the fluid with the surroundings.
A constant mass flow rate is considered at the fluid inlet section of the model. It is important to highlight that the velocity profile is not considered because of the effects of developing the boundary layer at this inlet section (which otherwise becomes reduced), affecting the goal of increasing the heat transfer coefficient. A constant heat flux is imposed on the bottom wall of the solid domain. Zero static pressure is assumed at the fluid outlet section. Symmetry conditions for both domains are considered at the symmetry walls. The walls between the domains are set as interface conditions. The upper wall of the channel and fins are set as adiabatic conditions.
C. Numerical Model
A commercial computational fluid dynamics (CFD) software (specifically, ANSYS Fluent) was used for numerically
Fig. 2.
Mesh generated in the offset micro pin-fin heat sink model formed by nearly 500 000 hexahedral elements.
solving the governing equations (2)–(5) for both domains under the assumptions and boundary conditions mentioned above. 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, while the
Simple algorithm was used for the pressure–velocity coupling
[28]. The residuals were set to 1
×
10
−
6
∇
U
=
0
ρ U · ∇ + P − = 0
∇ 2
T
=
0 for solid
ρ c p
U
· ∇
T
− k f
∇ 2
T
=
0 for fluid where involves the viscous effects generated in the system due to the relative velocity of the fluid through the channels [26]. The Reynolds number was in the range 100–200, which was well within the laminar domain. The temperature fields for both domains and the fluid velocity and pressure variations are the results presented in this paper. The mesh used in the numerical solution, as well as the accuracy of the numerical results with theory, was studied as well. These processes are described next.
D. Validation of the Numerical Model
Fluid flow
Silicon substrate
(2)
(3)
(4)
(5)
A mesh sensibility analysis is carried out in order to identify the appropriate number of elements to be used in the numerical analysis. This analysis is based on solving numerically the model subject to the boundary conditions and operating parameters mentioned previously, beginning with an initial number of elements. Once the solution is computed, the number of elements in the mesh is increased through a specific ratio (e.g., in the second approach, the number of elements was doubled from the initial mesh). Thus, a second mesh is obtained and used for computing the numerical solutions considering the same operational parameters and boundary conditions. Thereafter, the range of error is evaluated between both solutions comparing the bulk temperature and pressure

RUBIO-JIMENEZ et al.: PERFORMANCE OF ONLINE AND OFFSET MICRO PIN-FIN HEAT SINKS 89 drop along the channel length. This process is repeated until the difference between the current and previous mesh becomes negligible. In order to demonstrate this process, we present a mesh sensibility analysis carried out on a straight microchannel heat sink.
The initial mesh was formed by 26 800 tetrahedral elements
(Mesh 1). Then, the second mesh was created by doubling the number of elements in the initial mesh along the three directions (x -, y-, and z-axis). This second mesh (Mesh 2) was thus formed by 53 600 elements. After computing the numerical solution considering these two meshes, a comparison of the bulk temperature and pressure drop was done. Figs. 3 and 4 present the curves of these variations. As can be seen in these figures, the curves match well for a channel length smaller than 0.4. After this point, the difference becomes larger, mainly for the fluid temperature ( ∼ 1 K). Therefore, an increase in the number of elements was considered. Another three meshes were developed (Mesh 3, 4, and 5). The number of elements was 145 000, 290 000, and 514 800 tetrahedral elements, respectively. The numerical results computed with these meshes are presented in Figs. 3 and 4.
According to this analysis, the error generated in the hydraulic part by the mesh distribution is minimal when
Mesh 3 is used [since the difference between this one and the next (Mesh 4) is
∼
10 Pa]. However, this mesh significantly affects the thermal part: making a similar comparison of the bulk temperature between these two meshes, the difference is ∼ 1.2 K. Moving on to the comparison between Mesh 4 and Mesh 5, it is observed that the difference computed through each mesh is minimal for both thermal ( ∼ 0.1 K) and hydrodynamic (5 Pa) aspects. Thus, the numerical analyses of the micro pin fin-heat sink models studied in this paper are based on meshes with at least 300 000 tetrahedral elements.
