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#P'ZRGTKOGPVCN5VWF[QPVJG2GTHQTOCPEGQH/KPKCVWTG*GCV5KPMUHQT
(QTEGF%QPXGEVKQP#KT%QQNKPI
V. Egan, J. Stafford, P. Walsh, E. Walsh, R. Grimes,
Stokes Research Institute,Department of Mechanical & Aeronautical Engineering
University of LimerickLimerick, Ireland
Phone: (+353) 61 213487
Fax: (+353) 61 212039
Email: [email protected]
ABSTRACTIn recent years the design of portable electronic devices must
incorporate thermal analyses to ensure the device can beadequately cooled to acceptable temperatures. Consumer
demand for smaller, more powerful devices has lead to an
increase in the heat required to be dissipated and a reduction in
the surface area both of which result in an increased heat flux.In this paper, an experimental study is performed on one of the
smallest commercially available miniature fans, suitable forcooling portable electronic devices, used in conjunction with
both finned and finless heat sinks. Previous analysis has
shown that due to fan exit angle, flow does not enter the heat
sinks parallel to the fins or bounding walls. This results in anon uniform flow rate within the channels of the finned and
finless heat sink along with impingement of the flow at the
entrance giving rise to large entrance pressure losses. In thispaper straightening diffusers were attached at the exit of the
fan which resulted in aligning the flow entering the heat sinks
with the fins and channel walls. In designing the finned heatsink current optimization criterion for finned heat exchangers
has been applied to ensure maximum heat transfer rates; the
finless heat sink was designed to the same specifications. The
maximum overall footprint area of the cooling solution is534mm2 with a profile height of 5mm. The thermal
performance of each cooling solution was investigated byquantifying its thermal resistance over a range of fan speeds
and comparing the results to cases without diffusers. In orderto investigate the flow field, detailed velocity measurements
were obtained using Particle Image Velocimetry, which
provided a further insight into the physics of the flow in such
miniature geometries and in designing the straighteningdiffusers. The thermal analysis results indicate that the cooling
power of the solution is increased by up to 20% through the
introduction of a diffuser. Hence, demonstrating the need forintegrated fan and heat sink design of low profile applications.
KEY WORDS: low profile, forced convection cooling,
miniature fan
NOMENCLATURE
Aconv convective surface area, m2
b fin spacing, mmFOV Field of view, m
h convective heat transfer coefficient, W/m2 K
hFC forced convective heat transfer coefficient,W/m2 K
hf total Convective heat transfer coefficient,
W/m2 Kk
heat sinkthermal conductivity of heat sink material
W/m.K
L Length of heat sink, mmN number of pixels in interrogation region
'P pressure drop, PaQ volumetric flow rate, m3/s
QFC power dissipated by forced convection, W
Qinput input power, WQLosses power dissipated by secondary cooling
mechanisms, WRES resolution of camera, Pixels
RthT total thermal resistance,o C/W
RthFC thermal resistance of Forced Convection
Cooling, o C/W
RthLosses thermal resistance of Natural ConvectionCooling, o C/W
RPM revolutions per minute, RPMSP static pressure rise, Pa
tfin fin thickness, mm
Tf ambient air temperature,o C
Ts surface temperature,o C
Umax Maximum velocity, m/sux,y Velocity at local coordinates (x,y), m/s
W Total width of heat sink, mm
978-1-4244-1701-8/08/$25.00 2008 IEEE
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X Half of channel width, mmY Half of channel height, mm
Greek Symbols
D thermal diffusivity, m2/sP viscosity , N.s/m2
Subscripts
conv convective
FC forced ConvectionIR interrogation Region
Max maximum
s SurfaceT Total
f Ambient
INTRODUCTION
The design and integration of miniature cooling solutions intotodays portable electronic devices is moving to the forefront
of electronics cooling research. The drive behind this researchis consumer demand for smaller more powerful portable
devices. As the surface area available for power dissipation
reduces, along with technology advancements increasing the
devices power consumption, the resulting heat fluxes areconsiderably elevated. At present most manufacturers rely on
natural convection in conjunction with heat spreadingtechnologies to maintain temperatures at acceptable consumer
levels. However, a major flaw with this method of heat
dissipation is the resulting elevation in device case
temperatures. If the envisaged trend in increasing heat fluxescontinues, then natural convection and conduction
technologies will no longer be able to maintain devices atacceptable temperatures. Hence, there is a need for research
into cooling technologies that can offer higher heat transfer
rates compared to current natural convection and heat
spreading techniques.
Forced convection cooling is the preferred new coolingtechnology among designers of portable electronic devices.
