1-s2.0-s0142727x11001214-main

7/30/2019 1-s2.0-S0142727X11001214-main

1/13

A study on the flow field and local heat transfer performance due

to geometric scaling of centrifugal fans

Jason Stafford, Ed Walsh, Vanessa Egan

Stokes Institute, Mechanical, Aeronautical and Biomedical Engineering Department, University of Limerick, Limerick, Ireland

a r t i c l e i n f o

Article history:

Received 25 February 2011

Received in revised form 1 September 2011

Accepted 4 September 2011

Available online 28 September 2011

Keywords:

Radial flow

Centrifugal fan

Electronics cooling

Miniature scale

a b s t r a c t

Scaled versions of fan designs are often chosen to address thermal management issues in space con-

strained applications. Using velocity field and local heat transfer measurement techniques, the thermal

performance characteristics of a range of geometrically scaled centrifugal fan designs have been investi-

gated. Complex fluid flow structures and surface heat transfer trends due to centrifugal fans were found

to be common over a wide range of fan aspect ratios (blade height to fan diameter). The limiting aspect

ratio for heat transfer enhancement was 0.3, as larger aspect ratios were shown to result in a reduction in

overall thermal performance. Over the range of fans examined, the low profile centrifugal designs pro-

duced significant enhancement in thermal performance when compared to that predicted using classical

laminar flow theory. The limiting non-dimensional distance from the fan, where this enhancement is no

longer apparent, has also been determined. Using the fundamental information inferred from local veloc-

ity field and heat transfer measurements, selection criteria can be determined for both low and high

power practical applications where space restrictions exist.

2011 Elsevier Inc. All rights reserved.

1. Introduction

The widespread use of centrifugal fans in engineering has re-

sulted in many geometric variations of designs in order to meet

application requirements. Such applications range from large scale

industrial dryers and air conditioning units, to smaller scale blow-

ers for the purpose of augmenting heat transfer in portable elec-

tronics. The requirement of fans in the electronics industry has

substantially driven the demand for high performance, low noise,

and low cost units that can contribute to maintaining adequate

component temperatures within space restricted environments.

In addition, the continual increase in density of electronics within

devices suggests that future cooling solution designs will be fur-

ther limited by available space. Therefore, there is a necessity to

address the topic of miniaturization within the area of thermalmanagement, to prevent thermal issues from stalling the develop-

ment of future technologies. This is reflected in recent literature

examining such areas as phase change materials (Tan and Tso,

2004; Fok et al., 2010), thermo electric coolers (Wilson and Simons,

2005; Garimella et al., 2008), and microheat pipes (Langari and

Hashemi, 2000). However, despite the widespread use of fanheat

sink combinations in electronics cooling, there is limited informa-

tion available that fundamentally examines the influence of geo-

metric scaling on the flow field and local heat transfer

distributions produced by miniature centrifugal fans.

At larger scales, the extended use of centrifugal fans for fluid

movement has resulted in detailed research into the performance

attributes of many designs. Wu et al. (2008) investigated the veloc-

ity field at inlet, outlet, and tip leakage planes for a centrifugal de-

sign with seven unequally spaced blades that were also staggered

at different angles along the blade span from hub to shroud. The

authors present this design as an effective way to improve aerody-

namic performance and reduce noise. High levels of positive and

negative vorticity exist on fan outlet measurement planes indicat-

ing counter rotational vortices which were generated by the back-

ward curved airfoil blades in rotation. The majority of the mass

flow tended towards the impeller hub, with increased velocity fluc-

tuations at the shroud side, aided by small vortices created by leak-age flow near the impeller shroud. The influence of a scroll housing

on the non-dimensional fan performance was noted as being insig-

nificant at a certain flow coefficient, however below this point the

scroll housing offered an increase in total pressure and efficiency,

with a decrease in the same observed at the higher flow

coefficients.

Yen and Liu (2007) used a phase-locked PIV technique to deter-

mine the outlet flow field of a shrouded centrifugal fan design

which has dimensions suitable to laptop sized electronic applica-

tions. Two planes were considered in detail, and the exit flow from

the shroud was shown to exit at an off-angle to the fan housing.

This was similarly noted by Egan et al. (2009) in a study of the flow

0142-727X/$ - see front matter 2011 Elsevier Inc. All rights reserved.doi:10.1016/j.ijheatfluidflow.2011.09.002

Corresponding author.

E-mail address: [email protected] (J. Stafford).

International Journal of Heat and Fluid Flow 32 (2011) 11601172

Contents lists available at SciVerse ScienceDirect

International Journal of Heat and Fluid Flow

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j h f f
http://dx.doi.org/10.1016/j.ijheatfluidflow.2011.09.002mailto:[email protected]://dx.doi.org/10.1016/j.ijheatfluidflow.2011.09.002http://www.sciencedirect.com/science/journal/0142727Xhttp://www.elsevier.com/locate/ijhffhttp://www.elsevier.com/locate/ijhffhttp://www.sciencedirect.com/science/journal/0142727Xhttp://dx.doi.org/10.1016/j.ijheatfluidflow.2011.09.002mailto:[email protected]://dx.doi.org/10.1016/j.ijheatfluidflow.2011.09.002

7/30/2019 1-s2.0-S0142727X11001214-main

2/13

entering miniature heat sinks which were positioned adjacent to a

shrouded centrifugal fan outlet. It was found that increases of up to

20% in the overall thermal performance of the miniature coolingsolutions could be achieved by aligning the fan exit flow with

the heat sink channels. This highlights the benefit of designing

fan and heat sink collectively rather than separately as is com-

monly considered. The advantage of using a finless heat sink design

at this scale over a conventional finned design was also another

outcome of this work. Stafford et al. (2009a) showed that the ther-

mal performance of the finless design is under predicted using

laminar duct flow theory. It was hypothesized that unsteady flow

structures generated by the centrifugal fan were conserved in the

finless geometry, thereby promoting heat transfer. The finned de-

sign however, suppressed these flow features to the longitudinal

direction, forming a closer representation with theory. The authors

also presented a prediction tool to determine the cross over in de-

sign choice for finned and finless geometries.Previous studies examining the bulk performance of rotating

fan designs indicates a degrading effect on aerodynamic perfor-

mance when fans are geometrically scaled below a critical point.

Grimes et al. (2005) initially noted the adverse geometric scaling

effect on the performance of an axial fan design. A datum fan de-

sign with a 120 mm diameter was geometrically scaled down to

1/3, which indicated a reduction in fan efficiency. Quin and Grimes

(2008) examined the same designs including a 1/20 scale of the

same axial fan design for a range of blade Reynolds numbers from

283 to 39,700 based on chord length and blade velocity at the mid-

span. Below a Reynolds number of 1980, a viscous scaling effect

was observed, where fan performance was adversely affected and

could no longer be determined by the non-dimensional flow and

pressure coefficients of the datum fan. Neustein (1964) also deter-mined a Reynolds number effect on axial fan performance to occur

below 2000. The resultant influence of this scaling effect on local

heat transfer distributions using a miniature axial fan has recently

been documented by Stafford et al. (2010a). In a complimentarystudy by Stafford et al. (2010b), a larger axial fan with different

blade geometry and hub-tip ratio was found to produce similar

surface heat transfer distributions. This was attributed to the sim-

ilarity in motor support layout on the exit flow plane.