Momentum and energy balances were carried out for the system. The fluid temperature difference in the micro pin-fin heat sink model and the pressure drop in the microchannel heat sink model were calculated from the numerical results and compared with the analytical results. The average temperature and pressure values at the fluid inlet and outlet sections were determined by numerical surface integration
T
=
1
A c
1
A c
T x
, y d A c
| out
−
P
=
A c A c
T x
, y d A c
| out
−
Analytically, these differences are given
A c
T x
, y d A c
| in
A c
P x
, y d A c
| in
(6)
(7)
= q A s
(8)
P
=
2Po μ u L
Dh 2
+
K
ρ u 2
.
2
(9)
The numerical and analytical fluid temperature differences for online micro pin-fin heat sink model with operating conditions of 1 ml/s of water and 100 W/cm
2 of heat flux are 24.07 and 23.91 K, respectively. The error is less than
0.7%. Moreover, the numerical and analytical pressure drops in the microchannel heat sink subjected to the same operating
320
310
300
290
280
270
0.0
0
0.0
0.2
0.4
z*
0.6
0.8
1.0
Mesh 1
Mesh 2
Mesh 3
Mesh 4
Mesh 5
Fig. 3.
Mesh sensibility analysis for the bulk temperature in the fluid along the flow length.
35
30
25
20
15
10
5
0.2
0.4
z*
0.6
0.8
1.0
Mesh 1
Mesh 2
Mesh 3
Mesh 4
Mesh 5
Fig. 4.
Mesh sensibility analysis for the fluid pressure drop along the flow length.
conditions are 1.65 and 1.70 kPa, respectively. The error is around 3%. Although the hydrodynamic difference is slightly large, the overall results show good agreement with the analytical results.
IV. R ESULTS
According to the nomenclature used in [22], the two micro pin-fin heat sinks studied in this paper are designated as follows:
1) MF-50
×
100
×
200
−
66 on-line (micro pin-fin configuration studied in [22]);
2) MF-50
×
100
×
200
−
66 offset (this paper).
Both configurations are described in Table I. Fig. 5 shows the temperature profile along the dimensionless flow length for the microchannel heat sink and the pin-fin heat sinks with both online and offset fin configuration for 1 ml/s of water and 100 W/cm 2 of heat flux. The average temperature values

90 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 3, NO. 1, JANUARY 2013
350
340
330
320
310
300
290
0.0
0.1
Microchannel heat sink
MF-50x100x200-66 On-line
MF-50x100x200-66 Offset
Fluid temperature
0.2
0.3
0.4
0.5
0.6
Dimensionless flow length z/L
0.7
0.8
0.9
1.0
Fig. 5.
Temperature profile at the bottom wall of the heat sink along the dimensionless flow length for a microchannel heat sink and micro pin-fin heat sinks with variable fin density for both online and offset fin configurations.
q
=
100 W/cm
2 and the flow rate is 1 ml/s.
are 334.39, 314.15, and 309.63 K, respectively. Clearly, the offset micro pin-fin heat sink improves the heat dissipation and reduces the IC chip surface temperature (
∼
7.5% compared to a microchannel heat sink and 1.5% compared to the online micro pin-fin heat sink). As mentioned in [23], the constant development of the thermal boundary layer enhances the heat transfer coefficient and reduces the overall thermal resistance.
In order to ratify this, Fig. 6 presents a comparison of the contours of the velocity generated for both configurations along the flow length for the operating conditions mentioned above. The impact that the offset fin configuration generates on the fluid motion, and thus on the heat dissipation, is clearly observed in these contours. The fluid flowing through the online fin configurations has a straight motion, and a large part of the fluid passes through the straight gaps between the fins. Thus, the interaction between the coolant and the walls of the fins is significantly reduced, affecting the heat diffusion.
