Impingement Air Cooled Plate Fin Heat Sinks
Part II– Thermal Resistance Model
Zhipeng Duan* and Yuri S. Muzychka+
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
St. John’s, Newfoundland, Canada, A1B 3X5
Email: zpduan@engr.mun.ca, yuri@engr.mun.ca
ABSTRACT
Impingement air cooling with heat sinks is one attractive
solution in thermal management of electronic components. A
simple impingement flow thermal resistance model based on
developing laminar flow in rectangular channels is proposed.
Experimental measurements of thermal resistance are
performed with heat sinks of various impingement inlet
widths, fin spacings, fin heights and airflow velocities to test
the validity of the model. The accuracy of the predicted
thermal resistance was found to be within 20% of the
experimental data at channel Reynolds numbers less than
1200. The simple model is suitable for parametric design
studies.
KEY WORDS: Impingement Flow, Heat Sink, Thermal
Resistance, Model, Plate Fin, Airflow
NOMENCLATURE
Ab
As
b
h
heff
hrad
H
I
k
ka
L
Leff
Ls
Nf
Nu
Pr
Q
Q
Qloss
R
R1D
Rbare
Rbase
Rfins
Rrad
Rsink
base plate area, m2
heat source area, m2
fin spacing, m
heat transfer coefficient , W/m2 K
effective heat transfer coefficient , W/m2 K
radiation heat transfer coefficient, W/m2 K
fin height, m
current, A
thermal conductivity of heat sink, W/mK
thermal conductivity of air, W/mK
length of heat sink base, m
effective length, m
length of heat source, m
number of fins
Nusselt number
Prandtl number
total electrical power input, W
air volume flow rate, m3/s
ambient heat loss, W
thermal resistance, K/W
one-dimensional thermal resistance, K/W
prime surface thermal resistance, K/W
conduction thermal resistance of heat sink base, K/W
fin surface thermal resistance, K/W
radiation thermal resistance, K/W
overall heat sink thermal resistance, K/W
Rsp
Rtotal
Reb*
s
t
tb
T
Ts
Tamb
Tsource
Tbase
U
W
Ws
spreading thermal resistance, K/W
total thermal resistance, K/W
modified channel Reynolds number = (bVch/ν)(b/L)
impinging inlet width, m
fin thickness, m
base plate thickness, m
temperature, °C
heat source temperature, K
ambient temperature, K
mean heat source temperature, K
mean heat sink base temperature, K
voltage, V
width of heat sink base, m
width of heat source, m
Greek symbols
eigenvalues, =(δm2+λn2)1/2
βm,n
δm
eigenvalues, =mπ/c
ζ
dummy variable, m-1
λn
eigenvalues, = nπ/d
φ
spreading function
Subscripts
1
based upon vertical channel
2
based upon horizontal channel
amb
ambient
b
base
ch
channel
Dh
based upon hydraulic diameter
eff
effective
f
fin
s
heat source
INTRODUCTION
The heat dissipated in electronic components is increasing
with advances in the performance of modern computers.
Furthermore, the structure of these components is becoming
ever more compact. Therefore, thermal management in the
electronics environment is becoming increasingly difficult
due to high heat load and dimensional constraints.
Impingement air cooling with heat sinks is one attractive
solution to these problems.
Nottage [1] suggested that the heat sink fin and channel
may be thought of as a type of heat exchanger in which the hot
fluid stream is replaced with the solid fin. The counterflow
__________________________________________
∗
+
Graduate Research Assistant
Assistant Professor
0-7803-8357-5/04/$20.00 ©2004 IEEE
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arrangement has the greatest potential to achieve high
effectiveness. This requires an airflow direction normal to the
heat sink base, however, heat sinks with airflow directed
normal to the base have received little attention. Since the
impingement airflow in a heat sink is intermediate between
counterflow and crossflow, its thermal performance is
expected to exceed that of a crossflow heat sink.
The present work is focused on the impingement flow plate
fin geometry. The research objectives are to develop a robust
model for predicting thermal resistance of plate fin heat sinks
for impingement air cooling. Experimental measurements of
thermal resistance are performed with heat sinks of various
dimensions and airflow velocities to test the validity of the
model.