The miniaturization of centrifugal fan designs also results in a

similar scaling effect on fan performance as shown by Walsh

et al. (2009a, 2010). In the first study by Walsh et al. (2009a), the

influence of fan profile scaling for fan diameters of 1530 mm

was examined to address the issues associated with implementing

miniature fan designs in low profile applications. The fan charac-

teristics of flow rate, pressure rise, and power consumption were

experimentally measured while varying the blade profile alone. A

low Reynolds number effect was noted at 650 based on chord

length and blade tip velocity which resulted in a reduction of flowrate, and a simultaneous increase in power consumption over that

predicted using conventional scaling laws (Bleier, 1997). At the

miniature scale, these fan scaling laws were found to be valid only

for fan aspect ratios between 0.12 and 0.17. In a separate study,

Walsh et al. (2010) examined the same fan characteristics and

range of fan diameters but in this case varying blade chord length.

Similar trends in reduced fan performance were noted at low Rey-

nolds numbers, and the authors applied simple boundary layer

theory to determine the main contribution to this scaling effect

for miniature fans. In doing so, the authors proposed an alternative

empirical based correlation for determining the performance of

centrifugal fan designs operating at low Reynolds numbers.

Aside from studies relating to fan flow and pressure character-

istics, investigations into the acoustic emissions of centrifugal fandesigns has also received attention (Wolfram and Carolus, 2010;

Nomenclature

A surface area, m2

ar fan aspect ratioc chord length, mC specific heat capacity, J/kg KD fan diameter, m

Dh hydraulic diameter 4pDH/2(pD + H), mDin fan inlet diameter, mfmax max. frequency detectible, HzFC forward curvedH distance between plates, mHf fan profile height, mh heat transfer coefficient, W/m2 KI current, Ak thermal conductivity, W/mKNETD noise-equivalent temperature differenceNu Nusselt numberDP static pressure difference, Paq00 heat flux, W/m2

_Q volumetric flow rate, m3/sr radial direction from fan center, m

r non-dimensional distance from fan blade ((r (D/2))/Dh)/(ReDh Pr)

Re Reynolds numberT surface temperature, KTu turbulence intensity 1=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu02 v02

p=Uex

u, v radial, axial velocity components, m/su0, v0 fluctuating component of velocity, m/sU velocity magnitude

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2 v2

p, m/s

Uex mean fan exit velocity, m/sV voltage, V

Vt blade tip velocity, m/sx, y, z Cartesian coordinates, m

time average

Greek symbolse emissivityl dynamic viscosity, kg/m sx fan rotationq density, kg/m3

r StefanBoltzmann constant, W/m2 K4

rh normalized fluctuations in heat trans. coeff: ffiffiffiffiffiffih02

p=hfc

s time, s/ flow coefficientw pressure coefficient

Subscriptsaw adiabatic wall temperature, Kc blade chord conditions as referencec conduction

f foil (SS304)fc forced convectiongen inputmax maximumnc natural convectionp paintr radiation1 ambient

J. Stafford et al. / International Journal of Heat and Fluid Flow 32 (2011) 11601172 1161

7/30/2019 1-s2.0-S0142727X11001214-main

3/13

Walsh et al., 2009b). The acoustic emission of miniature centrifugal

fans ranging in diameters of 1532 mm has been investigated by

Walsh et al. (2009b) for numerous fan profiles down to just

0.5 mm. The application of the work was focused on handheld elec-

tronic devices, and as a result measurement procedures were de-

signed to reflect this. It was determined that the acoustic

measurements at the fan outlet were dominant over that measured

above the inlet. A new scaling law was introduced which accountsfor rotational speed, diameter, height and aspect ratios between

0.06 and 0.16. Guidelines were also outlined for the design of min-

iature centrifugal fans to minimize acoustic levels.

In summary, a wide range of fan designs have been investigated

through velocity field, fan performance, and acoustic emission

analyses. Studies on miniature designs in terms of fan performance

characteristics and acoustic emissions are now evident due to the

anticipated move towards miniaturization in electronics cooling.

Although the influence of miniaturization on fan performance

has now been documented, only preliminary studies exist on the

exit flow field and thermal performance of combined miniature

fanheat sink cooling solutions. The finless heat sink concept has

been shown to provide thermal performance at a similar level to

finned designs of equal exterior dimensions at miniature scales,

however further investigation is required to fundamentally under-

stand the reason this unconventional design produces the level of

enhancement shown by Egan et al. (2009) and Stafford et al.

(2009a). Even at the larger scales, there is an absence of experi-

mental studies examining the influence of unsteady and non-uni-

form velocity fields from fan assemblies on local thermal

performance. This is despite the primary intended use of fans in

electronic systems being the promotion of heat dissipation.

Therefore, the present experimental study examines the veloc-

ity field and local heat transfer performance of centrifugal fans that

discharge air between two parallel plates, representing a finless

heat sink design. A primary aim is to examine the fluidic mecha-

nisms that result in local heat transfer enhancement and spatial

variation of surface heat transfer coefficient. Six scaled versions

of a centrifugal fan design have been used to investigate the influ-ence of geometric scaling on the velocity field and thermal perfor-

mance within a finless heat sink. A range of fan diameters (15

59 mm) and profiles (26.5 mm) have been chosen to highlight

the local heat transfer performance that can be achieved through

geometric scaling, while also maintaining a relatively low profile

for implementation into space constrained environments.

2. Centrifugal fan design and performance

For the velocity field and heat transfer analyses, a number of

geometrically scaled centrifugal fans were investigated which have

aspect ratios 0.0686 ar6 0.433. The geometric specifications of

these fans are included in Table 1. In Fig. 1, the four different cen-trifugal fan diameters are presented. All fans consist of a forward

curved blade design, however one half of the fans were designed

to rotate in a clockwise direction and the remaining designs ro-

tated in an anti-clockwise direction. This was chosen to investigate

if the direction of the tangential velocity component of the fan out-

let flow had an influence on the surface heat transfer phenomena

observed from the local heat transfer measurements. All fans were

manufactured using polycarbonate, and designed to operate with-

out a volute, allowing air to discharge in the radial direction. Fig. 1e

provides the geometrical details of the chosen fan design.

The non-dimensional flow and pressure coefficients are defined

in Eqs. (1), (2). These coefficients are plotted in Fig. 2 for all fan de-

signs in Table 1 operating at blade Reynolds numbers Rec > 1000,

where Rec = qVtc/l. The data presented in this section was experi-mentally measured using a test facility designed in accordancewith BS848 (1980). This test facility was developed to accurately

measure the fan performance characteristics of flow rate and pres-

sure for miniature designs similar to that examined in the current

study. A detailed description of this test facility is provided else-

where (Grimes et al., 2005).

/ _Q

xD2Hf1

w DP

qx2D22

Fig. 2 indicates the issue associated with accurately predicting

fan characteristics for a range of aspect ratios using conventionalscaling laws. This observation was noted by Walsh et al. (2009a)

who presented results for a constant diameter forward curved ra-

dial fan with various aspect ratios from 0.01 to 0.63. As aspect ratio

was decreased, the maximum pressure coefficient was shown to

decrease which is also shown in Fig. 2. Walsh et al. (2009a) deter-

mined that the fan scaling laws could only predict the performance

of the fan design investigated for the limited range

0.126 ar6 0.17. The 15 mm fan with ar = 0.133, and 24 mm

fan with ar = 0.167 are within this range and appear to resemble

similar non-dimensional performance attributes with maximum

flow and pressure coefficients within 14%.