This is due to large number of factors including, cost,
reliability, power consumption, footprint area, and profile
height. Liquid cooling [1] and heat pipe [2] technologiesrequire secondary coolers but for forced convection air is the
working medium which is in abundant supply. Unlike phasechange materials [3], forced convection is capable of
efficiently dissipating heat over extended time periods. An
example of this is the unconventional design proposed by
Walsh et al [4], which gives a thermal resistance value of7.5C/W in a volume of 4.56mm2 with a profile height of 4mm
including the fan. As air cooling is currently in widespread usein industry the implementation costs are relatively low.Finally, with a sufficiently small footprint and profile, heat can
be dissipated directly at the source via a path of low thermal
resistance, resulting in a reduction in the temperature of allother components and surfaces of the device.
Over the past few years a number of groups have initiatedresearch to address the developing market of miniature forced
convective air cooling. The first series of papers on such
research examined the validity of the conventional scaling
laws [5-9] as the fan scale is reduced to miniature dimensions.The authors found that at low Reynolds numbers boundary
layer phenomena result in reducing the flow coefficient and
elevating the power coefficient. Day et al[10] also reported a
scale effect which resulted in the flow rate delivered beingsignificantly less than expected when operating at low
Reynolds numbers.
With regard to the integration of miniature fans with heat
sinks it is noted that impingement cooling emerges as one of
the best methods to dissipate large heat loads over small areas,with thermal resistances as low as 1.4 oC/W being reported
[11,12] for pin-fin heat sinks. However, to achieve such
performances, footprints areas of order 2000 mm2
and profileheights of order 100 mm were reported. Whilst this footprint is
relatively small, it is noted that such large profile heights
would most likely deem this technology unacceptable for usein most portable electronic devices. Also, when considering
miniature scale fans, the flow rates and pressure rises
attainable are considerably lower than those attained in theaforementioned studies for impingement cooling. Hence in
order to satisfy the constraints of low profile forced
convection cooling a fan and heat sink in parallel is the mostpractical solution. A recent analysis of fan and heat sink
arrangement in term of performance optimisation has been
carried out by Walsh et al [13, 14]. It was shown that bestthermal performance was achieved when the fan exit angle is
matched to the heat sink fin angle, i.e. flow enters the heat
sink parallel to the fins. A recent study by Egan et al[15, 16]investigated the thermal performance of a miniature fan used
in conjunction with a finned and finless heat sink. The overall
footprint area of the solution was 456mm2 with a profile of
5mm. Velocity measurements of the flow in the heat sinksshowed that flow exited the fan at an angle to the heat sink
walls and the fins. In the case of the finned heat sink it was
seen that the flow strongly impinged on the heat sink fins atthe entrance to the channels. The current study is focused on
developing the previous analysis of Egan et al [15, 16] to
reflect the finding of Walsh et al [13, 14] in designing asuitable cooling solution.
The primary objective is to determine the effect of
straightening the flow prior to entering the heat sinks through
the use of a diffuser. A number of different diffusers were
manufactured to obtain the optimum design giving parallelflow at entry to the heat sink. The optimum diffuser design
was determined from flow velocity measurements obtainedusing particle image velocimetry. Upon finding such a design
the fan, diffuser and heat sink solutions were characterised by
repeating the heat transfer measurements carried out in Egan
at al [15, 16]. Such results would conclusively show if thediffuser resulted in an overall enhancement of the heat transfer
rate of the finned and finless solutions. Particle imagevelocimetry measurements of the flow in the heat sink at
speeds ranging from 3000RPM to 8000RPM were also
obtained and provide a further insight into the flow field
within the heat sinks. The results of this study are valuable todesigners of such cooling solutions as enhanced heat transfer
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rates may be obtained by simply adding a diffuser between thefan and heat sink.
HEAT SINK AND DIFFUSER DESIGN
The fan tested for the current work is the Micronel U16LM-9having a footprint of 100mm2 and profile of 5mm (See Fig. 4).
This is currently one of the smallest commercially available
fans for forced convection cooling of electronics. The
pressure versus flow rate characteristics supplied by themanufacturer for a nominal speed of 6000RPM are shown in
Fig. 1. In determining this curve it is possible that only a small
number of experimental data points were recorded by thesupplier, hence resulting in a sharp change in flow rate once a
certain static pressure is reached. Also shown on this graph are
the curves for 3000RPM, 5500RPM and 8000RPM. Thesecurves were obtained using the fan scaling laws detailed in
Bleier [17] and defined here in equations 1 and 2.
vQ RPM (1)
2vSP RPM (2)
0
1
2
3
4
5
6
7
8
9
10
11
0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003
Volume Flow Rate [m3/s]
StaticPressure[Pa]
Supplier Curve Scaled to 8000RPM Supplier Curve Scaled to 5500RPM
Supplier Curve Scaled to 3000RPM Pressure V's Flow curve at 6000RPM
Fig. 1. Pressure versus flow rate characteristics for the
Micronel U16LM-9 low profile fan as supplied by Micronelfor 6000 RPM and scaled for speeds from 3000PRM to
8000RPM using the fan scaling laws.