LITERATURE REVIEW
Teertstra et al. [2] developed an analytical model to predict
the average heat transfer rate for air cooled plate fin heat
sinks. The Nusselt number is a function of the heat sink
geometry and fluid velocity. The model is asymptotic between
two limiting cases - fully developed and developing flow in
parallel plate channels. They validated the model with
experiments and found 2.1% RMS error and 6% maximum
error. Copeland [3] suggested using a laminar flow heat
transfer model for parallel flow in isothermal rectangular
channels to model the heat sink. The Nusselt number data was
taken from Shah and London [4] and fitted to an equation of
the Churchill-Usagi form.
s
Air inflow
Air outflow
t
b p
Air outflow
Plane Fin
H
W
Hf Hf
tb
L
Fig. 1 Geometry of a plate fin heat sink in impingement flow.
There have been few studies specifically on impingement
cooling with heat sinks. The geometry of a heat sink in
impingement flow is shown schematically in Figure 1. In this
flow arrangement the air enters at the top and exits out the
sides, i.e. TISE (top inlet side exit). Biskeborn et al. [5]
reported experimental results for a TISE design using unique
“serpentine” square pin fins. Sparrow et al. [6] performed heat
transfer experiments on an isothermal TISE type single
channel passage. Hilbert et al. [7] reported a novel laminar
flow heat sink with two sets of triangular or trapezoidal
shaped fins on the two inclined faces of a base. This design is
efficient because the downward flow increases the air speed
near the base of the fins where the fin temperatures are
highest. By having the cool air enter at the center of the heat
sink and exit at the sides, the length of the fins in the flow
direction is reduced so that the heat transfer coefficient is
increased. Sathe et al. [8] conducted a numerical and
experimental study of a TISE plate fin heat sink that was
notched in the center to reduce flow stagnation. A
combination of fin thickness of the order of 0.5 mm and
channel spacings of 0.8 mm with appropriate central cut-out
yielded heat transfer coefficients over 1500 W/m2K at a
pressure drop of less than 100 Pa. Copeland [9] performed
theoretical, experimental and numerical analyses on a
manifold microchannel heat sink with multiple top inlets
alternated with top outlets. At a given pumping power,
increasing the number of inlet/outlet channels requires an
increase in the volume flow rate, but permits higher flow
velocity, provides lower thermal resistance. Kang and Holahan
[10] developed a one dimensional thermal resistance model of
impingement air cooled plate fin heat sinks to understand how
the heat sink performance depends on the different geometry
variables. This simple model provides only an order of
magnitude estimate of the thermal resistance. Holahan et al.
[11] modeled the impingement flow field in the channel
between the fins as a Hele-Shaw flow. Conduction within the
fin is modeled by superposition of a kernel function derived
from the method of images. Convective heat transfer
coefficients are adapted from existing parallel plate
correlations. Kondo et al. [12] completed an experimental
study and reported a zonal model of a thermal resistance
prediction for impingement cooling heat sinks with plate fins.
The impingement flow over the plate fins was divided into six
regions. A set of correlations are proposed between the
thermal resistance of the heat sink and the geometry of the
plate fins. Dividing the heat sink into regions requires a large
number of equations and makes the model very complicated.
The accuracy of the predicted thermal resistance was found to
be within ±25% of the experimental data. Sathe et al. [13]
presented a computational analysis for three dimensional flow
and heat transfer in the IBM 4381 heat sink. Biber [14] carried
out a numerical study to determine the thermal performance of
a single isothermal channel with variable width impinging
flow. She numerically studied many different combinations of
channel parameters and presented the correlation for channel
average Nusselt number. Sasao et al. [15] developed a
numerical method for simulating impingement air flow and
heat transfer in plate fin heat sinks. Saini and Webb [16]
presented a modified Biber [15] model and validated this
model by experiments.
THEORETICAL MODELLING
Heat sink thermal circuit analysis
Heat sink models typically assume a uniform airflow at the
heat sink inlet. The flow in typical plate fin heat sinks used in
cooling electronic modules is laminar, because of the small fin
spacing and low airflow rates. The thermal resistance circuit
for heat flow from the electronic module surface temperature
(Ts) to ambient temperature (Tamb) is depicted in Figure 2. Heat
generated from an electronic module can be approximated as
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constant heat flux over area As. The electronic module surface
area (As) is usually too small to dissipate the heat, so a heat
sink is typically required. Since heat sink base area (Ab) is
usually larger than As, thermal spreading resistance (Rsp)
occurs when heat leaves a heat source of finite dimensions (As)
and enters into a larger region (Ab). Heat flux is assumed
uniform over the base of fins. Heat is conducted from the base
to the tip of the fins and it is convected from the fin surface
(Rfins). Heat is also convected from the prime surface (the
exposed portion of the base) (Rbare). The thermal resistance
from the fins and prime surface to the ambient air is the total
convection resistance of heat sink. The heat sink total
convection resistance is usually the dominant thermal
resistance in the thermal circuit for the electronic module
cooling.
