Enhancement of convective heat transfer in an air-cooled heat exchanger using interdigitated impeller blades

International Journal of Heat and Mass Transfer 54 (2011) 4549–4559

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Enhancement of convective heat transfer in an air-cooled heat exchanger using interdigitated impeller blades Jon M. Allison, Wayne L. Staats ⇑, Matthew McCarthy 1, David Jenicek, Ayaboe K. Edoh, Jeffrey H. Lang, Evelyn N. Wang, J.G. Brisson Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

a r t i c l e

i n f o

Article history: Received 11 January 2011 Received in revised form 9 June 2011 Accepted 9 June 2011 Available online 7 July 2011 Keywords: Heat exchanger Heat sink Fan Nondimensionalization Thermal management

a b s t r a c t The enhancement of convective heat transfer through a finned heat sink using interdigitated impeller blades is presented. The experimentally investigated heat sink is a subcomponent of an unconventional heat exchanger with an integrated fan, designed to meet the challenges of thermal management in compact electronic systems. The close integration of impeller blades with heat transfer surfaces results in a decreased thermal resistance per unit pumping power. The performance of the parallel plate air-cooled heat sink was experimentally characterized and empirically modeled in terms of nondimensional parameters. Dimensionless heat fluxes as high as 48 were measured, which was shown to be about twice the heat transfer rate of a traditional heat sink design using pressure-driven air flow at the same mass flow rate. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Thermal management is a critical bottleneck for high-power systems, such as phased-array radar and microwave and digital electronics, where performance and reliability are limited by the ability to dissipate heat efficiently. Fluidic-based cooling solutions have commonly been incorporated using traditional large-scale air-cooled fin-fan arrays and pumped liquid-based cooling [1–3]. The current work focuses on the convective heat transfer in an alternative air-cooled heat exchanger comprised of a loop heat pipe with an integrated fan. In contrast to a conventional pumped liquid system, it is self-contained and has no external fluidic connections. This device (Fig. 1) is 10 cm  10 cm  10 cm and is targeted to consume less than 33 W of electrical power while dissipating over 1000 W of heat with a thermal resistance of less than 0.05 K/W [4]. The integrated design utilizes a stack of rotating blades interdigitated between thermal stator plates, each of which is a condenser chamber of a loop heat pipe. A single evaporator layer is located at the bottom of the unit, which is in contact with the heat source and connected to the thermal stator plates via vertical pipes. Fig. 2 shows a cross-sectional schematic of the loop heat pipe. A low-profile radial-flux permanent magnet motor is ⇑ Corresponding author. Tel.: +1 617 253 2237; fax: +1 617 258 7754. E-mail address: [email protected] (W.L. Staats). Current address: Drexel University, Department of Mechanical Engineering and Mechanics, 3141 Chestnut Street, Philadelphia, PA 19104, USA. 1

0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.06.023

mounted on top and drives the rotors on a single shaft running through the condenser plates. Air enters the top through an axial intake and is forced radially outward between the condenser plates by the interdigitated impeller blades. The working fluid (water) evaporates in the primary evaporator wick; the vapor travels through vertical pipes to the condenser layers where it is convectively cooled to the liquid phase and then wicked back into the evaporator. The high thermal conductance of the loop heat pipe results in an isothermal condenser surface for heat removal; the radial outflow fan convectively cools the stack of condenser layers. More conventional finned heat sinks have been studied by many investigators. Tuckerman and Pease [5] studied a microchannel heat sink etched on silicon and minimized thermal resistance by choosing the appropriate channel width, fin width and aspect ratio subject to constraints on the geometry and pressure drop. Knight et al. [6] developed an analytical method to minimize thermal resistance of a heat sink with pressure driven flow in a closed finned channel by varying the geometry. Teertstra et al. [7] developed an analytical model to calculate the Nusselt number for a plate fin heat sink as a function of geometry and flow properties. Culham and Muzychka [8] presented a method of optimizing the geometry of plate fin heat sinks by minimizing the entropy generation rate while incorporating fan performance into their model. Several recent studies have shown that finless designs can provide improved performance in small heat sinks. Egan et al. [9] looked at a miniature, low profile heat sink with and without fins and used particle image velocimetry to detail flow structures and heat transfer. Stafford et al. [10] studied forced convection cooling on

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Nomenclature

DTLM A B Cf cp Dh G h hb hc hLMTD I Ie k Kb Kc _ m Nurf P Pr Q_ q00m r R Rarm Rex Rehc T To Uave V

log mean temperature difference area blade aspect ratio flow coefficient specific heat capacity of air hydraulic diameter flow channel aspect ratio convective heat transfer coefficient based on wall-toambient temperature difference height of blade height of flow channel convective heat transfer coefficient based on log mean temperature difference inlet size ratio electrical current thermal conductivity of air minor loss coefficient, bend minor loss coefficient, contraction mass flow rate Nusselt number for radial outflow pressure Prandtl number thermal power sunk by heat sink mean heat flux from wall to air radius convection thermal resistance motor armature resistance rotational Reynolds number flow Reynolds number temperature bulk outlet air temperature log mean velocity voltage

v _ W x y z

air velocity pumping power coordinate along exit plane coordinate along shaft axis coordinate normal to exit plane

Greek symbols efficiency dynamic viscosity of air rotational frequency Um dimensionless heat flux q density of air r slip factor e exchanger effectiveness

g l x

Subscripts amb ambient b blade, bearing/brush c air flow channel e electrical fan fan in pressure driven heat sink f fluid (air) i inlet max maximum mech mechanical m motor o outlet rf radial flow t blade tip w wall h azimuthal direction 1, 2, 3, 4 Points 1, 2, 3 or 4 in Fig. 4

low profile heat sinks with and without fins and showed that heat transfer rates of the finless designs were better than their finned counterparts. Typical air-cooled heat exchanger systems have separate fans ducted to the heat sink; the interdigitated impeller design offers increased heat transfer efficiency through several mechanisms.