Experiments were carried out in both finned and finless heat
sinks. In designing the finned heat sink the pressure versusflow rate characteristics at a fan speed of 8000RPM were
used. Fig. 2 (a) shows a schematic of this heat sink and
highlights the variables which were optimized; these include
the fin spacing, (b), and fin thickness, (tfin). The former ofthese was optimized using Eq. (3) which was developed by
Bejan [18] for flow between parallel plates using theintersection of asymptotes between a fully developed flow
limit and a flat boundary layer flow limit.1
4
22.73
PD ' u optimumb
L P
L(3)
Fig. 2. Schematic of finned and finless heat sinks outlining
the overall dimensions and the optimised parameters, b and tfin
In determining the optimum fin spacing, the pressure drop
('P) across the bank of channels, was set equal to 6.5Pa sothat the fin spacing of the heat sink is optimised for a fan
speed of 8000RPM and should correspond to a total
volumetric flow rate of approximately 2.5E-04m3/s passing
through the heat exchanger. In order to achieve this Eq. (3)requires that the fin spacing be approximately 1.1mm. The
second parameter examined is the thickness of the fins, tfin.This was optimized by ensuring that the fin efficiency is
greater than 99% and Ellison [19] shows this to be the case
when Eq. (4) is satisfied.
2
fin heat sink 40tt hL k (4)
Forced convection heat transfer coefficients for gases are
typically in the range 25-250 W/m2.K [20]. In the currentstudy the expected maximum velocities, based on the fan
blade top speed, were approximately 0.5m/s, hence a value of60 W/m2K was chosen for hin Eq. (4). Using copper as the
heat sink material, Eq. (4) reveals that the fin thickness should
be at least 0.06mm. However the technique used to
manufacture the heat sink required this dimension to be oforder 0. 3mm, hence ensuring a more than adequate fin
thickness. The result is that a finned heat sink with a
maximum of 6 channels could be manufactured whilstmaintaining the heat sink footprint constraints that were
applied. The finless heat sink was manufactured to have the
identical specifications of profile, footprint area and externalwall thickness and is shown in Fig. 2 (b).
As previously mentioned in order to achieve the optimum
thermal performance of a fan and heat sink in parallel, flow
must enter the heat sink aligned with the heat sink walls and
fins. Fig. 3 is a schematic of a velocity vector diagram for a
backward curved fan with a rotational speed,Z and radial
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velocity, Vr. The angle of the flow exiting the fan casing canbe measured using PIV and is dependant on system resistance.
A high system resistance such as that created by a finned heat
sink will result in a lower flow rate through the fan. This in
turn will result in reducing only the radial flow component andhence the angle at which fluid leaves the fan. It can be seen
that high system resistances will reduce J, whilst low systemresistances will result in increasing this angle.
In order to align the flow exiting the fan with the heat sinkwalls and fins a number of diffusers with angles varying
between 25o and 50o with both curved and straight walls weremanufactured from polycarbonate. As discussed above, it was
found that the optimum angle for flow alignment varied
between the finned and finless case. Each diffuser was tested
using PIV to measure the velocity of the flow in each of theheat sinks and it was determined from the measurements that a
25o curved diffuser and a 50o straight diffuser resulted in flowalignment within the finless and finned heat sinks respectively.
Fig. 3. Velocity triangle showing fan exit angle.
EXPERIMENTATIONThis section is structured as follows. Firstly the cooling
solution, encompassing the fan, diffuser and heat sink, is
described followed by a description of the experimentaltechnique employed in determining the thermal resistance.
Particle Image Velocimetry (PIV) was also used to visualizethe change in flow structures encountered by incorporating a
diffuser into the design; hence this technique is described in
the latter part of this section.
Experimental Configuration
The experimental configuration is shown in Fig. 4 consisting
of a finned and finless set-up. The results presented in this
paper are detailed in table 1. The current work presents results
from all four cases however, case 1 and 2 are detailed in a inEgan et al [15,16] and encompass tests performed without a
diffuser.
Fig. 4. Photograph of the experimental configurationemploying the straightening diffusers with the finned and
finless heat sinks.
TABLE 1. Experimental Test Description
Thermal Resistance Measurements
The experimental configuration consisted of a Micronel fan, a
flow diffuser and the optimized heat sink that was designed in
the preceding section. During experimentation the top cover ofthe heat sink, as shown in Fig. 4, was in position so as to
create a fully closed channel. This cooling solution has afootprint of 256mm2 for the fan, either 231mm2 or 278mm2 forthe heat sink and diffuser and a profile of only 5mm. The fan
was powered using a DC power supply and rotational speeds
ranging from 1000RPM to 8500RPM were measured using anoptical tachometer. The heat source used for experimentation
was a 66mm thin-film heater, available from Minco Inc., and
was attached to the base of the heat sinks. Three K-typethermocouples attached using a heat resistant tape to the centre
of the top, base and left wall of the heat sink. The ambient air
temperature was also recorded. The four thermocouples were
connected to a National Instruments 9211 USB High SpeedCarrier and temperatures were recorded and plotted using
LabVIEW 8. During experimentation, the entire heat sink wasfound to be almost isothermal, as a maximum temperature
difference between the hottest (base) and coldest (top) surface
of approximately 5% was measured. Also of significance, was
that the external surfaces of the heat sink were covered usinginsulating tape to reduce the heat loss due to secondary
cooling mechanisms such as natural convection and radiation.The purpose of this is to attempt to simulate the operational
environment for such a system in a typical portable electronic
device where the total set-up is likely to be confined within a
very small cavity.