Figure 2 illustrates the thermal circuit corresponding to the
heat transfer from a plate fin heat sink. The total heat sink
thermal resistance is
Rtotal =
Ts − Tamb
Q
Rbare Electronic Module As
Rfins
Tamb
tb
1
+
kAb heff Ab
Rsp =
Ts
Rrad
8 ∞ sin2 (δm Ls 2)
8 ∞ sin2 (λn Ws 2)
φ
δ
(
)
⋅
+
∑
∑ λ 3 ⋅φ(λn )
m
2
3
2
Ls LWkm=1
Ls LWkn=1
δm
n
+
(2)
∞ ∞
sin2 (δm Ls 2)sin2 (λn Ws 2)
16
⋅φ(βm,n )
∑∑
2
2
2
Ls Ws LWkm=1 n=1
δm λ2 βm,n
(5)
where
(3)
φ (ζ ) =
The thermal spreading resistance will depend on several
geometric and thermal parameters
R sp = f ( L, W , Ls , W s , t b , k , heff )
Rsp
Fig. 2 Thermal resistance circuit.
where R1D is the one dimensional resistance given by
R1D =
Rbase
Heat sink base Ab
(1)
The total thermal resistance may be modelled by considering
the heat sink as bare plate with effective film coefficient as
shown in Figure 3. The thermal resistance is now:
Rtotal = R1D + Rsp
Heat Sink
(4)
The spreading resistance vanishes when the heat flux is
distributed uniformily over the entire heat sink base surface.
The Rtotal is known from experimental measurements,
therefore, the effective heat transfer coefficient heff can be
calculated from Eq.(2).
Lee et al. [17] developed an analytical model for predicting
thermal spreading resistance in a circular plate with a uniform
heat flux on one surface and a convective boundary condition
over the other surface. Yovanovich et al. [18] reviewed the
previously published spreading resistance models and
presented simple correlation equations for ease of
computation. Yovanovich et al. [19] presented the thermal
spreading resistance of an isoflux, rectangular heat source on a
two layer rectangular flux channel with convective or
conductive boundary conditions at one boundary. The thermal
spreading resistance for the present research is obtained from
the following expression developed by Yovanovich et al. [19].
( e 2 t bζ + 1)ζ − (1 − e 2 t bζ ) h eff k
( e 2 t bζ − 1)ζ − (1 + e 2 t bζ ) h eff k
(6)
In all summations φ(ζ) is evaluated in each series using
ζ=δm, λn, and βm,n. The general expression for spreading
resistance consists of three terms. The single summations
account for two-dimensional spreading in the x and y
directions, respectively, and the double summation term
accounts for three-dimensional spreading from the rectangular
heat source. The eigenvalues are δm=2mπ/L, λn=2nπ/W,
βm,n=(δm2+λn2)1/2. The eigenvalues δm and λn, corresponding to
the two strip solutions, depend on the flux channel dimensions
and the indices m and n, respectively. The eigenvalues βm,n
for the rectangular solution are functions of the other two
eigenvalues.
Spreading resistance is important in heat sink applications.
The value of effective heat transfer coefficient heff is an
effective value which accounts for both the heat transfer
coefficient on the fin surface and the increased surface area, as
shown in Figure 3.
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Heat Sink
We need only study one half of the heat sink since the flow
field and temperature contours on the other half are a mirror
image due to symmetry. One half of the impingement cooling
heat sink channel is considered as two connected rectangular
channels; one is vertical and the other is horizontal. Their
effective lengths are Leff1 and Leff2, as illustrated in Figure 3.