Motor Shaft

Liquid Flow

Vapor Flow

Impeller Blades

Condenser Air Flow

Fig. 1. Schematic of the 10  10  10 cm integrated fan-heat sink device. The rotors are driven by a common shaft attached to the motor. Air enters axially at the top and is blown radially outward by the rotors. Air flows across the condensers, cooling and condensing the heat pipe fluid inside the condensers. The condensed fluid then travels down the vertical fluid connectors to the evaporator where it is heated and evaporates, returning to the condensers.

Evaporator Heated Surface Fig. 2. A simplified cross-sectional diagram of the integrated fan-heat sink showing the motor shaft, impeller blades, and loop heat pipe.

J.M. Allison et al. / International Journal of Heat and Mass Transfer 54 (2011) 4549–4559

The large heat transfer coefficients associated with the developing and high-shear flows slipping past the blades in the fan section are located directly on the fin surfaces. Additionally, the rotating blades shear off boundary layers and mix the air, while the rotary nature of the flow path increases the residence time of the air within the parallel plate geometry. These mechanisms are derived directly from the integration of the fan and heat sink structures. The combination of these components not only achieves high efficiency and a compact design, but also directly enhances the convective heat transfer between the air and heat sink. Accordingly, this work focuses on the experimental characterization of the convective heat transfer rates associated with impeller-driven flows through representative parallel plate geometries. Rather than studying the entire stack, a single layer was examined for experimental simplicity. Empirically derived correlations for the relevant nondimensional parameters are established focusing on thermal performance as a function of the interdigitated geometry. Additionally, the analysis and derivation of characteristic design charts for implementing such devices is reported. 2. Modeling A diagram of a single layer of the interdigitated design is shown in Fig. 3 along with the variables and geometric parameters affecting convective heat transfer from the plates. Ambient air at a temperature of Tamb is drawn in from the top of the stack through an _ Flow is driven outward inlet of radius of ri at a mass flow rate of m. through the parallel plates, separated by a distance of hc, by an impeller blade with a thickness of hb and tip radius of rt. The impeller spins at a rotational speed of x and is connected to a shaft (not _ to the air. shown). The impeller delivers a mechanical power of W The parallel plates are at a uniform temperature of Tw and transfer a thermal power of Q_ into the air between the plates, which exits the periphery of the plates at a mass-averaged temperature of T o . 2.1. Nondimensionalization The complexities of the flow field and the resulting thermal performance of the heat exchanger geometry shown in Fig. 3 cannot be easily modeled using closed form analytic techniques. Accordingly, this work focuses on the experimental characterization of the net heat transfer, fluid flow, and mechanical shaft power of the system for various geometries. These experimental results are then used to establish empirical correlations for the relevant nondimensional parameters governing such systems. In addition, performance characteristics and design charts have been developed for the resulting thermal resistance (R) from the wall temper-

Inlet Air - m, T amb Rotating Impeller - ω, W rt

ature to the ambient temperature as a function of mechanical _ required to drive the flow. power input to the fluid ðWÞ The independent control variables governing the thermal performance of the layer shown in Fig. 3 are the geometric parameters (hc, hb, ri, rt), the rotational speed of the impeller, x, and the fluid properties of the coolant air. In this work, the number of blades is five and is not varied. Using the tip radius, rt, as the characteristic length for system, three nondimensional geometric parameters are defined as:

hb rt hc G¼ rt ri I¼ rt

B¼

ð1Þ ð2Þ ð3Þ

B and G are the aspect ratios of the impeller blade and flow channel, respectively, and I is defined as the ratio of the flow inlet radius to the impeller blade tip radius. Accordingly, the ratio of B/G is the fill factor of the parallel plate gap height. A value of B/G = 1 corresponds to an impeller blade completely filling the flow passage, while B/ G = 0 represents a vanishingly thin blade as compared to the flow passage height. Both of these cases, however, are not physical possibilities due to manufacturing constraints. The impeller rotational speed and the fluid properties of air are characterized nondimensionally using the Prandtl number and the rotational Reynolds number (as in Beretta and Malfa [11]), defined respectively as

Pr ¼

cp l k

Rex ¼

ð4Þ r 2t

qx l

ri

Cf ¼

_ m

ð6Þ

qxr3t

The heat exchanger effectiveness (e) is defined as the ratio of the actual convective heat transfer rate to the maximum possible heat transfer rate. The maximum heat transfer rate to the air occurs when the air entering the channel at Tamb is heated to the wall temperature of the heat exchanger, or

y x hb

z

Outlet Air - m , T o

Fig. 3. Schematic representation of a single-layer of the heat exchanger device including a cutaway section showing the interdigitated impeller blade as well as the relevant variables and geometric parameters.