Test Number Description1 Finless Heat, No diffuser
2 Finned Heat, No diffuser3 Finless Heat, 25o curved diffuser
4 Finned Heat, 50o straight diffuser
Diffusers
Top cover of
heat sink
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The thermal performance of any cooling solution can becharacterized by its thermal resistance which is defined by
equation (5).
sT
Input
thT T
RQ
f (5)
QInput is the total power supplied to the thin-film heater, Ts is
the steady state temperature of the heat sink surface and T isthe temperature of the ambient air. However, it should be
noted that this power was not only dissipated by forcedconvection, but also by the secondary cooling mechanisms
already mentioned so that that total power supplied to the heat
sink is dissipated by:
Input FC LossesQ Q Q (6)
Hence, the total thermal resistance of the cooling solution can
also be defined by:
FC Losses
TFC Losses
th thth
th th
R R
R R R (7)
and the forced convection thermal resistance by
T Losses
FC
T Losses
th thth
th th
R RR
R R
(8)
It should be noted, however, that the power dissipated by these
secondary mechanisms is highly dependant on factors that
vary from application to application. Such factors include:
available air for free convection currents; temperature of
surrounding surfaces and any contact of conducting materialswith the heat sink surface. In order to remove this ambiguouspower dissipation from the characteristics reported herein, all
of the experiments were conducted whilst maintaining the heat
sink surface temperature constant at 70oC and ambient at
25oC. An experiment was then conducted with the fanswitched off (i.e. QFC = 0) and resulted in directly measuring
QLosses. Since the same temperatures were maintained
throughout all experiments, the heat lost through secondarymechanisms should remain constant throughout. This allowed
for the calculation of the heat dissipated by just forced
convection giving a more representative result of the forcedconvection cooling.
The total and forced convective heat transfer coefficients werecalculated using Eq. (9) and Eq. (10) respectively.
1
T
T
th conv
hR A
(9)
1
FC
FC
th conv
hR A
(10)
Where, h, is the heat transfer coefficient in W/m2 K and Aconvis the convective surface area of the finned heat sink in m 2.
The convective surface area of the finned and finless heat
sinks was calculated to be 0.000984m2 and 0.00044m2
respectively with an accuracy of 1E-06m2. The heat transfercoefficient is inversely proportional to the convective surface
area of the heat sink as shown in Eq. (9) and (10), this meansthat the finless heat sink with a lower Aconv will result in a
higher heat transfer coefficient.
Uncertainty analysisAn uncertainty analysis was performed, [21], giving the
thermal resistance an error of less than 5%. The uncertainty
was greatest for natural convection and decreased withincreasing fan speed.
The optical tachometer used to measure the rotational speed ofthe fan has a resolution of 1RPM. However, during
experimentation it was observed that the speed varied up to
50RPM.
Velocity Measurements
The second set of experiments involved detailed velocity
measurements of the flow within the channels of the heat sink.
Particle Image Velocimetry (PIV) was employed to obtainthese velocity measurements. However, in order to obtain the
optical access required for this technique, the copper top cover
of the heat sink was replaced with a glass slide. Hence all PIVresults were obtained without heat transfer. The following
paragraphs detail the principle of the technique and the set-up
used during experimentation.
PIV works on the principle of introducing seeding or tracer
particles to the flow and tracking their motion over known
time intervals. Ideally the particles should be small and theirdensity matching the working fluid density. Gravitational
forces will produce an error depending on the density
mismatch of the particles and if the particles are large theywill be unable to follow the exact motion of the fluid. A water-
based oil consisting of monopropalene glycols or CO2 fog wasused for the seeding which was produced using a JEM Stage
Hazer 2000. The size of seeding particles produced were of
approximately 10Pm diameter with relative density of1.05kg/m3 at 293K, [22]. In order to contain the seeding
particles the experimental apparatus was placed in a glasswalled enclosure of dimensions 400mm(L) 250mm(H)
250mm(W). Once the particles were released into the
enclosure a laser illuminated a plane in the heat sink and thelight subsequently emitted by the particles was recorded on a
camera positioned perpendicular to the illuminated plane.
Velocity measurements were taken for a plane at mid-depth inthe heat sink channels. A schematic of the experimental set-up
is shown in Fig. 5
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Fig. 5. PIV Experimental Set-up showing camera and laser
positions with respect to fan and heat sink. The diffuser is
inserted between the fan and heat sink.