This consideration is justifiable if one imagines a typical
streamline, for example near the middle of the impingement
slot. This streamline length is better approximated by the Lshaped path of height 0.5H and length 0.5L-0.25s after a 90°
turn.
tb
Tsource
Heat sink base
Electronic Module
Tbase
Ab
As
heff
shroud
Tbase
Tsource
0.5s
Heat sink base Ab
Electronic Module
As
Leff1
Vch2
Vch1
H
Leff2
Fig. 3 Schematic showing the effective heat transfer
coefficient.
heff =
0.5L
Fig. 4 Impingement flow geometric configuration.
1
Ab Rsin k
(7)
The average heat transfer coefficient for the heat sink is
modelled as
The overall heat sink resistance is given by
Rsin k =
b
1
Nf
+ h( Nf −1)bL + hrad Arad
R fin
h = hch1
(8)
s
L−s
+ hch 2
L
L
(13)
As s→0 the flow is nearly parallel through the entire sink,
while s→L the flow is fully perpendicular through the sink.
Thus, the total heat resistance can be expressed as
Rtotal = Rsp + Rbase + Rsink
(9)
EXPERIMENTAL FACILITY
Heat transfer model
The heat transfer coefficient, h, will be computed using the
following model developed by Teertstra et al. (1999). This
model is applicable to both fully developed and developing
flows.
−3
−3


3.65  
 Reb * Pr  
1/ 3

Nub = 
 + 0.664 Reb *Pr 1+
 2  
Reb *  



h ⋅b
Nu b =
ka
Reb * = Reb


⋅


b 

L 
−1/ 3
(10)
Figure 5 shows a schematic of the thermal tester. Two
electrical heaters were used to simulate an electronic module.
These electrical heaters were put into a 76.2 mm square cross
section 12 mm high copper block. Insulation was applied to
the bottom and the periphery of the copper block. The heat
loss was estimated to be less than 5 % of the heat input, and a
correction was applied in the data reduction. The heat input to
the heat sink was determined at the time of test by the product
of measured voltage and current (UI) corrected for ambient
heat loss (Qloss).
(11)
(12)
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Air in flow
and Holman [21]. The uncertainty in the total measured
thermal resistance (Rtotal) was a maximum of 2.6 % for the
validation test data. Further details on uncertainty analysis and
experimental data can be found in Duan [22].
Heat Sink
RESULTS AND DISCUSSION
Thermocouples at copper block
The model is validated with the experimental data taken on
four heat sinks and other experimental data from the published
literature. Figure 6 – 9 shows the measured and predicted
thermal resistance of Heat Sink #1 – #4 for different
impingement inlet widths. The highest Reynolds number in
the experimental data was 1270, which is in the laminar
regime. The differences between predictions and test results
increase slightly with increasing flow rate.
upper surface
Heat sink base
Insulation
Thermocouples at copper block Copper
lower surface
block
Heater
Fig. 5 Schematic of the thermal tester.
0.6
Table 1 Geometry of the heat sinks used in the experiments.
Configur
ation
L (mm)
W (mm)
tb (mm)
t (mm)
b (mm)
H (mm)
Nf
Heat
Sink #1
127
122
12.7
1.2
2.25
26.5
36
Heat
Sink #2
127
122
12.7
1.2
2.25
50.0
36
Heat
Sink #3
127
116
12.7
1.2
4.27
34.0
22
Heat
Sink #4
127
116
12.7
1.2
4.27
50.0
22
s=10%L, experiment
s=10%L, model
s=25%L, experiment
s=25%L, model
s=50%L, experiment
s=50%L, model
s=75%L, experiment
s=75%L, model
s=100%L, experiment
s=100%L, model
Thermal resistance Rtotal (K/W)
0.5
0.4
0.3
0.2
0.1
1
2
3
Channel velocity Vch2 (m/s)
4
5
Fig. 6 Thermal resistance comparison for Heat Sink #1.
0.6
s=10%L, experiment
s=10%L, model
s=25%L, experiment
s=25%L, model
s=50%L, experiment
s=50%L, model
s=75%L, experiment
s=75%L, model
s=100%L, experiment
s=100%L, model
0.5
Thermal resistance Rtotal (K/W)
Five copper-constantan thermocouples were attached to the
upper surface of the copper block to measure the upper surface
average temperature. Another five thermocouples were
attached to the lower surface of copper block to measure the
lower surface average temperature. The upper and lower
surfaces are divided into four equal areas. The five
thermocouples are placed at the centroids of the four equal
areas and the center of the whole surface, respectively. The
mean temperature of the heat source was represented as the
average of the ten readings of thermocouples. The ambient
temperature was measured with three other thermocouples.