Fig. 2 also highlights the importance of selecting a blade profile

within the maximum limit where the inlet chokes the flow and no

further benefits in flow rate are experienced. The maximum bladeprofile recommended by Bleier (1997) for forward curved blade

designs is Hf,max = 0.6Din (ar = 0.431) which equates to 6.46 mm

for the 15 mm fan design. In contrast, Walsh et al. (2009a) found

that above an aspect ratio of 0.35 no benefit in flow rate was

achieved. This is confirmed in the maximum flow rate measure-

ments, as shown in Fig. 3, of the 15 mm fan with ar = 0.431 which

provides minimal increase in flow rate over the 15 mm fan with

ar = 0.267. Consequently, velocity field measurements on the

15 mm fan were only considered for the maximum flow rate

fan design with Hf = 4 mm (ar = 0.267). Velocity field measure-

ments were also considered for the other fan diameters with

Hf = 4 mm to examine the influence of decreasing aspect ratio on

the flow field. Heat transfer measurements were compiled for all

fan sizes outlined in Table 1.Although an aspect ratio ar = 0.133 reduces the flow rate, the

static pressure level is maintained as the flow accelerates during

the 90 turn in the fluid from an axial to radial direction. An accel-

eration in flow occurs when the inlet area to the blade passages

(pDinHf) is less than the inlet orifice area pD2in

.4

. This is reflected

in Fig. 3 for a range of fan speeds. The linear regime for flow rate

Table 1

Fan specifications.

Diameter (mm) 15 15 15 24 32 59

Rotor speed (rpm) 50010,000 50010,000 50010,000 50010,000 5008000 2005000

Blade profile height (mm) 2 4 6.5 4 4 4

No. of blades 18 18 18 18 18 18

Blade design FC FC FC FC FC FC

Aspect ratio, ar 0.133 0.267 0.433 0.167 0.125 0.068

1162 J. Stafford et al. / International Journal of Heat and Fluid Flow 32 (2011) 11601172

7/30/2019 1-s2.0-S0142727X11001214-main

4/13

and power law trend for static pressure also confirms the scaling

relationship with fan rotational speed (Bleier, 1997).

3. Experimental details

The geometric specifications and bulk performance of the cen-

trifugal fans considered for this study have been presented in Sec-

tion 2. In the following sections, the velocity field and heat transfer

measurement procedures are discussed, including a description of

the experimental facilities created for the purpose of assessing the

influence of geometric scaling.

3.1. Velocity field analysis

A velocity field analysis was undertaken to characterize the ra-

dialaxial exit flow field of the scaled centrifugal fans. Particle Im-age Velocimetry (PIV) was chosen to complete this analysis as it is

a full field, non-intrusive measurement technique. The experimen-

tal arrangement for the velocity field analysis is provided in Fig. 4.

Each centrifugal fan was positioned between two parallel plates,

with the top plate containing an orifice that acted as the fan inlet,

having an equal diameter to the fan. In all cases a clearance gap of

0.5 mm was set between the base of the fan and base plate, and

also the top of the fan blade and top plate. An Edmund Industrial

Optics translation stage was used to achieve accurate fan position-

ing relative to the top and base surfaces. This stage allowed incre-

mental movements of 0.01 mm in the vertical direction. The fan

was rotated above the inlet to accommodate an infrared camera

and provide full optical access for experiments which visualized

the base plate heat transfer. Any effects of fan blockage due tothe presence of the motor (Maxon 110124 22 mm diameter

12VDC) and the positioning stage were alleviated by extending

the 3 mm diameter input shaft such that the motor to fan inlet dis-tance was 45 mm. A TTi dual DC power supply was used to control

fan rotational speed that was monitored using an Omega HHT13

optical tachometer.

The experimental arrangement was contained within a glass

walled enclosure of dimensions 600 mm (L) 300 mm(W) 300 mm (W) 300 mm (H). In this enclosure, tracer parti-cles were introduced using a glycol solution and Rosco 1700 fog

machine, and illuminated using a Nd:YAG laser in a single plane

of interest. An 11 mega-pixel CCD camera was positioned perpen-

dicular to the laser sheet. Images were recorded at 1 Hz and pro-

cessed using TSi Insight 3G software providing randomly

sampled, uncorrelated velocity field data. As a result, the conver-

gence of velocity field statistics was monitored against sample size

to ensure sufficient data samples were considered. An ensemble ofbetween 750 and 1000 vector maps was chosen to represent the

velocity field statistics. In the proceeding results section, this

ensemble averaged data shall be referred to as time-averaged. All

velocity field data was recorded with both top and base plates at

ambient temperature, as the main focus was to examine the effect

of geometric scaling on fan outlet flow.

3.2. Heat transfer analysis

The local heat transfer performance was quantified using infra-

red thermography and a heated-thin-foil technique. A schematic of

the experimental apparatus for the measurement of local heat

transfer coefficients is also presented in Fig. 4, where the heated-

thin-foil represents the top and base plates being cooled by thecentrifugal fan. A stainless steel 304 grade foil with a measured

Fig. 1. Centrifugal fan designs of (a) 15 mm, (b) 24 mm, (c) 32 mm, and (d) 59 mm diameters with fan profile height of 4 mm. (e) Geometrical details of the selected fan

design.

0 0.2 0.4 0.6 0.80

0.02

0.04

0.06

0.08

0.1

15mm 0.133

15mm 0.267

15mm

ar

0.433

24mm 0.167

32mm 0.125

59mm 0.068

10000 rpm

10000 rpm

10000 rpm

4000 rpm

4000 rpm

3000 rpm

D

Fig. 2. Non-dimensional flow and pressure coefficients.

0 2000 4000 6000 8000 100000

1

2

3

4

5

6

Fan speed (RPM)

Qx

104(m3/s)

ar= 0.133

ar= 0.267

ar= 0.433

0

5

10

15

20

25

30

P(Pa)

P

Fig. 3. Variation in maximum flow rate and static pressure (gray data points) with

fan aspect ratio using a 15 mm fan.


7/30/2019 1-s2.0-S0142727X11001214-main

5/13

thickness of 14.3 lm is clamped and tensioned using copper bus-

bars and a tensioning mechanism that prevents deflection of the

plates. An electric current is passed through the electrically resis-

tive thin-foil resulting in heating of the plate by Joule effect to pro-

duce a constant heat flux condition. The air leaving the fan outlet is

confined to exit in the radial direction, preventing recirculation of

heated air back into the fan inlet. Base and top plates could be

heated separately, and only the plate of interest was heated when

recording the temperature measurements. Due to the orifice in thetop plate, it was not possible to achieve a uniform heat flux over

the entire top surface when joule heated. Ideally, a fully heated

top plate with an inlet orifice centrally located on the heated-

thin-foil would determine the full field heat transfer distribution

on the top plate. However, initial experiments of this design were

unsuitable due to the local variation of the input heat flux q00gen, over

the surface of the heated-thin-foil. Due to the discontinuity of the

fan inlet orifice, electrical current is diverted around the orifice

resulting in non-uniform q00gen. To overcome this, only a portion of

the top plate highlighted in Fig. 4 and tangent to the inlet orifice

was heated. This was sufficient as the fan outlet flow was found

to be axisymmetric about the axis of fan rotation.