Raffel et al. [23] discuss the science and technical aspects of a
PIV system in full. Almost all PIV systems use a laser systemas lasers emit intense and monochromatic light, which after
being passed through a series of lenses is easily shaped into athin light sheet for illuminating the seeding particles. A
Nd:YAG, 532nm, semiconductor laser was used giving a
1.5mm thick light sheet. To measure the velocity of the
particles the laser was pulsed twice with a time delay chosenso that the distance travelled by the seeding particles between
images is discernable and that particles do not leave theilluminated plane within the period. The exposure time of the
camera was long enough to capture the position of the
particles and short enough to avoid blurring of the image. To
ensure this, TSI Inc [24] suggest that the time between pulses
be calculated from:
s in IR
max
*
4U
pixel
FOVN
RES(11)
where FOV is the field of view, RES is the resolution of thecamera in the direction of flow, Npixels in IR is the number of
pixels in an interrogation region and Vmax is the expected
maximum in-plane velocity. Prior to experimentation, in order
to calibrate the subsequent measurements, a scaling devicemust be inserted in the test section to obtain the correct scaling
factor for the velocity measurements. This was achieved byplacing a calibrated ruler in the measurement plane.
A PowerViewTM Plus 2MP CCD camera of resolution 1600
1200 with a 60mm focal length lens was used to record thescattered light from the illuminated particles and their images
appear as bright spots on a dark background. The images arerecorded on separate frames from the double pulsing of the
laser. This technique is called multi-frame/single exposure
PIV. A statistical PIV evaluation using Insight 3G software
supplied by TSI Incorporated was applied to the recorded data
in order to extract the required displacement information. Therecordings were divided into regions known as interrogation
areas and a correlation technique cross-correlation, was
applied to determine the displacement of the particles within
the interrogation area. The size of the interrogation area wasset according to the time between pulses so that the seeding
particles would not travel more than 25% of the interrogationarea length. If seeding particles travel much more than this
distance then too many seeding particles will have left the
interrogation area when the second image is taken. These
particles will not be available for velocity measurement andwill be a source of noise. This problem can be overcome by
overlapping interrogation areas but again care must be taken to
ensure that seeding particle displacements between pulses arenot too small. Interrogation area overlap was set to 50% of the
interrogation area height and width for the current results and
the interrogation area size was set at 32 32 pixels. Thevelocities were calculated from the displacements and the
duration of the illumination pulse. A series of post-processing
steps were applied to the PIV data.
RESULTS AND DISCUSSION
The objectives of this work are to provide optimized thermalmanagement solutions based on a previous analyses, [13-16],
using one of the smallest commercially available fans
combined with finned and finless heat sink geometries.Optimization of such solutions has been considered using
velocity field and thermal resistance measurements presented
in this section. Velocity measurements are considered first inorder to develop a suitable diffuser for each case based on
design criterions previously discussed. Thermal resistance
measurements, heat transfer and flow rate results proceed fromthe flow field analysis, quantifying the influence of the
introduction of diffusers on both heat sinks over a range of fan
rotational speeds.
Fig. 6 and Fig. 7 depict the flow at the entrance regions to the
heat sink for finned and finless geometries without the use of a
diffuser [15,16]. While Fig. 8 and Fig. 9 present the velocitymagnitude data for flow in the finless and finned heat sinks
with the inclusion of diffusers at the entrance to the heat sink.A range of diffusers were examined for both heat sink
geometries producing various heat sink fan orientations from
25o to 60o. Therefore due to the quantity of PIV results
analyzed, the data presented for this work is only consideredfor the diffusers which would optimize flow alignment and
distribution in both heat sink cases. It was found that a 25ocurved diffuser for the finless heat sink, and a 50o straight
diffuser for the finned heat sink were beneficial.
The velocity results presented in all figures are velocitymagnitudes with vector length and color varying accordingly;
longer vectors represent high velocity regions. Therelationship between color and velocity magnitude is indicated
in the legend provided with each figure. The data presented for
the current work was obtained by averaging 70 instantaneous
results, each taken at a frequency of 14.5Hz.
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The PIV results for the finless heat sink and 25o curveddiffuser are shown in Fig. 8 for fan rotational speeds between
3000RPM and 8000RPM. Each velocity magnitude plot
shown in Fig. 8 presents the fluid flow through the diffuser
and heat sink, with the dashed line indicating the entrance tothe heat sink from the diffuser. Considering the data presented
in Fig. 8 and Fig. 6 for a fan speed of 3000RPM, it is possibleto distinguish noticeable differences in the flow distribution
due to the introduction of a diffuser. In Fig. 8 the flow is
distributed relatively evenly in the channel of the finless heat
sink for all three speeds tested. This implies that the effects offorced convection should also be relatively even across the
channel section, reducing the possibility of raised
temperatures in localized areas of the heat sink. However, inFig. 6, a large region of low velocity exists near the right wall
at the entrance. Hence forced convective cooling in this region
will have little effect on the right wall temperature. Byintroducing the diffuser at the entrance to the heat sink, flow
now enters the finless channel parallel to the heat sink walls as
seen from the velocity magnitude plot of Fig. 8.