The three thermocouple readings were averaged to give the
average ambient temperature. The measurement includes the
spreading resistance.
Tests were conducted for four heat sink geometries for
impingement flow. Heat sink thermal resistance data were
taken for different flow rate conditions and different
impingement inlet widths. For each heat sink, the
experimental measurements were carried out at seven different
velocities in the plenum chamber (Vd), 0.4 m/s, 0.5 m/s, 0.6
m/s, 0.7 m/s, 0.8 m/s, 0.9 m/s, 1.0 m/s, and six different
impingement inlet widths, 5%L, 10%L, 25%L, 50%L, 75%L,
100%L, respectively. In total, 168 data points were collected
for thermal resistance. The details of the heat sinks used for
the tests are summarized in Table 1.
0.4
0.3
0.2
0.4
The uncertainty analysis for the test data was conducted
using the root sum square method described in Moffat [20]
440
0.8
1.2
1.6
Channel velocity Vch2 (m/s)
2
2.4
Fig. 7 Thermal resistance comparison for Heat Sink #2.
2004 Inter Society Conference
on Thermal Phenomena
0.6
0.3
Thermal resistance Rtotal (K/W)
Thermal resistance Rtotal (K/W)
0.4
s=10%L, experiment
s=10%L, model
s=25%L, experiment
s=25%L, model
s=50%L, experiment
s=50%L, model
s=75%L, experiment
s=75%L, model
s=100%L, experiment
s=100%L, model
0.4
0.2
Saini and Webb test data
Analytical model
0.1
0.2
0.8
0
1.2
1.6
2
2.4
Channel velocity Vch2 (m/s)
2
2.8
4
5
6
Channel velocity Vch2 (m/s)
7
Fig. 10 Thermal resistance comparison for Saini and Webb
[17] test data.
Fig. 8 Thermal resistance comparison for Heat Sink #3.
0.7
0.14
s=10%L, experiment
s=10%L, model
s=25%L, experiment
s=25%L, model
s=50%L, experiment
s=50%L, model
s=75%L, experiment
s=75%L, model
s=100%L, experiment
s=100%L, model
0.5
Holahan et al. test data
Analytical model
0.12
Thermal resistance Rtotal (K/W)
0.6
Thermal resistance Rtotal (K/W)
3
0.4
0.1
0.08
0.06
0.3
0.04
0.4
0.8
1.2
Channel velocity Vch2 (m/s)
1.6
0
2
3
6
9
12
Channel velocity Vch2 (m/s)
Fig. 11 Thermal resistance comparison for Holahan et al.
[11] test data.
Fig. 9 Thermal resistance comparison for Heat Sink #4.
Figure 10 shows the comparison between the Saini and
Webb [16] experimental data and the analytical model
predictions of total thermal resistance. Overall, the trend is
very good. Figure 11 shows the comparison between the
Holahan et al. [11] experimental data and the predictions of
total thermal resistance. The experimental data and predictions
are in excellent agreement.
It was found that all experimental data errors are within
±20% with an RMS errors of 11.1%. Although the thermal
resistance prediction algorithm is based on a very simple
model, it succeeds in representing the trends of the
experimental values fairly well. The agreement is quite
satisfying in view of the simplicity of the model. Given the
uncertainties of thermal resistance measurements, the model is
reasonably well validated.
The effects of impingement inlet width on thermal
resistance are shown in Figures 6 – 9. From these figures it
can be seen that, for the same flow rate, the total thermal
resistance decreases when the impingement inlet width
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becomes smaller. This is due to the high impingement channel
velocity, which makes the impingement heat transfer
coefficient large in the case of small inlet widths.
increases. Thus, the impingement heat transfer coefficient
decreases and thermal resistance increases.
0.5
0.6
Thermal resistance Rtotal (K/W)
0.5
sink #2
sink #4
sink #2
sink #4
s=10%L
s=10%L
s=25%L
s=25%L
test
test
test
test
Heat
Heat
Heat
Heat
data
data
data
data
Thermal resistance Rtotal (K/W)
Heat
Heat
Heat
Heat
0.4
sink
sink
sink
sink
#1
#2
#1
#2
s=10%L
s=10%L
s=25%L
s=25%L
test data
test data
test data
test data
0.4
0.3
0.3
0.2
0.004
0.2
0.004
0.008
0.012
Air flow rate Q (m3/s)
0.016
Fig. 13
Effects of fin spacing on thermal resistance.