The thermal images of each plate were acquired using a

ThermaCam Merlin camera with an InSb detector operating inthe 35 lm MWIR spectral range. A 25 mm lens was used giving

a field of view of 22 16 and providing a temperature resolutionof 312.5 lm for all cases examined. A calibration of the infrared

camera was conducted to ensure accurate temperature measure-

ments (Stafford et al., 2009b). To ensure accuracy in the IR camera

calibration during image recording, a single K-type thermocouple

remained mounted to the foil in a location void of large gradients

in temperature. A K-type thermocouple was used to obtain the

ambient air temperature and was positioned 200 mm upstream

of the fan inlet. The effect of ambient air circulations and nearby

radiation sources was removed by positioning the experimental

facility in a large enclosure with a single provision for the infrared

camera lens. 60 thermal images were recorded at 1 Hz once the foil

reached a quasi-steady state. In this state, time-varying fluctua-tions in temperature were noted due to the unsteady fluid flow

interacting with the thin-foil surface. In the time-averaged analy-

sis, the images were averaged to reduce noise and time-varying

fluctuations in the temperature profile that were a magnitude of

103 of the averaged temperature map.On the camera observation side, the thin-foil is coated with an

opaque matt black spray paint to provide an emissivity of 0.96 on

the surface. Both foil and paint thicknesses were measured to ac-

count for the contribution of tangential conduction in the energy

balance of Eq. (3) which has been shown by Stafford et al.(2009b) to produce significant errors in the forced convection heat

transfer coefficient if ignored at this scale. Eq. (3) defines the forced

convection heat transfer coefficient

hfcq00gen q

00nc q

00r q

00c

T Taw3

where q00gen is the input heat flux, q00r is the radiation heat flux, and q

00c

is the contribution of the conductive heat flow in the foil and paint

layers, all of which are defined in Eqs. (4)(6). The surface of the

thin-foil on the camera observation side also dissipates heat by nat-

ural convection, q00nc, which was measured experimentally.

q00gen VI

A4

q00r er T4 T41

5

q00c kftf kptp@2T

@x2

@2T

@y2

! qfCftf qpCptp

@T

@s

6

The time-averaged heat transfer coefficient was solved using a

time-averaged temperature profile and neglecting the energy stor-

age term in Eq. (6) which contains the additional effect of heat flow

over time interval, os. The root-mean-square of the fluctuations inheat transfer coefficient was calculated to determine the effect of

turbulence and fluid unsteadiness on the surface heat transfer dis-

tribution. This was achieved by solving for the instantaneous heat

transfer coefficient using the energy balance of Eq. (3) and usingthe full expression in Eq. (6) over the recording interval.

Fig. 4. Experimental schematic for velocity field and heat transfer measurements.


7/30/2019 1-s2.0-S0142727X11001214-main

6/13

The acquisition of the fluctuating heat transfer coefficient is

limited due to the time constant of both the foil and paint layers.

Consequently, the amplitude of the recorded temperature fluctua-

tions is dependent on both the amplitude and frequency of the

heat transfer fluctuations due to the thermal inertia of the com-

bined foil and paint layers. Eq. (7) has been adapted from Nakam-

ura (2009) to reflect this and determine the maximum frequency of

the fluctuations which can be detected.

fmax eDhfcT T1

2pqfCftf qpCptpDTNETD7

where DTNETD is the noise-equivalent temperature difference of the

infrared camera. For the range of experiments considered, the max-

imum detectible frequency of heat transfer coefficient fluctuations

was approximately 5 Hz.

The Nusselt number is defined in Eq. (8) based on the character-

istic dimension Dh. This represents the hydraulic diameter where

the flow exiting the fan enters the channel.

NuDh hfcDh

kair8

where kair is the fluid thermal conductivity.

The relationship between heat transfer and fluid dynamics can

be examined through the scaling of non-dimensional Nusselt num-

ber with Reynolds number. The previously defined Rec is inappro-

priate for this as it only characterizes fan aerodynamics and is

independent of the flat plate heat transfer due to the scaling effect

that exists at miniature scales. Therefore, Reynolds number was

defined as:

ReDh qUexDhl

9

where Uex is the mean fan exit velocity entering the channel, calcu-

lated from flow rate measurements. This provided a range

45 < ReDh < 5700.

3.3. Uncertainty

The influence of measurement uncertainties on the calculated

data presented has been accounted for using an uncertainty anal-

ysis (Moffat, 1997). Uncertainties in the measurement of pressure

and volumetric flow rate were 5% and 2.8% respectively. Uncer-

tainty in the measurement of velocity was determined to be

5.44%. The maximum uncertainty in the heat transfer coefficient,

Nusselt and Reynolds numbers were estimated at 10.9%, 11.2%

and 3.1% respectively. The optical tachometer used for measuring

fan rotor speed has an accuracy related to the resolution limit of

1 rpm. For the fan speeds considered however, uncertainty was

noted as approximately 10 rpm, due to variations in speed moni-

tored over the test duration. Experimental uncertainty bands have

been neglected when presenting the data for clarity.

4. Results and discussion

The experimental results of the local velocity field at the fan

blade exit are presented first to determine the flow features that

are generated by various scaled centrifugal fans with radial dis-

charge. This information is then used to discuss the local and aver-

age heat transfer distributions which occur on the surface of the

parallel plates that confine the exit flow, and represent the finless

design. Finally, non-dimensional radial distributions in heat trans-

fer are presented to examine the relationship between the fan exitflow, and the resultant heat transfer profiles.

4.1. Velocity field

Fig. 5 presents the time-averaged velocity and streamlines in

the radialaxial plane between base and top plates when using a

15 mm fan with aspect ratio ar = 0.267. This example has been

chosen to present the similar flow features observed for all cases

examined. All velocity field data has been normalized with the

mean fan exit velocity Uex. The air flow exits the fan blades produc-ing a high shear flow with a large velocity gradient on the base

plate. The high shear flow enters the finless channel at approxi-

mately one half of the channel height, and extends in the radial

direction to a radial distance which is dependent on Reynolds

number. This type of fan exit flow profile results from much of

the airflow tending towards the back plate of the fan due to the

inertia forces that are generated as the fan redirects the axial inlet

flow 90 to produce a radial outlet flow. For the Reynolds number

range examined using this fan, a primary vortex is evident which is

promoted by the high velocity exit flow interacting with the lower

velocity fluid in the remaining half of the channel. This velocity

profile at the fan exit also influences the downstream flow features

within the channel. As air exits the lower section of the fan blade, it

expands in the radial and axial directions. This expansion results in

an adverse pressure gradient which forces the high velocity flow to

separate from the base plate. This separation drives the impinge-

ment which occurs on the top plate. The impinging air flow is then

deflected back towards the base plate resulting in a secondary

impingement also highlighted in Fig. 5. A product of the separation

and both impingements is a secondary vortex which rotates in the

opposite direction to the primary vortex. It is apparent when com-

paring Fig. 5ac that increasing Reynolds number shifts the point

of impingement in the radial direction away from the fan. This shift

is due to an increase in pressure in the fan exit flow over the ad-

verse pressure produced by the expanding air flow. Consequently,

at ReDh = 1615, the secondary vortex is elongated in the radial

direction compared to that observed for the lower Reynolds num-

ber examples.