The results from PIV analysis on the finned heat sink and 50o
straight diffuser are presented in Fig. 9. The diffuser and heatsink are labeled in Fig. 9(a) and also color contrasted to
distinguish the fins (black) from their shadows in the diffuser
(grey). These were unavoidably created by the laser beamused to illuminate the seeding particles within the heat sink.
Consequently particle tracking was not possible in these
regions of the diffuser. However, this does not affect thevalidity of the current work as flow structures are still visible
in the diffuser, and concentration on flow characteristics
within the heat sink is of primary interest for optimizing this
thermal management solution.
Fig. 6. PIV velocity magnitude plot, in m/s, from Egan et al
[16] of the flow in the entrance region of the finless heat sinkwith no diffuser attached for 3000RPM. All velocities are
normalised with respect to the maximum velocity of 4m/s.
For each case considered in Fig. 9, the flow entering the heat
sink shows minimal impingement on the fins as opposed to
Fig. 7, where no diffuser is used at 8000RPM. Under fullydeveloped conditions the maximum and minimum velocity
and hence flow rate is recorded in channel 3 and channel 6
respectively for all three fan speeds (see equations 12 and 13).The percentage difference in flow rates between channel 3 and
6 for fan speeds of 3000RPM, 5500RPM and 8000RPM is
42%, 48% and 43% respectively. However the standard
deviation of the flow rates and velocities in for all six channelsis higher for a fan speed of 8000RPM suggesting that the flow
distribution between channels is not as uniform at higherspeeds. It can be seen from Fig. 9(c) that the angle of the flow
entering the diffuser changes at 8000RPM and that a longer
diffuser but of the same angle may be required.
Fig. 7. PIV velocity magnitude plot, in m/s, from Egan et al.
[15] showing the flow field in the entrance region to the finned
heat sink at 8000RPM with no diffuser. All velocities are
normalised with respect to the maximum velocity of 2.7m/s.
Following the selection of a diffuser for the finned and finlessheat sinks using the flow field analyses discussed, the
experimentation was arranged to obtain a measure of the total
thermal resistance for a range of fan speeds from 0RPM to
8000RPM. The data recorded are plotted in Fig. 10. Thisfigure, along with all subsequent figures discussed, also
compares data recorded for the finned and finless cases whereno diffuser was used [15,16]. From Fig. 10 it can be seen that
a reduction in thermal resistance can be obtained through the
use of a diffuser. For the finned heat sink at low velocities, the
measured thermal resistances are of similar magnitude forboth set-ups. However, as rotational speed of the fan
increases, the heat sink and diffuser combination clearly outperforms the solitary heat sink case. For a finless heat sink
there is a constant reduction in total thermal resistance
achieved when using a diffuser between approximately
4000RPM and 8000RPM. Below this range of speeds, large
reductions in thermal resistance are seen by using a diffuser toalign the flow exiting the fan. In order to achieve a thermalresistance of lower than 40oC/W using a finned heat sink anddiffuser combination, the fan must operate at a rotational
speed greater than 5000RPM. Alternatively, the use of a
finless heat sink and diffuser combination produces similarthermal resistances from a fan speed of just 3000RPM. A
benefit of this is that lower operating speeds are sufficient for
similar cooling effects when using the optimized finlessarrangement. In terms of fan reliability, noise and pumping
power this proves highly advantageous.
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(a) Finless Heat Sink at 3000RPM
(b) Finless Heat Sink at 5500RPM
(c) Finless Heat Sink at 8000RPM
Fig. 8. PIV velocity magnitude plots depicting the flow within the diffuser and finless heat sink for fan speeds of (a)3000RPM (b) 5500RPM and (c) 8000RPM respectively. The respective velocity scale bars in m/s are shown above each image.
The dashes lines represent the entrance to the heat sink from the diffuser.
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(a) Finned Heat Sink 3000RPM
1
2
3
45
6
Diffuser Heat Sink
(b) Finned Heat Sink 5500RPM
(c) Finned Heat Sink 8000RPM
Fig. 9. PIV velocity magnitude plots of flow in finned heat sink and 50o straight diffuser at 3000RPM, 5500RPM and8000RPM. Respective scale bars for velocities in m/s are given above each result. Flow is from left to right. Regions in gray are
shadows from the heat sink fins which result from the laser light entering from the right.
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A plot of the forced convection thermal resistance comparingall cases with and without diffusers is presented in Fig. 11.
This plots only the forced convection cooling achieved from
the fan and not the heat dissipated by secondary cooling
mechanisms. For the current work these secondary coolingmechanisms were found to give a thermal resistance, Rth-Losses,
of 63oC/W. Hence, by using Eq. (9) and the results for Rth-Tpresented in Fig. 10, a corresponding forced convection plot of
the forced convection thermal resistance, Rth-FC was obtained
and is presented in Fig. 11 . For a fan speed of 8000RPM,
using the diffuser designed for the finned heat sink, a decreaseof approximately 23% in forced convection thermal resistance
is obtained. At the same operating speed, the finless heat sink
and combined diffuser provide a decrease of 15.3% over afinless heat sink without diffuser. It is therefore apparent that
in the case of a fan and heat sink in parallel aligning the flow
with the heat sink fins produces lower thermal resistances thanimpinging flows [13].