The effects of fin spacing on thermal resistance are
illustrated by the results for Heat Sinks #2 and #4, which have
the same dimensions except for fin spacing (b). Figure 12
shows the experimental values of the thermal resistance with
changes in the spacing between fins for impingement inlet
widths of 10% and 25%L. The experimental values increase
with an increase in fin spacing for the same volumetric flow
rate. This is due to the fact that channel velocity decreases
when the fin spacing increases. Thus, the impingement heat
transfer coefficient decreases and thermal resistance increases.
When the fins are closely spaced, the surface area of the
heat sink increases, the contraction pressure loss at the
impingement inlet and the expansion pressure loss at outlet of
the heat sink increase, and this effect dominates. When the fin
spacing becomes larger, although the pressure drop decreases,
the surface area of the heat sink also decreases and this makes
the rate of heat transfer lower. Furthermore, the pressure drop
increases remarkably and volumetric flow rate decreases as
the spacing between the fins becomes smaller, if the
performance of the cooling fan is taken into account.
The effects of fin height on thermal resistance are illustrated
by comparison of the results for Heat Sinks #1 and #2, and
Heat Sinks #3 and #4. Heat Sinks #1 and #2 have the same
dimensions except for fin height (H). Heat Sinks #3 and #4
have the same dimensions except for fin height (H). Figure 13
depicts the experimental values of thermal resistance for Heat
Sinks #1 and #2, and Figure 14 demonstrates the experimental
values of thermal resistance for Heat Sinks #3 and #4 for
impingement inlet widths of 10% and 25%L. As shown in the
figures the thermal resistance increases with an increase in fin
height for the same volumetric flow rate. This is due to the
fact that the channel velocity decreases when the fin height
0.012
0.016
Air flow rate Q (m3 /s)
0.02
Effects of fin height on thermal resistance for Heat
Sinks #1 and #2.
0.6
Heat
Heat
Heat
Heat
Thermal resistance Rtotal (K/W)
Fig. 12
0.008
0.02
sink
sink
sink
sink
#3
#4
#3
#4
s=10%L
s=10%L
s=25%L
s=25%L
test
test
test
test
data
data
data
data
0.5
0.4
0.3
0.004
Fig. 14
0.008
0.012
Air flow rate Q (m3 /s)
0.016
0.02
Effects of fin height on thermal resistance for Heat
Sinks #3 and #4.
CONCLUSIONS
This paper investigated thermal resistance of impingement
air cooled plate fin heat sinks for a variety of impingement
inlet widths, fin spacings and fin heights. The analytic model
is developed for the low Reynolds number laminar flow and
heat transfer in the interfin channels of impingement flow
plate fin heat sinks. The simple model is suitable for heat sink
parametric design studies. The accuracy range of the analytical
model was established by comparison with experimental
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measurements of four actual heat sinks and other obtainable
experimental data.
The major thermal resistance in the thermal circuit is the fin
surface resistance. Research on impingement flow plate fin
heat sink modelling was pursued to obtain tools for parametric
design studies and optimization of heat sinks. The analytical
thermal resistance model predictions agree with
experimentally measured values within ±20% and 11.1%
RMS for the range 300<Re<1200. In general, the thermal
resistance model tends to underpredict. The thermal resistance
model includes the spreading resistance for a smaller module
attached to a larger heat sink. The complicated zonal model
[13] predictions are in agreement with the experimental data
within ±25%. The thermal resistance model is implemented
for laminar flow, since the expected practical operating range
of this type of high performance heat sink would typically
produce flows in the range of Re < 1200. The thermal
resistance decreases when the impingement inlet width
becomes smaller for the same flow rate. Thermal resistance is
very sensitive to changes in fin spacing. The thermal
resistance increases significantly with an increase in fin
spacing for the same volumetric flow rate. Increasing fin
height slightly increases the heat sink thermal resistance for
the same flow rate. The fin efficiencies were almost the same
for the heat sinks tested, therefore, fin efficiency did not pose
a problem in the present study.
ACKNOWLEGEMENTS
The authors acknowledge the support of the Natural
Sciences and Engineering Research Council of Canada
(NSERC), and R-Theta Inc. for providing heat sinks for the
present study.
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