ð7Þ

The effectiveness e is then

hc

Q_

e¼ _ mcp ðT w  T amb Þ

Impeller

ð5Þ

where cp, l, k, and q are the specific heat capacity, viscosity, thermal conductivity, and density of the ambient air. The relevant parame_ mechanical ters for the heat exchanger are the mass flow rate ðmÞ _ heat flow rate into the air (Q_ Þ wall temperature shaft power ðWÞ (Tw) and the mass-averaged exit flow temperature ðT o Þ. These terms have been nondimensionalized as follows. The flow coefficient (Cf) is a turbomachinery parameter [12] relating the net flow rate through the plates, the tip speed (xrt) and the area swept out by the impeller blades (which is proportional to r 2t ). It is given by

_ p ðT w  T amb Þ Q_ max ¼ mc Heated Wall - Q, T w

4551

ð8Þ

Using the mass-averaged temperature of the exiting flow ðT o Þ; e can be rewritten as the ratio of the outlet flow temperature to the wall temperature taken relative to the ambient inlet conditions. Since the specific heat does not significantly vary over the expected temperature range, Eq. (8) simplifies to

e¼

T o  T amb T w  T amb

ð9Þ

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The slip factor (r) is another turbomachinery parameter [13] given by

_ W

r¼ _ 2 2 mx r t

ð10Þ

for designing heat sinks and evaluating the trade-offs between the effective thermal resistance from the heat load to the ambient air and the mechanical power necessary to operate the device. The total thermal resistance between the isothermal wall and the ambient air is given by

A slip factor of one implies the fluid streamlines follow the contours of the rotor, which can be seen by substituting the Euler turbine equation (with no pre-swirl) [14]

R¼

_ ¼m _ xr t v h ðr t Þ W

Inserting Eqs. (4)–(9) into Eq. (16) and rearranging yields

ð11Þ

into Eq. (10). The Euler turbine equation relates the power required to turn the impeller rotor with the mass-averaged tangential velocity at the rotor tip (vh(rt)). Accordingly, Eq. (10) characterizes the amount of flow slipping past the impeller blades as they rotate. It is the ratio of the tangential velocity of the air at the blade tip to the velocity of the blade tip itself that describes how well the flow is driven by the impeller. In the limit of no slip, the tangential velocity at the tip (vh(rt)) approaches the blade tip velocity (xrt) and as a result the slip factor approaches unity. The primary nondimensional parameter of interest for this device is the dimensionless heat flux (Um), defined by Shah and London [15] as

Um ¼

q00m Dh kðT w  T amb Þ

ð12Þ

Here, k is the thermal conductivity of the air, the hydraulic diameter is defined as Dh = 2hc, and q00m is the mean heat flux from the walls into the air. The dimensionless heat flux (Um) can be thought of as a Nusselt number whose temperature scale is based on the wall temperature and the inlet temperature (which is equal to the Tamb in this heat sink). An average convective heat transfer coefficient (h) for the device can be defined by Newton’s Law of Cooling as

h¼

q00m Q_ ¼ ðT w  T amb Þ AðT w  T amb Þ

ð13Þ

where Q_ is the net heat transfer rate to the air. The area over which the heat is transferred is the inner surface of both plates, accounting for the inlet hole, and is given by

A ¼ 2ð4r 2t  pr 2i Þ

ð14Þ

The average heat transfer coefficient (h) is defined using the difference between the isothermal wall temperature and the ambient inlet flow temperature. By doing so, the heat transfer rate through the system is quantified relative to the variables pertinent to real world implementation, namely the temperature of the device and the surrounding ambient environment. By combining Eqs. (12)–(14), along with the definition of the hydraulic diameter, the dimensionless heat flux can be rewritten in terms of the previously defined nondimensional parameters from Eqs. (2)–(9) as

Um ¼ eC f Rex



PrG

4  pI2

 ð15Þ

The independent variables in Eq. (15) (G, I, Rex, Pr) are determined by the device geometry, coolant fluid, and the rotational speed of the impeller. However, the heat exchanger effectiveness (e) and flow coefficient (Cf) are dependent parameters varying with device geometry, impeller speed and fluid properties. Accordingly, correlations for the dimensionless heat flux are developed by empirically characterizing the effectiveness and the flow coefficient as functions of geometry and operating speed. While the dimensionless heat flux can be used as a measure of the effective heat transfer within a system, it is also useful to evaluate the resulting thermal resistance and the input mechanical power required. These two parameters are of particular interest

T w  T amb Q_

ð16Þ

R ¼ ðeC f Rex Prkrt Þ1

ð17Þ

Similarly, the mechanical power delivered to the fluid can be evaluated by combining Eqs. (6) and (10) and rearranging terms, resulting in

_ ¼ C f rqx3 r 5 W t

ð18Þ

2.2. Radial flow model For comparison purposes, the performance of a similar heat exchanger geometry without the interdigitated impeller blade is evaluated here. The resulting performance of such a system can be confidently modeled using closed form analysis and existing correlations for convective heat transfer in radially outward fluid flow through a parallel plate gap. This model is used to compare the performance of the integrated fan-heat sink design to a traditional fin-fan design, where pressure-driven flow is used to convectively cool the parallel plate heat sink. In this scenario, a fan provides power to drive the flow between the parallel plates in a radially outward direction from the center inlet section to the outer periphery. The effect of the four corner regions (where r > rt) on the pressure drop is neglected. Suryanarayana et al. [16] performed an experimental study on the heat transfer in radial outflow between parallel discs held at uniform temperature, both stationary and rotating, with an inlet radius ri and outer radius rt separated by a gap of hc. The geometries studied in the present work (in particular I and G) are within Suryanarayana’s experimentally characterized range. Accordingly, the average Nusselt number for the radial flow can be calculated using his correlation for stationary plates as