At 8000RPM the finned diffuser case results in a lower
thermal resistance compared to the finless diffuser solution.
This is an expected result as the design of the finned heat sinkwas optimized for 8000RPM, based on boundary layeranalyses discussed in the preceding section. As previously
mentioned, a difference in velocity magnitudes for both
geometries can be seen in Fig. 8 and Fig. 9. This can be
accredited to a higher system resistance due to the finned heatsink, which implies that higher mass flow rates are evident in
the finless heat sink for each rotational speed recorded. Highermass flow rates commonly result in increased heat transfer
rates; however Fig. 10 and Fig. 11 enforce the influence of
boundary layer analysis used in the finned heat sink design,
i.e. the optimum spacing of fins in a heat sink for a givenpressure drop is determined based on the boundary layers
merging just at the exit of the heat sink. Thermal resistance
measurements for the finned case drop below that of thefinless case at approximately 7500RPM. It is also apparent
that the boundary layer optimization criterion is proven for
both situations with and without the use of a diffuser for lowprofile solutions. However, the thermal resistance values for
the finless-diffuser case are lower compared to finned case.
(test 1). Even at 8000RPM where the forced convectivethermal resistance appears to be reaching a constant value with
increased rotor speed, there is a reduction of 11.3% over the
forced convective thermal resistance of the finned heat sinkwithout a diffuser. This is significant considering the 25o
diffuser used for the finless heat sink only increases the
overall footprint area of the thermal solution by approximately
6%. It was also noted that the 50o
diffuser used to optimize thefinned heat sink increases the overall footprint area of the
thermal solution by approximately 16%. This resultdemonstrates the need to design integrated and optimized fan
and heat sink solutions for the low profile market.
0
10
20
30
40
50
60
70
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Rotor Speed (RPM)
Rth(oC/W)
Finned + diffuser
Finless + diffuser
Finned
Finless
Fig. 10. Plot showing total thermal resistance for fan speedranges between 0RPM and 8300RPM.
0
25
50
75
100
125
150
175
200
225
250
275
300
3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000Rotor Speed (RPM)
RthFC(oC/W)
Finned + Diffuser
Finless + Diffuser
Finned
Finless
Losses
Fig. 11. Plot of forced convection thermal resistance withvarying RPM. Also indicated are the effects due to secondary
cooling mechanisms (Losses).
Similarly to a combined fan and heat sink cooling solution,sizing issues may also be associated with the power supply
necessary for operation. Considering the power requirements
of a cooling solution, it is reasonable to measure shaft powersupplied to the rotor when characterizing fan performance.
This provides designers with power requirements for the fan
alone which, may deviate considerably from the motor powerrequired especially when considering small scale fans. The
current work is not examined in this manner, as there is an
enclosed motor and fan assembly designed for combined use.Power requirements are therefore presented for the motor and
fan collectively. The manufacturer provides a nominal
operating speed of 6000RPM. To achieve this rotationalspeed, a power input of 0.163W is required. This value
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increases to 0.320W to reach an operating speed of 8000RPM.The scale law for power consumption predicts a 1.77 factor
[(8000/6000)3] increase however, the power is seen to almost
double. This is due to the efficiency of the driving motor
dropping off at higher speeds as bearing losses become larger.Power is therefore conserved to a greater extent when
operating the cooling solution below the nominal operatingspeed of 6000RPM as opposed to above this speed where
power requirements rise sharply for small increases in
rotational speed. Hence, depending on the level of restrictions
evident with power supply choice and the thermalperformance requirements, it may be beneficial to integrate a
finless heat sink and diffuser design as it outperforms the
finned heat sink cases below 6000RPM, shown in Fig. 10 andFig. 11. It is also of interest to note that this level of power
consumption could be supplied by a high end mobile phone
battery (Nokia BP-4L Battery) for a period of 34hrs ofcontinuous use. In reality however, the fan would only be in
use while the device is in high processing mode so the actual
lifetime is likely to be limited by phone functionality ratherthan by cooling solution.
In Fig. 12 and Fig. 13, the heat transfer coefficient is presentedfor combined cooling and forced convection cooling. Similar
to the thermal resistance measurements, this data is based on
the average heat transfer coefficient of the heat sink. The data
presented in Fig. 12 is that of the total heat transfer coefficientand it can be seen that the finless cases achieve more than
twice the average heat transfer coefficient compared to thefinned cases over the rotor speeds tested. This is highly
dependant on the convective surface area of both heat sinks as
given in Eq. (9). With reference to Fig. 10 and Fig. 11, which
show thermal resistance plotted against fan speed, it ispossible to conclude that in general over the range of speeds
examined, the finless design will dissipate a similar, and in
some cases favorable magnitude of heat per unit oftemperature compared to the finned design. The heat transfer
coefficient quantifies this relative to the convective surface
area of the heat sink. The finless heat sink considered here hasa convective surface area 44.7% less than the convective
surface area of the finned heat sink. It is therefore expected
that the heat transfer coefficient values will be greater for thefinless design as it dissipates a similar magnitude of heat using
almost half the convective surface area of the finned design.