Moreover, when the fluid is moving through the offset fin configuration, the thermal diffusion is enhanced due to the fact that the fluid has better interaction with the heat transfer areas along the flow length. Therefore, in Fig. 6 it is observed that the offset fin configuration produces a more uniform temperature profile and reduces the peaks/valleys caused by the change of section (SI–SII and SII–SIII). The uniformity of the bottom temperature impacts directly the temperature gradients along the flow length.
The average gradient values for the online and offset fin configurations are 1.63 °C/mm and 1.19 °C/mm, respectively.
In [22], for the online fin configuration, the average temperature gradient at the vicinity of the change of sections
(SI–SII and SII–SIII) was 2.7 °C/mm. The offset micro pinfin heat sink shows a significant reduction of these local temperature gradients, mainly in the second zone. Temperature gradient values of 2.29 °C/mm and 0.9 °C/mm are generated, respectively. These results impact directly the performance and lifetime of the IC chip.
Fig. 7 shows the thermal resistance and pressure drop variations of the MF-50 × 100 × 200 − 66 micro pin-fin heat sinks for online (solid line) and offset (dotted line) configurations subject to different flow rates. Overall, the flow rate reduces the thermal resistance of the systems; however, the curves show a large negative slope when the flow rate is less than 2 ml/s and a smaller decrease after this point.
In Fig. 7, the offset micro pin-fin heat sink presents almost
1.3 times lower thermal resistance than the online micro pinfin heat sink at the same operating conditions. This is a clear manifestation of the passive thermal enhancement caused by the offset arrangement. Otherwise, the pressure drops in both fin configurations show an almost constant rise with the increase of the flow rate; however, this energy lost is larger in the offset micro pin-fin heat sink. The decrease of the
“apparent hydraulic diameter” that this fin configuration has
(the cross-sectional area is reduced by half at each section) causes this pressure drop penalty. Overall, the offset micro pin-fin heat sink generates almost 2.5 times larger pressure drop than the online microcooling system.
According to these results, both micro pin-fin heat sinks are capable of cooling the IC chips of 2016, since their overall thermal resistances lie in the range required by the
ITRS (0.14–0.25 K/W) [2]. However, the operating conditions required by these systems are different. The MF-50
×
100
×
200
−
66 online requires up to 3.8 ml/s of water for obtaining the lower value of thermal resistance (0.14 K/W), whereas the offset fin configuration needs only 2 ml/s of coolant to get the same thermal resistance condition. Moreover, the pressure drops are similar in both systems ( ∼ 90 kPa) for this thermal performance. Considering the pumping power that the system requires to work as a parameter of comparison, the offset fin configuration presents a better performance since it only requires 0.18 W of pumping energy to get a thermal resistance of 0.14 K/W. The online fin configuration requires almost twice the pumping energy (0.35 W) to obtain a similar thermal performance. In summary, the offset micro pin-fin heat sink is more reliable for near-future applications because of the following reasons:
1) it generates more uniform temperature profiles on the IC chip (overall temperature gradient of 1.2 °C/W);
2) the maximum heat expected by the IC chip of 2016
(288W) can be dissipated appropriately with only
0.18 W of energy to be supplied into the system.
Table II shows a comparison between different cooling devices found in the literature. The online and offset micro pin-fin heat sinks working with the appropriate operating conditions to get a thermal resistance of 0.14 have been included in this comparative table. The water flow rate for each configuration is 3.8 and 2.0 ml/s, respectively. Clearly, these configurations can dissipate appropriately the heat generation expected by the IC chips of 2016. The offset fin configuration requires a lower amount of energy than the online arrangements and also the other heat sinks listed in Table II
(e.g., conventional microchannel heat sink and the Colgan et al. heat sink). In this line, the micro pin-fin heat sinks are only topped by cooling systems based on boiling cooling [29].
Moreover, a large part of our work is aimed at generating cooling systems with thermal resistances lower than 0.1 K/W.

RUBIO-JIMENEZ et al.: PERFORMANCE OF ONLINE AND OFFSET MICRO PIN-FIN HEAT SINKS
(a)
91
(b)
Fig. 6.
Contours of velocity at the middle of the channel section (y
=
300
μ m) for (a) online and (b) offset microchannel pin-fin heat sink with variable fin density.