Nurf ¼

hLMTD hc ¼ 0:0332Re0:782 hc k

ð19Þ

where hLMTD is the average heat transfer coefficient based on the log mean temperature difference between the heated plate and the air and Rehc is the Reynolds number based on the plate spacing (hc) and the log mean velocity. The Nusselt number in the Suryanarayana correlation, Eq. (19), uses the plate spacing as the length scale, which is important to note when comparing this to the dimensionless heat flux in this work, which uses Dh = 2hc as the length scale, as defined in Eq. (12). Furthermore, in contrast to Eq. (13) which defines the heat transfer coefficient using the temperature difference between the wall and the ambient, Suryanarayana’s heat transfer coefficient in Eq. (19) references the log mean temperature difference

hLMTD ¼

Q_ ADT LM

ð20Þ

The log mean temperature difference DTLM for this heat sink is defined as

DT LM ¼

  ðT w  T amb Þ  T w  T o   ln TTw TTamb w

o

ð21Þ

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The Reynolds number in Suryanarayana’s correlation (Eq. (19)), Rehc, is given by

Rehc ¼

qU ave hc l

ð22Þ

inserting the dimensionless variables described above, the pressure difference between points 3 and 4 in Fig. 4 becomes

P3  P4 ¼

where Uave, the log mean velocity, can be calculated as in [16] as

U ave ¼

_ ln ðrt =r i Þ m 2pqhc r t  r i

 _ p mc hLMTD A 1  exp _ p mc A

ð24Þ

where A is the total wetted area as given by Eq. (14). By determining the average heat transfer coefficient (h) using Eqs. (19) and (22)– (24), the total convective thermal resistance can be determined as

R¼

1 hA

ð25Þ

where A is once again the total area over which convective heat transfer between the parallel plates and the air occurs. The power required to drive air radially outward through the parallel plates can determined in several steps. Fig. 4 shows a diagram of the pressure driven radial flow model. In essence, a fan is used to bring stagnant, atmospheric pressure air to a pressure and velocity sufficient to drive the flow through a channel between two parallel discs; the work requirement of the fan can be determined for a specified mass flow rate. First, the pressure difference between points 3 and 4 in Fig. 4 is calculated using an expression derived by Moller [17]. Moller determined an approximate solution for the pressure distribution of a turbulent radial outflow in a parallel plate gap by using an integral solution to the momentum equation. Moller also derived a laminar solution; however, the error introduced by using the turbulent solution compared to a composite laminar-turbulent solution was found to be small for the cases considered in this work. Therefore, for simplicity, the turbulent solution was used; this has the form

PðrÞ  Pðrt Þ ¼

"

_2 m 4

2qhc

 2  2 16 hc rt  1 63p2 r t r

þ    0:007089

hc l0:25 1 1:682  _ 0:25 r 0:75 ð2r t Þ0:75 m

!# ð26Þ

Applying Eq. (26) between the entrance to the parallel plate gap (point 3 in Fig. 4, r = ri) and the exit (point 4 in Fig. 4, r = rt) and

1

Welec,fan

Patm Adiabatic Exterior Surface

Fan

hc rt

Heated Walls

 16 2  2 G I 1 2 63p 2q #  0:25   _ m 0:75 0:75 þ    0:007089  G I  1:682  2 lr t 4 hc

ð23Þ

The average heat transfer coefficient based on the temperature difference between the plate and the inlet air, as defined in Eq. (13), is related to the heat transfer coefficient in Eq. (19) (hLMTD) by the conservation of energy as

h¼

"

_2 m

2

ri

3 Air Flow

CL

Patm 4

Adiabatic Exterior Surface

Fig. 4. Schematic of the radial flow model. A fan forces air axially into a parallel plate gap where it then flows radially outward, providing convective cooling to the heated walls.

ð27Þ For the geometries investigated in this work, the flow from point 3 to point 4 experiences a pressure increase due to the increasing cross sectional area. Since the flow exits the parallel plate gap into atmospheric conditions as a jet, the pressure at the exit (P4) is atmospheric. The pressure upstream of the parallel plate gap entry (that is, point 2 in Fig. 4) is determined using the head loss equation:

P2

q

þ

v 22 2



 P3

q

þ

v 23 2

¼ ðK b þ K c Þ

v 23 2

ð28Þ

where v2 and v3 are the velocities at points 2 and 3, and Kb and Kc are the minor losses associated with the right angle bend and the contraction from point 2 to point 3 respectively. The turning loss is assumed to be Kb = 1, which is typical of a sharp right angle bend [18]. The contraction loss is given by Fay [18] as

 A3 K c ¼ 0:4 1  A2

ð29Þ

where A2 and A3 are the flow areas at points 2 and 3, given by

A2 ¼ pr2i A3 ¼ 2pr i hc

ð30Þ

A3 must be smaller than A2 in Eq. (29). Rearranging Eq. (28) gives the pressure difference from point 2 to point 3 as

P2  P3 ¼ ð1 þ K b þ K c Þ

qv 23 2



qv 22 2

ð31Þ

Mass conservation can be used to simplify Eq. (31) by eliminating v2 and v3, giving the pressure difference as a function of the mass flow rate as

P2  P3 ¼

" # _ 2 ð1 þ K b þ K c Þ 1 m  2q A23 A22

ð32Þ

Finally, the ideal work required to bring stagnant air at atmospheric pressure (point 1 in Fig. 4) to the pressure and velocity at point 2 in Fig. 4, determined using the conservation of energy, is

 P1  P 2 v 22 _ f;fan ¼ m _ W  q 2

ð33Þ

_ f;fan is the useful work delivered to the fluid (air) by the fan. where W Eliminating v2 and reformulating in terms of the mass flow rate using continuity, Eq. (33) becomes