A comparison between the instantaneous flow fields shown inFig. 6a and b indicates the high level of unsteadiness which exists

at the outlet of centrifugal fans and within the finless channel. Vor-

tices which are evident in the upper half of the channel intermit-

tently disrupt the high velocity shearing flow along the base

plate. This is caused by axial movement of vortices which encom-

pass a level of vorticity that results in acceleration and deceleration

of the shear flow upon interaction. This is observed in the instan-

taneous velocity fields in Fig. 6 as regions of increased and de-

creased velocity magnitude are apparent in the region r/D < 1.

The instantaneous distributions also highlight the detachment

due to the adverse pressure gradient produced by the radial expan-

sion. In Figs. 5 and 6, the location of the flow impingements and

detachments are indicated by arrows which point to the radial

location where the radial wall shear stress l @u@z 0.The time-averaged turbulence statistics for this example are

presented in Fig. 6c. The radialaxial turbulence intensity increases

to 50% of the mean fan exit velocity in the region near the fan

blades. Two shear layers emerge as a result of the interaction of

the high velocity fan exit flow with the surrounding low velocity

fluid within the channel. The upper shear layer exists from the

fan outlet until impingement occurs on the top plate. The lower

shear layer is only evident once the high velocity flow is forced

to detach from the base plate.

Over the range of Reynolds numbers examined for the 15 mm

fan, both time-averaged vortices and impingements were evident.

Common fluidic mechanisms within the channel were also found

to exist with geometric scaling. However, one main difference with

the exit flow field of the 15 mm fan is the absence of a secondaryvortex within the radialaxial flow field above a critical Reynolds


7/30/2019 1-s2.0-S0142727X11001214-main

7/13

number. These critical Reynolds numbers were found to be 1350,

1010, and 880 for the 24 mm, 32 mm and 59 mm diameter fans

of constant fan profile height. This has been attributed to a change

in expansion with increasing fan diameter, as it is the expanding

fan outlet flow which governs the adverse pressure gradient. As

fan diameter is increased, the ratio of the fan exit flow area (inlet

area to channel) to the channel exit flow area approaches unity,

and the radial expansion is no longer dominant. Consequently,

the adverse pressure gradient produced by the expanding flow is

insufficient to result in flow detachment along the base surface.

When the detached flow along the base plate is absent, the local re-

gion of impingement on the base plate is removed and may resultin reduced thermal performance at this local position. However, by

overcoming the adverse pressure gradient, the detachment of the

high velocity flow exiting the fan no longer occurs, and velocity

gradients at the surface are increased which would lead to heat

transfer enhancement. In the following section, the influence of

this secondary vortex on local heat transfer of both plates is

discussed.

Sample velocity fields for the fan diameters 2459 mm and r/

D < 1.1 are presented in Fig. 7. At ReDh = 2770, the flow field pro-

duced by the 24 mm fan contains only a primary vortex. In con-

trast, the flow field due to the 32 mm fan and ReDh = 415

contains both counter rotating vortices as it is below the critical

ReDh previously discussed. In Fig. 7c, the location of a single vortex

accommodates a much smaller area of the flow field than the pri-

mary vortex for the larger aspect ratio fans of Fig. 7a and b. Thevelocity profile appears to be directed towards the top plate to

some extent for 0.5856 r/D6 0.754. It is anticipated that the pres-

sure variation across the curved streamlines of the single vortex re-

sults in a net force acting perpendicular to these streamlines and

towards the center of curvature (Massey, 2006). This net force

causes the high velocity flow to bend towards the top plate, follow-

ing the curvature of the primary vortex rather than continuing in a

solely radial direction along the base plate. In contrast to the larger

aspect ratio fans (including that of the 15 mm fan in Fig. 5), the

outlet flow of the 59 mm fan is distributed over a larger portion

of the blade profile, and therefore the channel. Consequently, the

low velocity region within the channel is much smaller than for

ar > 0.125.

The normalized velocity profiles ofFig. 8 suggest that as fan as-pect ratio is decreased for a constant plate spacing, the flow within

the channel approaches a near parabolic profile much sooner than

for aspect ratios ar > 0.125. This is particularly evident when using

the 59 mm fan with ar = 0.068. A theoretical velocity profile for r/

D = 1.09 is included in Fig. 8 based on the measured flow rate and

the Hagen-Poiseuille profile for fully developed flow between par-

allel plates. For r/D > 0.754, the experimental velocity profile al-

most resembles a parabolic shape with a maximum velocity near

the center of the channel. All of the velocity profiles presented in

Fig. 8 have been normalized with the maximum velocity magni-

tude at r/D = 0.585.

For all fan diameters investigated, the velocity field analyses

have illustrated an unsteady flow exiting the fan which contains

vortex structures that disrupt the high velocity shearing flow inthe entrance region to the channel. This disruption of the boundary

(a)

(b)

(c)

Fig. 5. Time-averaged velocity field for a 15 mm fan (ar = 0.267) and (a) ReDh = 85, (b) ReDh = 705, and (c) ReDh = 1615.

(a)

(b)

(c)

Fig. 6. Instantaneous velocity field at time (a) s and (b) s + 1 s. (c) Turbulenceintensity for a 15 mm fan (a

r= 0.267) and Re

Dh= 1615.


7/30/2019 1-s2.0-S0142727X11001214-main

8/13

layer along the plate surfaces can enhance heat transfer with tur-

bulent diffusion. In Sections 4.2 and 4.3, local and radial heat trans-

fer distributions are presented to determine the level of

enhancement the unsteady flow within the channel produces,

and also the contribution of the previously discussed exit flow fea-

tures on the spatial and temporal heat transfer performance.

4.2. Local heat transfer

The apparatus for the measurement of local heat transfer coef-

ficients using a centrifugal fan has been presented in Section 3.2.

This was used to determine if a wide range of fan aspect ratios,

with the same geometric design, provided similar heat transfertrends that could be related to the velocity fields illustrated in

the previous section.

The base and top plate Nusselt number distribution are pre-

sented in Fig. 9 for a 15 mm fan (ar = 0.267) and ReDh = 1615.

The outline of the fan has been superimposed on all local distribu-

tions for the purpose of discussion, with the location of the fan cen-

ter at (x/D,y/D) = (0,0). In Fig. 9a, the influence of the fan outlet

flow along the base plate on local heat transfer performance is

apparent. In this region, local Nusselt numbers of over 50 are pro-

duced from the large velocity gradients at the exit of the fan blades.