TABLE II
P ERFORMANCE OF M ICRO H EAT S INKS U SING L IQUID C OOLING T ECHNOLOGIES
Author Description P (kPa) R (K/W)
Tuckerman and Pease (1981) [3]
Knight et al. (1992) [10]
Rectangular microchannel heat sink
Rectangular microchannel heat sink using turbulent flow
207
207
0.090
0.056
Gillot et al. (2000) [11]
Peles et al. (2005) [16]
Colgan et al. (2007) [18]
Huscin and Kim (2008) [12]
Rectangular microchannel heat sink for multichips modules
Micro heat sink with circular staggered pin fins
Micro heat sink with “semielliptical” staggered pin fins
Optimized microchannel heat sink
180
203
<
35
–
0.092
0.039
0.105
0.081
Daguenet–Frick et al. (2010) [29]
Escher et al. (2010) [20]
Rubio–Jimenez et al. [22] (2011)
This paper (2011)
Radial heat sink with boiling fluid
Heat sink formed by manifold channels
MF-50
×
100
×
200
−
66 on-line
MF-50
×
100
×
200
−
66 offset
<
–
10
90
86
0.080
0.087
0.14
0.14
*Considering a 1
×
1 cm IC chip with maximum design temperature of 85 °C and an ambient temperature of 25 °C.
Pump
Power (W)
2.3
>
10
.
0
∼
47
.
0
–
<
0
.
9
–
0.05
∼
0
.
15
0.34
0.18
q max
(W/cm
∗
2 )
>
650
>
1000
>
650
>
1500
>
500
>
700
750
>
680
430
430
0.30
300 2.5
MF-50x100x200-66 on-line
MF-50x100x200-66 offset
0.25
250
2
0.20
200
1.5
0.15
150
1
0.5
0.10
100
0
0.05
50
[3] [18] [22] Current work
0.00
1 2 3
Flow rate (mL/s)
4 5
0
Fig. 8.
Thermal resistance and pressure drop variation with different flow rates for micro pin fin heat sinks with variable fin density and both online and offset fin configuration. q
=
100 W/cm
2
.
Fig. 7.
Thermal resistance and pressure drop variation with different flow rates for micro pin-fin heat sinks with variable fin density and both online and offset fin configuration. q
=
100 W/cm
2
.
Considering this thermal performance in both micro pin-fin heat sinks, an important increase of the pressure drop is clearly observed in Fig. 7, mainly for the offset fin configuration. However, when the requirements of pumping power are compared, interesting results are observed. In order to get an overall comparison, Fig. 8 presents the pumping power required by a conventional microchannel heat sink [3], a robust micro cooling system [18], and both online and offset micro pin-fin heat sink with variable fin density. All these cooling systems are operating at specific conditions in order to obtain a thermal resistance of 0.1 K/W. A very significant reduction

92 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING AND MANUFACTURING TECHNOLOGY, VOL. 3, NO. 1, JANUARY 2013 in the input energy is clearly observed with these last three cooling systems compared to conventional microchannel heat sinks (
∼
100%). Also, the robust cooling system and the offset micro pin-fin configuration present similar values of pumping power (
∼
0.9 W). Therefore, the assertion that the offset micro pin-fin heat sinks are a very good alternative for cooling near future IC chips is ratified. Furthermore, this cooling system presents an easy integration in 2-D and 3-D IC chip packaging.
Following this comparison of the pumping power, the offset micro pin-fin heat sink presents a better performance when the flow rate is less than 5 ml/s (thermal resistance around
0.1 K/W and pumping power less than 0.45 W) than the online fin configuration. Apart from this thermal resistance value, both configurations have almost similar overall pumping power requirements. Thus, novel and reliable micro cooling systems capable of generating uniform junction temperature should be looked for, for obtaining thermal resistances smaller than 0.1 K/W.
V. F UTURE W ORK
The analysis presented in this paper clearly identifies the benefits of using an offset micro pin-fin heat sink with variable fin density. We are continuing with the efforts to experimentally validate these findings and also for 3-D IC packaging integration.