_3 _ 1  P2 Þ mðP _ f;fan ¼ m  W 2 2 q 2q A2

ð34Þ

Of course, only a fraction of the electrical power input to the fan is available as useful fluid power. To determine how much mechanical work input would be required by the fan, 9 commercially available fans in the 1–8 W fluid power range were surveyed (Delta AHB1448EH/SH/VH, Delta AFC0948DE-TP20, Delta FFB1012EHE, Sunon PMD4809PMB1-A/2-A/3-A, Delta FFB0912SH). Fan curves (static pressure rise vs. volume flow) from the manufacturer’s datasheets were used to produce fluid power vs. volume flow curves. The point of maximum fluid power was determined from these curves; these

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J.M. Allison et al. / International Journal of Heat and Mass Transfer 54 (2011) 4549–4559

powers were divided by the specified electrical power input to determine an overall fan efficiency

_ W

goverall;fan ¼ _ f;fan W e;fan

ð35Þ

Of the fans surveyed, the highest overall efficiency observed was 0.33 (Delta AHB1548EH). Therefore, in this analysis, an overall fan efficiency of 0.35 was used as an optimistic estimate for a well designed fan of this size. Ultimately, the mechanical power requirement of the fan must be determined to give a fair comparison to the impeller driven flow. The efficiency of the motor must be considered to determine the mechanical power input to the fan.

gmotor;fan ¼

_ mech;fan W _ e;fan W

ð36Þ

All of the fans in the survey described above are driven by brushless DC motors. An efficiency of 0.85 is typical for a well designed motor of this type and size, based on manufacturers’ datasheets (e.g. Maxon 339285). Eq. (34) can be rewritten in terms of the mechanical fan power by using Eqs. (35) and (36) as

_ mech;fan ¼ W

_3 m

 2

_ 1  P2 Þ mðP

2q2 A2

!

q

gmotor;fan goverall;fan

ð37Þ

Eqs. (37), (32) and (27) can be solved to determine the mechanical power input required by the fan to yield an arbitrary mass flow rate. This power estimate represents a well designed commercial motorfan combination based on an assessment of fans and motors the power range expected in the radial flow comparison. 3. Testing Using the relations developed in Section 2.1, the flow coefficient (Cf), slip factor (r), and the heat exchanger effectiveness (e), were evaluated experimentally as a function of rotational Reynolds number (Rex), and geometry. Using these relations the dimensionless heat flux as well as the total thermal resistance and mechanical power required to drive the flow have been correlated to the independent variables. Fig. 5 shows the setup used to experimentally characterize the various thermal and fluidic parameters relevant for developing an empirical model of device performance.

Fig. 5(a) is a schematic representation of the entire assembly, while Figs. 5(b) and (c) show a cross section of the flow test section and the impeller design, respectively. Two 6 mm thick, polished square copper plates with an edge length of 100 mm are used to simulate the parallel condenser plates. The top plate has a 40 mm diameter hole cut through it to function as the air inlet. Thermal power is supplied to the parallel plates with polyimide film insulated heaters (Omega KHLV-102/ (10)-P) while the wall temperature is monitored using embedded thermocouples (Omega 5TC-TT-J-30-36). The backsides of the plate assembly are insulated with balsa wood to reduce the heat lost to the environment. The top plate is mounted above the bottom using annular shims in the corners to define the channel height (hc). The plates, insulation, and shims, have clearance holes and are fastened with machine screws to an aluminum stand. Multiple impeller rotors were laser cut out of acrylic sheets (with various thicknesses) and separately mounted and aligned within the parallel plate flow section using a drive shaft and bearing assembly adjusted with a positioning stage. The rotor blades are shaped as the trailing end of a NACA 0011 airfoil, as shown in Fig. 5(c). The rotor blades used for this work are simple extrusions of the two-dimensional airfoil geometry with no complex out-of-plane contours. The blade profile begins radially at r = 0 and transitions at a constant rate to a sweptback angle of 45° at the trailing edge, which is rounded off with a circular arc of radius 1.3 mm. The shaft is supported by two self-aligning, double-row, unshielded, oiled ball bearings (SKF 126TN9). The shaft is connected to a commercially available DC motor (Maxon 110930) using a flexible coupling. The experiments were carried out for a fixed impeller blade profile as well as inlet radius, ri = 2 cm, and blade tip radius, rt = 5 cm. These fixed geometries were chosen as optimal solutions from a 3D finite element simulation using ANSYS FLUENT [4,19], while taking into consideration realistic manufacturing and size constraints. These numerical results showed that the dominant parameters affecting performance of the layer were the channel and blade thicknesses. Accordingly, the experiments have been conducted for a variety of channel heights and impeller blade thicknesses created by adjusting the spacers within the assembly and varying the impeller blades used. During testing, electrical power is delivered to the heaters while monitoring the wall temperature and calculating the total heat transfer rate to the fluid accounting for the heat lost to the environment [19]. Similarly, the rotor is controlled by supplying electrical power to the DC motor and monitoring the

(a) Heated Copper Plate

Machine Screw Film Heater

y Shaft

(b) Thermal Insulation

z

Shim x

Machine Screw

Shaft

Impeller

Thermal Insulation

Heated Copper Plates

Film Heaters

Impeller

Bearing

Aluminum Table

Motor

5 DOF Stage

(c)

Fig. 5. Schematic representation of the experimental set-up showing (a) the exploded assembly, (b) a cross section of the flow section, and (c) the impeller blade geometry.

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_ e ¼ Ie V W _ m ¼ I2 Rarm W e

ð39Þ

0.1

0.5

y (mm)

0.9 60

80

100

x (mm)

(b) 25

30

30 0

20

15

2.5 2 1.5 1 0.5

25 20

To – Tamb (°C)

30

40

60

80

100

x (mm) Fig. 6. (a) Normalized air velocity perpendicular to the exit plane and (b) temperature rise above ambient of air on the exit plane, where the blades and flow are rotating from right to left. ðQ_ ¼ 90W; hb ¼ 1:65 mm; hc ¼ 2:80 mm; x ¼ 2  60  3000 rpm; m_ ¼ 3:69g=s; T o  T amb ¼ 28:5  CÞ.