The area occupied by the secondary vortex is also evident, as well

as an annular region of increased heat transfer produced by the

secondary impingement observed in the velocity field measure-

ments of Fig. 5. The primary impingement and vortex zones pro-

vide an increase in local heat transfer on the top plate, as shown

in Fig. 9b. The top plate has a lower magnitude of Nusselt number

due to the majority of air exiting the lower portion of the fan

blades. As previously discussed in Section 3.2, the heated portion

of the top plate is that shown in the color contour region of

Fig. 9b which is tangent to the fan inlet. The slight dissimilarity

in the local Nusselt number between x/D < 0 and x/D > 0 is due to

an unheated entrance effect, as thermal boundary layers only begin

to develop at the heated foil leading edge. However, this asymme-

try is relatively minor, and the local heat transfer distributions are

adequately captured.Fig. 10 presents the local Nusselt number on the base plate for

the larger fan diameters investigated and corresponding to the

velocity fields of Fig. 7. By operating above the critical Reynolds

number where flow detachment is avoided, the heat transfer rates

on the base surface due to the 24 mm fan decrease gradually from

the fan blades in the radial direction. This is also observed for the

59 mm fan in Fig. 10c. In Fig. 10b however, detachment produces

a local heat transfer distribution similar to that shown in Fig. 9a for

the 15 mm fan. A twofold increase in the local Nusselt number

over the secondary vortex region is observed in an annular area

where the fluid deflected from the top plate (Fig. 7b) impinges

the base surface.

The local heat transfer distributions highlight regions where

significant improvement in heat dissipation can be achieved, butalso regions to be avoided if the intended use of the centrifugal

fan is to cool discrete heat sources. Therefore, the heat transfer pro-

files on base and top plates can differ substantially when vortices

are apparent, from the typical monotonic behavior that is com-

monly assumed when predicting local thermal performance for

flow between parallel plates.

The spatial variation of Nusselt number using centrifugal fans

has been discussed using Figs. 9 and 10, however the fluctuating

nature of unsteady fan flows is often overlooked when analyzing

heat transfer performance using time-averaged information.

Hence, it is also important to determine the influence of unsteady

fan outlet flows on heat transfer performance over time. This may

be particularly useful if, like in electronics, reliability of compo-

nents can be adversely affected by cyclic thermal loading. In thecurrent study, the 15 mm fan with ReDh = 1615 has been chosen

(a)

(b)

(c)

Fig. 7. Time-averaged velocity field for (a) 24 mm fan (ar = 0.167) and ReDh = 2770, (b) 32 mm fan (ar = 0.125) and ReDh = 415, and (c) 59 mm fan (ar = 0.068) and

ReDh = 1075.

0 0.2 0.4 0.6 0.8 10

0.017

0.034

0.051

0.068

0.085

Normalized U

z/D

0.5850.7540.9241.09

(1.09)

r / D

Fig. 8. Normalized velocity profiles for a 59 mm fan (ar = 0.068) and ReDh = 1075.


7/30/2019 1-s2.0-S0142727X11001214-main

9/13

to convey this information. In Fig. 11, the normalized fluctuations

in heat transfer coefficient (rh) on the base plate are up to approx-

imately 10% and cover an annular region on the surface where theseparated flow and secondary vortex occurs, shown previously in

the time-averaged heat transfer measurements of Fig. 9a and

velocity field ofFig. 5c. The results presented in Fig. 11 imply a lar-

ger amplitude of normalized fluctuations in heat transfer coeffi-

cient exist when this secondary vortex is apparent in the flow

field. However, due to the limitations of the experimental tech-

nique in resolving the true amplitude of high frequency fluctua-

tions (Section 3.2), it is not possible to confidently arrive at this

conclusion. It is however, possible to conclude that normalized

fluctuations in heat transfer coefficient with an approximate fre-

quency less than 5 Hz are a maximum when this secondary vortex

is in the flow field. Using this information, this annular region of

increased heat transfer fluctuations could potentially be avoided

if positioning discrete heat sources near centrifugal fan flows.

4.3. Radial heat transfer

This section discusses the influence of fan profile and diameter

scaling on thermal performance of centrifugal fans through mea-

surements of radial distributions in heat transfer. Although fan as-

pect ratio has been shown in Section 2 to be an important

parameter in the selection of fan designs from a bulk flow rate

and pressure perspective, the influence of this parameter on heat

transfer augmentation has not yet been confirmed.

Fig. 12 presents the axisymetric radial distribution of heat

transfer coefficient, circumferentially averaged and normalized

by the maximum heat transfer coefficient hfc(max) on base and top

plates. In Fig. 12a, hfc(max) is the maximum heat transfer coefficientover the entire range of 15 mm fan aspect ratios examined. Sim-

ilarly, Fig. 12b is normalized with the equivalent maximum ob-

served on the top plate. A range of fan aspect ratios are shown

using a 15 mm radial fan and operating at a constant

10,000 rpm. The base plate data show that similar heat dissipation

levels are achieved in the shearing flow region for all aspect ratios.

For ar = 0.267, a greater surface area is covered by the shearing flow

and secondary impingement zones due to the increased flow rate

for this fan profile. At this fan rotational speed, the ar = 0.433 fan

has a similar heat transfer distribution however with the absence

of an increase in heat transfer due to a secondary impingement.

It is anticipated that the secondary vortex does exist in the flow

field, as observed for the other aspect ratios. However, due to the

(a) (b)

Fig. 9. Local Nusselt number on the (a) base and (b) top plates for a 15 mm fan (ar = 0.267) and ReDh = 1615. Contour level: 1.5.

x / D

y/D

2 1.5 1 0.5 0 0.5 1 1.5 22

1.5

1

0.5

0

10

20

30

40

50

60

70

80

90

Nu

x / D

y/D

1.5 1 0.5 0 0.5 1 1.51.5

1

0.5

0

5

10

15

20

25

Nu

x / D

y/D

0.5 0 0.5

1

0.8

0.6

0.4

0.2

0

5

10

15

20

25

30

35

40

Nu

(a) (b) (c)

Fig. 10. Local Nusselt number on the base plate for (a) 24 mm fan (ar = 0.167) and ReDh = 2770, (b) 32 mm fan (ar = 0.125) and ReDh = 415, and (c) 59 mm fan (ar = 0.068)

and ReDh = 1075. Contour levels: (a) 3, (b), (c) 1.

Fig. 11. Normalized fluctuations in hfc on the base plate for a 15 mm fan

(ar = 0.267) and ReDh = 1615. Contour level: 0.005.


7/30/2019 1-s2.0-S0142727X11001214-main

10/13

larger channel spacing combined with no increase in flow rate over

the ar = 0.267 fan (Fig. 3), the primary impingement on the top

plate is at a much lower velocity. This is confirmed when examin-

ing the top plate radial heat transfer distribution in Fig. 12b. The

heat transfer performance in this zone using an ar = 0.267 fan is

approximately twice that of the ar = 0.433 fan. Consequently, with

the deflection of air from the top plate to the base plate, the ap-

proach velocity for the second impingement is also considerablylower when using a fan with ar = 0.433.

On the base plate, the normalized heat transfer coefficient be-

neath the fan back plate is similar for all profiles as expected. In

this region, it is anticipated that a Couette flow drives heat transfer,

and is independent of fan profile for a constant fan diameter and

blade Reynolds number, Rec. A velocity gradient exists between

the base plate and the underside of the fan back plate. Although

a piezometric pressure difference is absent in this region, this gra-

dient occurs as a result of the moving boundary that is the fan back

plate.