VI. C ONCLUSION
An offset micro pin-fin heat sink configuration with variable fin density was studied numerically in this paper. This heat sink is based on Configuration III analyzed in [22]. The results show that this offset fin configuration improves the heat dissipation and reduces at least by 1.3 times the system thermal resistance. This represents 1.5% and 7.5% reduction in the overall bottom wall temperature compared to the online micro pin-fin heat sink and a microchannel heat sink, respectively. Furthermore, the offset fin configuration improves the temperature uniformity since the peaks/valleys that the online fin configuration presents at the change-of-section zones are smoothed. This has an important impact in the overall temperature gradient, which is reduced to 1.19 °C/W.
Hydraulically, the pressure drop rises significantly when the offset fin configuration is used in the micro pin-fin heat sink.
However, the amount of coolant that this offset fin system requires to obtain a specific thermal resistance is less than that required by the online fin configuration due to the heat transfer enhancement. The pumping power is a very good parameter for comparison. According to this parameter, these micro pinfin heat sinks have an almost similar overall performance as the Colgan et al. cooling device with a thermal resistance of
0.1 K/W.
The results show that the offset micro pin-fin heat sink is highly reliable for cooling systems with thermal resistances larger than 0.1 K/W since the pumping power is less than the pumping energy required by the online fin configurations. For cooling systems that require thermal resistances much lower than 0.1 K/W, this micro pin-fin configuration with variable fin density is not recommended because of their large increase of the pressure drop.
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Satish G. Kandlikar received the Ph.D. degree from the Indian Institute of Technology Bombay (IIT
Bombay), Mumbai, India, in 1975.
He was a Faculty Member with IIT Bombay until
1980. He is currently the Gleason Professor of mechanical engineering with the Rochester Institute of Technology, Rochester, NY. He is involved in research on advanced single-phase and two-phase heat exchangers incorporating smooth, rough, and enhanced microchannels. He is currently involved in a project on fuel cell water management under freezing conditions, which is sponsored by the Department of Energy. He has authored or co-authored more than 180 journal and conference papers. His current research interests include heat transfer and fluid-flow phenomena in microchannels and minichannels.
Dr. Kandlikar was the recipient of the RIT’s Eisenhart Outstanding Teaching
Award in 1997 and the Trustees Outstanding Scholarship Award in 2006.
He is a fellow of the 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 (Begell House).
Carlos A. Rubio-Jimenez received the B.S. and
M.S. degrees in mechanical engineering from the
University of Guanajuato, Guanajuato, Mexico, in 2007 and 2008, respectively, where he is currently pursuing the Ph.D. degree in mechanical engineering, specializing in the design of reliable microheat sinks for cooling high-tech electronic devices.
He is currently a CONACYT Scholar. He has authored or co-authored papers in refereed journals and conferences.
Mr. Rubio-Jimenez was a recipient of the Fulbright Garcia-Robles
Scholarship for research at the Rochester Institute of Technology.
Abel Hernandez-Guerrero received the B.S. degree from the University of Guanajuato, Guanajuato,
Mexico, and the Ph.D. and M.S. degrees from Oregon State University, Corvallis.
He is currently with the University of Guanajuato.
He has authored or co-authored more than 230 scientific papers in journals and international energy conferences.
Dr. Hernandez-Guerrero was a recipient of the
2001 ASME Student Section Advisor Award and the
2006 ASME Johnson Medal. He was the President of the Mexican Society of Mechanical Engineering from 2000 to 2002, the Chair of the ASME Student Sections Committee from 2006 to 2010, the Chair of the
ASME Advanced Energy Systems Division from 2007 to 2008, and has been a member of the Mexican System of Researchers (National Top Honors Society) since 1992. He is an Associate Editor of the ASME International Journal of
Fuel Cell Technology and an Editorial Board Member for many journals, including the International Journal of Exergy, the International Journal of
Energy Research, and the International Journal of Thermodynamics. He is a fellow of the ASME.