ð41Þ

The left hand side of Eq. (41) is the mechanical shaft power, which is _ f ) plus the the power delivered to the fluid by the impeller blades (W _ b ). The mechanical power lost in the bearings and brushes (W mechanical losses can be calibrated as a function of rotational speed _ f ¼ 0) by rotating the shaft without an impeller attached (so that W _ ¼ and evaluating Eq. (41) for the unloaded condition W b _ f ¼ 0Þ. Using this calibration the mechanical power delivered _ b ðW W to the flow can be written as

_  ðxÞ _ f ðxÞ ¼ Ie V  I2 Rarm  W W b e

40

ð40Þ

where Ie is the current, V is the voltage, and Rarm is the armature resistance of the DC motor. Inserting these relations into Eq. (38) and rearranging yields

_ f þW _ b ¼ Ie V  I2 Rarm W e

20

25

The electrical power input to the motor and the motor losses are given by

0.5

30

ð38Þ

0.9

30

_ mþW _ bþW _f _ e¼W W

0.5

2.5 2 1.5 1 0.5 0 0

y (mm)

_ e Þ is converted The electric power supplied to the DC motor ðW _ m Þ, mechanical losses into three components: motor losses ðW _ b Þ, and the power delivered including bearing and brush losses ðW _ f Þ according to to the fluid ðW

vz / vz,max 0.1

_ f 3.1. Mechanical power characterization – W

(a) 0.5

rotational speed. The mechanical power delivered to the flow is calculated accounting for the motor, shaft, and bearing losses. The exit air flow rate and average temperature are measured using hot-wire anemometry at the periphery of the assembled stack.

ð42Þ

Using the calibration for the mechanical losses, the mechanical power delivered to the fluid is evaluated at every test condition based on the electrical excitation of the motor and the mechanical losses at the resulting rotational speed. _ To 3.2. Thermofluidic characterization – m; The heat transfer rate to the flow ðQ_ Þ is measured by monitoring the electrical input to the heaters and adjusting for heat lost to the ambient through natural convection [19]. The temperature at the wall surface is simultaneously measured using several thermocouples embedded within the copper plates. In the actual heat exchanger device shown in Figs. 1 and 2, the walls of the flow passages are parallel condensers of a loop heat pipe and will operate at near isothermal conditions. Accordingly, the experimental apparatus considered in this work uses 6 mm thick copper plates to ensure isothermal conditions across each plate. In addition to these values, measurements of the average exit flow conditions are necessary to evaluate the nondimensional parameters in Eqs. (6)–(15). _ and mass-averaged flow temperature The mass flow rate ðmÞ ðT o Þ are measured at the exit of the single layer’s periphery. By scanning a hot-wire anemometer (TSI 1210-60) and a thermocouple probe (Omega 5TC-TT-J-30-36) across the exit plane, contour plots of exit velocity (vz) and flow temperature (To) have been generated for each geometry. The anemometer and thermocouple probe were continuously scanned vertically (y direction) at multiple discrete horizontal (x direction) locations. Using these data sets velocity and temperature contours at the flow exit were created. Fig. 6 shows contours for normalized flow velocity perpendicular to the exit plane as well as the exit flow temperature relative to ambient conditions, where the impeller blades (and therefore flow) rotate from right to left. Fig. 6 shows that the flow conditions are

non-uniform over the exit plane, where the effects of the corner supports are evident by the reduced speeds and temperatures at the rightmost sections. Using contours similar to the ones shown in Fig. 6, the maximum and mass-averaged flow temperature and velocity can be found for each geometry and at each operating condition. It was found that the location of the maximum and average values for both temperature and velocity did not vary substantially with the impeller speed or heat input. Therefore, for testing simplicity, the contours shown in Fig. 6 were used to determine the placement of the anemometer and thermocouple probe such that the maximum velocity and average temperature were recorded in subsequent tests. This greatly reduced the complexity and length of the testing procedure with little effect on the resulting data. The experimental techniques used for acquiring mass flow rates and temperatures via scanned hot-wire anemometry and thermocouple probes, as well as corrections for flow entrainment, are discussed in detail elsewhere [19]. Using these techniques, the mass _ were averaged exit temperature ðT o Þ and total mass flow rate ðmÞ experimentally determined. 4. Results and discussion The experimental measurements were carried out using air as the working fluid (Pr = 0.72) for a fixed impeller tip radius (rt = 5 cm) and inlet flow radius (ri = 2 cm), resulting in a value of I = 0.4. Using the measurement scheme outlined in Sections 3, 3.1, 3.2, data was collected for ten independent geometries corresponding to channel heights of hc = 1.6  3.4 mm, blade thicknesses of hb = 0.5  2.8 mm, and for rotational speeds of 3000  7000 rpm. Nondimensionally, this corresponds to blade aspect ratios of 0.01 < B < 0.49, flow passage aspect ratios of 0.032 < G < 0.068, and rotational Reynolds numbers of 4.7  104 < Rex < 1.1  105. 4.1. Empirically-derived correlations The major dependent parameters to be empirically correlated to the geometry and the rotational speed are the net mass flow rate _ the net heat flow rate from the wall to through the system ðmÞ, the air ðQ_ Þ, and the net mechanical power delivered to the fluid