The ar = 0.133 fan produces the greatest peak in heat transfer at

r/D = 0.6, which may be attributed to the increase in acceleration of

the fluid upon exiting the blade passage pDinHf < pD2in

.4

, as

previously discussed in Section 2. As aspect ratio increases, the re-duced acceleration results in a peak of lower magnitude at r/

D = 0.6. Bleier (1997) indicated that the fluid can accelerate over

the blade tip speed, when exiting at the fan blade pressure side.

This is confirmed in the heat transfer measurements, as the peak

in maximum heat transfer is outside the blade tip location of r/

D = 0.5. For r/D > 0.6, a decrease in heat transfer is experienced as

the high momentum fluid exiting the fan detaches from the base

plate, due to an adverse pressure gradient, and provides impinge-

ment cooling for the top plate at r/D = 0.7 using the ar = 0.133fan. The fan with ar = 0.267 has this peak in heat transfer at r/

D = 0.9, owing to the increase in flow rate extending the shearing

area on the base plate surface. It is postulated that the largest as-

pect ratio fan ar = 0.433 produces this peak at a lower r/D as the

outlet flow is subjected to a greater expansion while maintaining

a flow rate with similar magnitude to the lower aspect ratio fan

of ar = 0.267 (Fig. 3).

Upon impingement, the high momentum fluid is then deflected

back towards the base plate resulting in the creation of a secondary

peak in heat transfer for the ar = 0.133 and ar = 0.267 fans over the

entire range of Reynolds number investigated. For ar = 0.433 pre-

sented in Fig. 12a however, this secondary peak is absent and there

is a gradual reduction in heat transfer from the local maximum.

The level of heat transfer from the top plate surface in Fig. 12b is

also greatly reduced over the ar = 0.133 and ar = 0.267 fans, as the

fluid predominately exits the fan blade along the base plate.

Although the ar = 0.133 fan supplies 57% of _Q for the ar = 0.267

fan at this rotational speed, the ar = 0.133 fan provides a similar

magnitude of radial heat transfer on the top plate as the

ar = 0.267 fan. It is estimated that the mean velocity within the

channel is similar for both, as %40% reduction in flow rate is cou-pled with a 40% reduction in exit flow area due to the plate spacing

reducing from 5 mm (Hf = 4 mm) to 3 mm (Hf = 2 mm). Therefore

fan profile selection can greatly influence the heat transfer perfor-

mance of both base and top plates of this design.

The radial distribution of Nusselt number is presented in Fig. 13

for fan diameters of 24 mm, 32 mm, and 59 mm and a range of

Reynolds numbers, 190 < ReDh < 5700. Non-dimensional heat

transfer data is presented using the laminar flow relationship withReynolds number, NuDh=

ffiffiffiffiffiffiffiffiffiffiReDh

p. The theoretical solution for lami-

nar duct flow is also included to provide a comparison with the

measured data for centrifugal fans. This is an idealized solution, de-

rived from the theoretical relationship for flat plate heat transfer

and based on a zero pressure gradient assumption; however it is

useful for assessing the thermal performance of the centrifugal

fans. The theoretical model assumes laminar flow in the channel

entrance region with a constant heat flux boundary condition on

the surface, NuDh 0:453=ffiffiffiffir

pPr1=6 where r is the non-dimen-

sional distance from the fan blade. This model has been selected

as previous studies by Sparrow (1955) and more recently by Staf-

ford et al. (2009a) indicate that this approach can adequately rep-

resent the entrance region Nusselt numbers for simultaneously

developing hydrodynamic and thermal boundary layers withinparallel plate and rectangular channels.

The Reynolds numbers where the secondary peak in heat trans-

fer occurs are highlighted (blue1) in Fig. 13a and c. This peak shifts

outwards in the radial direction as Reynolds number is increased,

until a point where the expanding flow no longer causes a flow sep-

aration on the base plate. The shift in the peak in Nusselt number on

the top plate is also discernible in Fig. 13b and d. This peak becomes

less pronounced as Reynolds number increases, as it is the flow

detachment from the base plate which provides the primary

impingement on the top surface. For all cases examined, the theoret-

ical solution under predicts the thermal performance of the centrif-

(a)

(b)

Fig. 12. Radial distribution of the normalized heat transfer coefficient on (a) base

and (b) top plates for 15 mm fans with aspect ratio 0.1336 ar6 0.433.

1 For interpretation of color in Figs. 1, 411, 13, 14, the reader is referred to the webversion of this article.


7/30/2019 1-s2.0-S0142727X11001214-main

11/13

ugal fans up to r/D % 2 for the base plate, and r/D % 1.5 for the topplate. Above these non-dimensional distances from the fan blade,

the heat transfer performance begins to correlate with theory, as

the unsteady vortical structures have dissipated into the mean flow.

This suggests that centrifugal fans, used for heat dissipation pur-

poses, should be selected based on these limiting radial distances.

In the regions near the fan exit, significant improvements in

thermal performance are observed along the base surface aside

from the regions where separation occurs. This can be related to

the velocity field measurements presented in Figs. 5 and 7. Theoutlet velocity above the base surface in this region ranges be-

tween 1.5Uex and 2.5Uex depending on fan aspect ratio. Conse-

quently, the velocity gradients that result from the centrifugal

fan outlet flow are greater than that assumed in the prediction,

as the heat transfer prediction utilizes the mean outlet velocity

Uex. The increased velocity gradients combined with the flow

unsteadiness observed in Fig. 6, result in the substantial increase

in radial distribution of heat transfer in this region.

In Fig. 13a and c, the heat transfer performance in the secondary

vortex region (r/D % 1) reduces considerably, and is of similar mag-

nitude to that theoretically predicted. Once separation no longeroccurs at the higher Reynolds numbers, this reduction in heat

(a) (b)

(c) (d)

(e) (f)

Fig. 13. Nusselt and Reynolds number scaling relationship on base (left) and top (right) plates using (a) and (b) 24 mm (ar = 0.167); (c) and (d) 32 mm (ar = 0.125); and (e)

and (f) 59 mm (ar = 0.068) geometrically scaled centrifugal fans.


7/30/2019 1-s2.0-S0142727X11001214-main

12/13

transfer performance is avoided. However, the separation and

resultant secondary impingement, also increases the thermal per-formance locally for 1 < r/D < 1.6.

The influence of the primary vortex and impingement on heat

transfer performance on the top surface is shown in Fig. 13b, d

and f. The low velocity region of the primary vortex near the inlet

orifice, as shown in the velocity field measurements of Fig. 7, re-

sults in a lower heat transfer performance compared to the theo-

retical solution. The thermal performance then increases to a

peak which is produced by the primary impingement. This peak

eventually flattens out with increasing Reynolds number for the

reasons discussed previously.

Fig. 13 also indicates that the local thermal performance does

not scale towards a laminar flow regime for the majority of radial

locations. If this was so, the measured data for each Reynolds num-

ber would collapse to a single profile, as is the case for the theoret-ical profile. This is due to the unsteady flow produced by the fan,

where vortices interact with the base and top surfaces, as shown

in Fig. 6a and b for the 15 mm fan. This unsteady flow increases

mixing and results in the thermal performance to scale towards

that of a turbulent flow regime. This is shown for the example of

the 24 mm fan and base plate heat transfer in Fig. 14. Fig. 14 con-

sists of the data ofFig. 13a, however expressed using a Reynolds

number exponent of 0.65. This exponent was chosen as it produces

the lowest local standard deviations ( 0.5. The main deviation from this relationship in

the lower Reynolds numbers is due to the change in the velocityprofile when separation occurs, resulting in a secondary vortex

and impingement along the base.