This also applies to Fig. 13 for the forced convection heattransfer coefficient data. Increasing rotational speed results in
an increasing difference in heat transfer coefficient between
heat sinks using diffusers and heat sinks without diffusers. At
8000RPM, the finned heat sink achieves an increase ofapproximately 27% through the introduction of the selected
diffuser. For the same rotor speed, an increase ofapproximately 15% is achieved for the finless heat sink using
the diffuser to align the flow. The effect of convective surface
area results in a heat transfer coefficient for the finned case
with diffuser to be 51% of the heat transfer coefficient for thefinless case with diffuser, considered for a rotor speed of
8000RPM.
0
10
20
30
40
50
60
70
80
90
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Rotor Speed (RPM)
h(W/m
2oC)
Finned + diffuser
Finless + diffuser
Finned
Finless
Fig. 12. The total heat transfer coefficient for both finned andfinless heat sinks.
0
5
10
15
20
25
30
35
40
45
50
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Rotor Speed (RPM)
hFC(W/m
2oC)
Finned + diffuser
Finless + diffuser
Finned
Finless
Fig. 13. The forced convection heat transfer coefficient for
both finned and finless heat sinks.
As seen in Fig. 9 the flow within the finned heat sink channels
is seen to fully develop which makes it possible to describe the
velocity profile across the entire channel cross section usingthe solution provided by Purday [25]. This solution describes
the velocity distribution in rectangular channels of varyingaspect ratios and is adapted in Eq. (12) to describe the flow in
channels with an aspect ratio of , such as those in the heat
sink analysed herein. In this equation X and Y correspond
to half the channel width and half the profile heightrespectively. While x and y correspond to the local
positions measured from the mid-width and mid-depth of thechannel respectively.
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2 3
( , ) max 1 1x yx y
u UX Y
.7
(12)
Hence, the volumetric flow rate in each channel can be
calculated from Eq. (13).
( , ) max2 4.743 3.7
Y X
x y
Y X
Q u dydx XY U
(13)
The maximum velocity measured using PIV within each of theheat sink channels was substituted into Eq. (13) which yielded
the corresponding flow rates in each channel. These were
summed for all 6 channels to obtain the total volumetric flowrate passing through the system. The results are presented in
Fig. 14 and compared to volumetric flow rates for the tests
carried out without a diffuser [15]. It is seen that the flow ratein the finned heat sink with the diffuser attached at the
entrance is on average 15% higher that just the fan and heat
sink arrangement. However the increase in volumetric flow
rate at 8000RPM is lower compared to 3000RPM and5500RPM. A possible explanation for this is a higher variation
in flow rate between the heat sink channels at 8000RPM dueto higher speeds affecting the flow distribution. The accuracy
of the velocity measurements are due to a number of
experimental factors and are estimated at 5%.
0.E+00
1.E-05
2.E-05
3.E-05
4.E-05
5.E-05
6.E-05
7.E-05
8.E-05
9.E-05
0 1500 3000 4500 6000 7500 9000
Rotational Speed (RPM)
TotalVolumetricFlowR
ate(m3/s)
Heat Sink +Diffuser
Heat Sink
Fig. 14. Graph depicting the volumetric flow rates through
heat sink measured using Eq. (12) along with the PIV data
presented in Fig. 9 and [13] over the three fan speed tested
CONCLUSIONS
A miniature low profile cooling solution suitable for
integration into a range of portable electronics devices has
been characterized through thermal resistance and velocityfield measurements.
This paper presents an analysis on fan exit angle with resultsshowing that a reduction in thermal resistances are obtained
for flow entering the heat sink aligned with the fins. Flow
alignment has been achieved through the introduction of a
diffuser at the entrance to the heat sink. By accounting for fan exit angles, the thermal
resistance has been reduced by up to 23% for afinned heat sink and 15% for a finless heat sink. In
order to achieve these reductions the footprint area
has been increased by 16% and 6% respectively.
A finless heat sink and diffuser outperforms theconventional finned heat sink solution over a range
of fan speed tested.
The finned heat sink was designed using anoptimization criterion based on the fin spacing which
results in thermal boundary layers merging at the exit of
the heat sink. This was applied for a fan speed of8000RPM.
Results presented show that this optimization
criterion was confirmed for miniature scalesolutions as the finned heat sink outperforms the
finless case at 8000RPM
Finally the results also provide a basis for designers of heatsto analyze fan exit angles and a move towards integrated fan
and heat sink solutions.
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