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_ f Þ. Accordingly, the nondimensional versions of these parameðW ters have been correlated to the geometry and the rotational Reynolds number using a functional dependence of the form

independent parameters. Using a least squares fit applied to Eq. (43) for each experimentally measured parameter yields

B f ðG; B; Rex Þ ¼ C 1 þ C 2 G þ C 3 B þ C 4 þ C 5 Rex G

C f ¼ 0:32G þ 2:4B  0:035

ð43Þ

This correlation used to relate the flow coefficient (Cf), the heat exchanger effectiveness (e), and the slip factor (r), to the relevant

(a)

B G B e ¼ 1  7:2G þ 4:5B  0:55 G

r ¼ 0:11  0:96G  3:5B þ 0:54

ð44Þ ð45Þ B G

ð46Þ

Fig. 7 shows the correlation results where the measured data is plotted relative to the calculated values from Eqs. (44)–(46). While Eq. (43) was found to accurately correlate the geometric effects to first order, it also showed little to no dependence of Cf, e, or r on the rotational Reynolds number (Rex). Using the correlations for Cf, e, and r in Eqs. (44)–(46) the dimensionless heat flux can be expressed in terms of nondimensional geometric parameters and the rotational Reynolds number using Eq. (15). Fig. 8 shows the experimentally measured dimensionless heat flux plotted against the developed correlation. Dimensionless heat fluxes as high as 48 have been measured at a rotational Reynolds number of 1.0  105, corresponding to an average convective heat transfer coefficient of h = 197 W/m2 K at a rotational speed of 7000 rpm. 4.2. Characteristic design charts

(b)

The empirical correlations in Eqs. (44)–(46) can be substituted into Eqs. (17) and (18) to evaluate the thermal resistance and the mechanical power required to drive the flow. Using these relations, design charts of the form shown in Fig. 9 can be generated for a given characteristic device size operating at a fixed speed. Fig. 9 shows contour plots of the device thermal resistance and required pumping power as a function of the flow channel geometric parameters, B and G. Alternatively, Fig. 10 shows the thermal resistance plotted directly as a function of pumping power for eight experimentally characterized flow geometries. Multilayer heat exchangers with interdigitated impeller blades can be designed and optimized using the empirical correlations developed in this work along with characteristic design charts similar to those presented in Figs. 9 and 10. The analysis and modeling presented here can be used to balance the design trade-offs of a single layer geometry against the total number of layers permissible in a given application. This is exemplified by examining Fig. 10, which shows increased performance for designs with a larger parallel plate aspect ratio, G. For a multilayer stack with negligible

(c)

Fig. 7. Comparison of experimentally measured values and empirically derived correlations for (a) flow coefficient, (b) heat exchanger effectiveness, and (c) slip factor as a function of nondimensional geometric parameters B and G.

Fig. 8. Experimentally measured dimensionless heat flux plotted relative to the developed empirical model.

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1.4

R - Thermal Resistance (K/W)

(a)

0.45

5 0.5 0.6

5

0.6

8 0.

0.7

0.65 0.7

0.75 0.04

0.05

0.06

G = hc / rt W f - Pumping Power (W) 1. 6 1.4

0.04

1.2

1 0.03

0.8

0.6

0.02 0.4

0.05

.010 .016 .010 .023 .036 .010 .029 .049

0.8

0.6

0.4

0

0.5

1

1.5

2

2.5

Wf - Pumping Power (W) Fig. 10. Calculated thermal resistance of the single layer as a function of pumping power (Eqs. (17), (18) and (44)–(46)) for various geometries. The inset table shows the values of B and G corresponding to each symbol in the main plot. The markers indicate linearly spaced rotational speeds ranging from 2000 to 8000 rpm in increments of 500 rpm.

4.3. Comparison with traditional approaches

(b)

0.04

1

0.2 0.55

0.6

5

R - Thermal Resistance (K/W)

0.03

0.5

B = h b / rt

0.4

0.02

B = hb / rt

.032 .032 .050 .050 .050 .067 .067 .067

1.2

0.04

0.8

G = hc / rt B = hb / rt

0.06

G = hc / rt Fig. 9. Contour plots of (a) the convective thermal resistance between the wall and ambient air, and (b) power required to drive the flow for a single layer based on the developed correlations with rt = 5 cm and 5000 rpm (Rex = 7.8  104). The dashed lines represents a limit of manufacturable geometries; above this line the blade thickness becomes too close to the gap thickness.

inlet resistance, the total required pumping power will increase linearly with the number of layers, while the total thermal resistance will be inversely proportional to the number of layers. If a multilayer device is to be designed to fit inside of a cube of a given size, a design with a larger flow passage will have a lower thermal resistance per layer but fit a fewer number of total layers. This model allows a designer to determine the heat transfer for a given geometry, which can be considered along with manufacturing limitations to optimize application-specific performance requirements.