Through examination of bulk thermal performance of miniature

and low profile finless cooling solutions, Stafford et al. (2009a)

hypothesized that such designs typically correlate towards that

of a turbulent flow regime, despite operating at low Reynolds num-

bers in many cases. The current study confirms this finding, pro-

viding an insight into the fluidic mechanisms which promote

heat transfer when using low profile centrifugal fans as part of

an integrated cooling solution.

5. Conclusions

The influence of geometric scaling on the velocity field and localheat transfer of centrifugal fans have been highlighted over a wide

range of fan dimensions, with the primary focus on low profile de-

signs. Local velocity field and heat transfer measurements have

been developed to assess the fluid mechanisms produced by cen-

trifugal fan exit flows which are fundamental to cooling solution

performance and optimization. It was determined that miniature

centrifugal fans should be designed with an aspect ratio less than

0.3 to avoid reductions in thermal performance. This has been

attributed to a reduction in flow coefficient, as no further increasein flow rate is achieved above this aspect ratio. It is postulated that

the common exit flow profile for centrifugal fans occurs due to

inertia forces, as the fan directs the axial inlet flow to a radial outlet

flow. As aspect ratio decreases and flow rates increase, this effect is

reduced and the outlet flow is distributed over the majority of the

blade height. The expanding flow from centrifugal fans within a

parallel plate channel produced an adverse pressure gradient that

resulted in flow separation along the base plate, creating multiple

time-averaged vortices and impingements. As fan diameter in-

creased and aspect ratio decreased, this separation was no longer

evident above a critical Reynolds number. When this occurs, the

spatial and temporal heat transfer distributions are substantially

altered, and begin to approach a monotonic decay in local heat

transfer with distance from the fan blade tip. Unsteady flow within

the parallel plate channel results from the interaction of vortices

with the high velocity exit flow. The interruption of the fan exit

flow by these unsteady fluidic mechanisms disrupts boundary

layer growth within the channel, promoting heat transfer above

that predicted using laminar flow theory.

References

Bleier, F.P., 1997. Fan Handbook: Selection, Application and Design. McGraw-Hill.BS848: Fans for General Purposes, Part 1: Methods for Testing Performance, 1980.Egan, V., Stafford, J., Walsh, P., Walsh, E., 2009. An experimental study on the

performance of miniature heat sinks for forced convection air cooling. J. HeatTransfer. 130 (7), 071402 (19).

Fok, S.C., Shen, W., Tan, F.L., 2010. Cooling of portable hand-held electronic devicesusing phase change materials in finned heat sinks. Int. J. Therm. Sci. 49 (1), 109117.

Garimella, S.V., Fleischer, A.S., Murthy, J.Y., Keshavarzi, A., Prasher, R., Patel, C.,Bhavnani, S.H., Venkatasubramanian, R., Mahajan, R., Joshi, Y., Sammakia, B.,Myers, B.A., Chorosinski, L., Baelmans, M., Sathyamurthy, P., Raad, P.E., 2008.Thermal challenges in next-generation electronic systems. IEEE Trans. Comp.Packag. Technol. 31 (4), 801815.

Grimes, R., Walsh, E.J., Quin, D., Davies, M., 2005. The effect of geometric scaling onaerodynamic performance. AIAA J. 43 (11), 22932298.

Langari, A., Hashemi, H., 2000. A system level cooling solution for cellular phoneapplications. Electron. Cool. 6 (2), 17.

Massey, B., 2006. Mechanics of Fluids, eight ed. Taylor & Francis, Inc.Moffat, R.J., 1997. Uncertainty analysis. In: Azar, K. (Ed.), Thermal Measurements in

Electronics Cooling. CRC Press, pp. 4580.Nakamura, H., 2009. Frequency response and spatial resolution of a thin foil for heat

transfer measurements using infrared thermography. Int. J. Heat Mass Transfer.52 (2122), 50405045.

Neustein, J., 1964. Low Reynolds number experiments in an axial flow

turbomachine. J. Eng. Power. 86 (3), 257295.Quin, D., Grimes, R., 2008. The effect of Reynolds number on microaxial flow fanperformance. J. Fluids Eng. 130, 101101 (110).

Sparrow, E.M., 1955. Analysis of laminar forced convection heat transfer in entranceregion of flat rectangular ducts. NACA Tech. Note 3331, 142.

Stafford, J., Walsh, E., Egan, V., Walsh, P., Muzychka, Y.S., 2009a. A novel approach tolow profile heat sink design. J. Heat Transfer. 132 (9), 091401 (18).

Stafford, J., Walsh, E., Egan, V., 2009b. Characterizing convective heat transfer usinginfrared thermography and the heated thin-foil technique. Meas. Sci. Technol.20, 105401 (111).

Stafford, J., Walsh, E., Egan, V., 2010a. Local heat transfer performance and exit flowcharacteristics of a miniature axial fan. Int. J. Heat Fluid Flow 31 (5), 552560.

Stafford, J., Walsh, E., Egan, V., Grimes, R., 2010b. Flat plate heat transfer withimpinging axial fan flows. Int. J. Heat Mass Transfer. 53 (2526), 56295638.

Tan, F.L., Tso, C.P., 2004. Cooling of mobile electronic devices using phase changematerials. Appl. Therm. Eng. 24 (23), 159169.

Walsh, P., Egan, V., Grimes, R., Walsh, E., 2009a. Profile scaling of miniaturecentrifugal fans. Heat Transfer Eng. 30 (1), 130137.

Walsh, E., Walsh, P., Punch, J., Grimes, R., 2009b. Acoustic emissions from active

cooling solutions for portable devices. IEEE Trans. Comp. Packag. Technol. 32(4), 776783.

Fig. 14. Collapse of Nusselt and Reynolds number scaling relationship on the base

plate using a 24 mm (ar = 0.167) centrifugal fan and a Reynolds number exponent

of 0.65. Symbols correspond to that presented in Fig. 13a.


7/30/2019 1-s2.0-S0142727X11001214-main

13/13

Walsh, P.A., Walsh, E.J., Grimes, R., 2010. Viscous scaling phenomena in miniaturecentrifugal flow cooling fans: theory, experiments and correlation. J. Electron.Packag. 132 (2), 021001 (18).

Wilson, J., Simons, R.E., 2005. Advances in high-performance cooling for electronics.Electron. Cool. 11 (4), 122.

Wolfram, D., Carolus, T.H., 2010. Experimental and numerical investigation of theunsteadyflow field and tonegeneration in an isolated centrifugal fan impeller. J.Sound Vib. 329 (21), 43804397.

Wu, Y.D., Ouyang, H., Tian, J., Du, Z.H., 2008. Particle image velocimetryinvestigation of the flow field in a centrifugal impeller with unequally spacedblades. Proc. Inst. Mech. Eng. Part A J. Power Energy 222 (A4),389401.

Yen, S.C., Liu, J.H., 2007. PIV measurements of exit flow field of centrifugal fans withconditional sampling. J. Mar. Sci. Technol. Taiwan 15 (3), 232240.


1-s2.0-s0142727x11001214-main

Documents