The novelty of the proposed heat exchanger design is the direct integration of the fan and heat sink components. Traditionally, a separate and independent fan is used to force air over a highsurface-area heat sink, convectively cooling the structure. Using the correlations developed for this work, the integrated fan-heat sink design can be compared to traditional separate fin-fan approaches where pressure-driven flow is used to cool the heat sink. In this comparison, the traditional pressure-driven design has geometry identical to the parallel plate structure studied in the current work but without an impeller, taking the configuration described in Section 2.2. The empirical correlations from Section 2.2 were used to determine the convective heat transfer and pressure drop in the traditional pressure-driven design’s simultaneously developing radial flow through parallel plates. Fig. 11 shows a direct comparison of the two designs for mass flow rate, heat transfer coefficient, thermal resistance, and required pumping power at two different plate spacings. In both of the impeller-driven cases, the impeller occupies 75 percent of the plate spacing; that is, B/G = 0.75. This B/G ratio represents a readily manufactured design at these channel spacings. The integrated impeller-driven design is presented over the range of operating conditions directly measured and empirically modeled in this work alongside the corresponding performance of the traditional pressure-driven design. Fig. 11(a) shows the average heat transfer coefficient over the internal surfaces of the parallel plates as a function of mass flow rate for both approaches, showing higher heat transfer for impeller-driven flow at a fixed mass flow rate. This enhancement in the heat transfer coefficient is thought to be a consequence of increased mixing of the flow, higher velocity magnitudes due to the spiral-shaped path the air takes through the gap, and the developing boundary layer being repeatedly sheared off with each passing blade. As would be expected, smaller channel heights lead to higher heat transfer coefficients for both approaches. Fig. 11(b) shows the net mass flow rate pumped through the plates as a function of required pumping power for both approaches. It can be seen that the impeller-driven flow is more efficiently pumped through geometry as compared to the pressure-driven flow and, as would be expected, larger plate spacings lead to more flow per unit power. This demonstrates how the

J.M. Allison et al. / International Journal of Heat and Mass Transfer 54 (2011) 4549–4559

(a)

200

hc = 3 mm hc = 4 mm

150

hb = 0.75 · hc

100 Predicted performance of a pressure-driven, radial flow heat sink, based on empirical correlations [Eqs. (19) and (33)]

50 0

hc = 3 mm hc = 4 mm

0

2

4 6 8 10 m − Mass Flow Rate (g/s)

12

14

1.5

(b)

12

m − Mass Flow Rate (g / s)

Predicted performance of an impeller-driven heat sink, based on empirical correlations developed in the current work

R − Thermal Resistance (K / W)

h − Heat Transfer Coeff. (W / m 2K)

4558

9

6

3

0

0

0.5

1 1.5 2 2.5 3 W − Pumping Power (W)

3.5

4

(c) 1

0.5

0

0

0.5

1 1.5 2 2.5 3 W − Pumping Power (W)

3.5

4

Fig. 11. Performance of the integrated impeller-driven device as compared to a pressure-driven radial flow heat sink: (a) the average heat transfer coefficient as a function of mass flow rate, (b) the mass flow rate as a function pumping power, and (c) the resulting thermal resistance from the heat sink to the air as a function of pumping power. The uncertainties in the impeller-driven device performance are based on the propagation of uncertainties in the underlying empirical correlations (Eqs. (44)–(46)). The uncertainties in these correlations are based on the standard deviations of the errors when compared to experimental data. The markers in the impeller-driven series represent equally spaced rotational speeds ranging from 2000 to 6500 rpm.

integration of the fan directly within the heat sink improves the fluidic performance. The pumping power in the pressure-driven design is an underestimate in this analysis because entry losses to the fan section were neglected and generous estimates for both fan efficiency and motor efficiency were employed. The total thermal resistance between the structure and the ambient air as a function of pumping power is the most relevant metric of heat exchanger performance and is plotted in Fig. 11(c). A single layer thermal resistance as low as 0.4 K/W has been achieved for the impeller-driven design with a plate spacing of hc = 4 mm at a pumping power of 2 W. This corresponds to an increase in device performance of over a factor of two as compared to the pressure-driven approach. Interestingly, the larger plate spacing (hc = 4 mm) performs better than the smaller plate spacing (hc = 3 mm) for impeller-driven flow, while the opposite is seen for pressure-driven flow. This can be explained by examining Figs. 11(a) and (b), where the heat transfer coefficient is greater for smaller spacings (at a fixed mass flow rate), but the power required to drive the flow is larger. The combination of these two effects results in an increase in performance for a single layer with larger plate spacings (hc). Realistically, this effect is balanced by the number of layers that can be included in a design with a fixed total height; designs with larger spacing can accommodate fewer layers. As would be expected, this is not seen for pressure-driven flow due to the weaker dependence of heat transfer coefficient on mass flow rate as seen in Fig. 11(a). 5. Conclusions A single layer of an air-cooled parallel plate heat exchanger system driven by interdigitated impeller blades has been experimen-

tally characterized. The parameters dictating the performance of the system have been correlated to independent control variables using a set of nondimensionalized correlations. These correlations relate the parallel plate geometry and rotational speed to the resulting thermal resistance and the power required to drive the flow. It has been shown that the use of impeller blades integrated directly within the heat exchanger results in a factor of two increase in performance over traditional approaches for millimeter-scale plate spacings. The developed correlations provide a comprehensive set of guidelines for designing such devices to meet next-generation cooling requirements using ambient air as the coolant. The results of this work will be used to model and design an interdigitated heat exchanger and fan design with multiple layers driven using an integrated permanent magnet motor. Acknowledgements This work was supported by the DARPA Microtechnologies for Air-Cooled Exchangers (MACE) program, grant # W31P4Q-09-10007, under program manager Dr. Thomas Kenny. The authors thank Dr. Barbara Hughey for her assistance with hot-wire anemometry. References [1] I. Mudawar, Assessment of high-heat-flux thermal management schemes, IEEE Trans. Compon. Pack. Technol. 24 (2001) 122–141, doi:10.1109/6144.926375. [2] S. Garimella, V. Singhal, D. Liu, On-chip thermal management with microchannel heat sinks and integrated micropumps, Proc. IEEE 94 (2006) 1534–1548, doi:10.1109/JPROC.2006.879801. [3] S.S. Anandan, V. Ramalingam, Thermal management of electronics: a review of literature, Thermal Sci. 12 (2008) 5–26.

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