26
Cooling ATCA and PICMG Chassis with Ambient Air Refrigeration The Thermal Performance of Microchannel and Macrochannel Cold Plates Thermosyphons: How They Work and Their Practical Limitations Thermal Interface Materials: What’s New, What’s Next? MARCH 2009 | VOLUME III | ISSUE II IN THIS ISSUE pedia

IN THIS ISSUE · along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing

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Page 1: IN THIS ISSUE · along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing

Cooling ATCA and PICMG Chassis with Ambient Air Refrigeration

The Thermal Performance of Microchannel and Macrochannel Cold Plates

Thermosyphons: How They Work and Their Practical Limitations

Thermal Interface Materials: What’s New, What’s Next?

March 2009 | VoluMe III | Issue II

IN THIS ISSUE

pedia

Page 2: IN THIS ISSUE · along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing

Advanced Thermal Solutions is a leading engineering and manufacturing company supplying com-plete thermal and mechanical packaging solutions from analysis and testing to final production. ATS provides a wide range of air and liquid cooling solutions, laboratory-quality thermal instrumentation, along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing partners. For more information about Advanced Thermal Solutions, Inc., please visit www.qats.com or call 781-769-2800.

EDITOR KaVeh aZar, Ph.D. President & CEO, Advanced Thermal Solutions, Inc.

MANAGING EDITORBahMaN TaVassolI, Ph.D. Chief Technology Officer, Advanced Thermal Solutions, Inc.

NORTH AMERICA aDVaNceD TherMal soluTIoNs, INc. 89-27 Access Road Norwood, MA 02062 USA T: 781.769.2800 | F: 781.769.9979 | www.qats.com

EUROPE aDVaNceD TherMal soluTIoNs, B.V.De Nieuwe Vaart 50 | 1401 GS Bussum The Netherlands T: +31 (0) 3569 84715 | F: +31 (0) 3569 21294 www.qats-europe.com

All rights reserved. No part of this publication January be reproduced or

transmitted in any form or by any means, electronic, mechanical,

photocopying, recording or otherwise, or stored in a retrieval system

of any nature, without the prior written permission of the publishers

(except in accordance with the Copyright Designs and Patents Act 1988).

The opinions expressed in the articles, letters and other contributions

included in this publication are those of the authors; and the publication

of such articles, letters or contributions does not necessarily imply that

such opinions are those of the publisher. In addition, the publishers

cannot accept any responsibility for any legal or other consequences

which January arise directly or indirectly as a result of the use or adaptation

of any of the material or information in this publication.

ADVERTISING To Place aN aD IN QPeDIa: Contact Ray Santos at 781.769.2800Qpedia was launched in 2007 as a technology eMagazine focused on the thermal management of electronics. It is designed as a resource to help the engineering community solve the most challenging thermal problems. The eMagazine is published monthly and distributed at no charge to over 21,000 engineers worldwide. Qpedia is also available online or for download at www.qats.com/qpedia.Qpedia’s editorial team includes ATS’ President & CEO, Kaveh Azar, Ph.D., and Bahman Tavassoli, Ph.D., the company’s chief technologist. Both Azar and Tavassoli are internationally recognized experts in the thermal management of electronics.

For more information on how you can generate awareness about your company or products, contact ray santos at 781.769.2800.

SUBSCRIBE ON LINE AT: www.qats.com/qpedia

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2216106

March 2009 | VoluMe III | Issue II

� March 2009 |Qpedia

Features

6 Future CoolingCoolingATCAandPICMGChassiswithAmbientAirRefrigerationRefrigeration is a useful cooling method. A coolant (air or liquid) can be chilled to sub-ambient conditions, and a sub-cooled plate can re-duce the temperature of a component, PCB or chassis. The concept of refrigeration for electronics was discussed in a previous Qpedia issue. In this article, we present the salient features that are readily observed when using refrigeration for electronics cooling.

12 Thermal AnalysisTheThermalPerformanceofMicrochannelandMacrochannelColdPlatesIn recent years, intense activity has gone into improving the capa-bilities of cold plates. Specifically, the use of microchannels has pro-vided great improvements in cold plate thermal performance. In this article, we will look at equations which can be used for heat transfer coefficients when determining thermal performance, regardless of a cold plate’s channel size.

16 Thermal Minutes

Thermosyphons:HowTheyWorkandTheirPracticalLimitationsIn electronics cooling, heat pipes are used to transfer heat dissipating from devices into the environment. Thermosyphons follow the same principal as heat pipes and are widely used in energy systems. But, unlike heat pipes, thermosyphons are not widely used in the electronics industry. This article helps explain why this is so by discussing their operation.

22 Thermal FundamentalsWhatarePitotTubesandHowDoTheyMeasureVelocity?Pitot tubes are devices for measuring fluid velocity. Applications requiring flow measurement, such as the flow over a wing or through an enclosure, can benefit from the use of Pitot tubes. A Pitot tube is a device in which the pressure differential, based on the energy equation, is translated into velocity.

65

12

19

23

30

35

17

15

4

2

0 10 20 30 40 50 60 70

Junction Temperature (°C)

Conventional cooling

Cold plate (200W brd)

Cold plate (300W brd)

Cold plate (400W brd)

Cold plate (500W brd)

Fan assisted air jet

Fan assisted air jet-Highperformance heat sink

Compressor assisted air jet

Spray cooling

Water Jet

Junction Temperature Rise for Different Cooling Schemes

55°C Limit

Conventional Cooling is not

adequate for high power devices

Vapor Flow Feed Channels Liquid Flow

MicrogroovedSurface

Heated Surface

a)

b)

Page 4: IN THIS ISSUE · along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing

Advanced Thermal Solutions’ Thermal Mange-ment Design Kit contains 96 of its best-selling maxiFLOW™ heat sinks and maxiGRIP™ sink attachment systems, to quickly provide opti-mum component cooling solutions during the prototyping, trouble shooting and final design stages.

There are 288 parts in all, including heat sink, frame clip, spring clip and pre-applied thermal interface material for 16 of the most common component sizes available. This allows engi-neers to have the best cooling solution avail-able for nearly every application.

ATS maxiFLOW heat sinks feature a low profile, spread fin array to maximize surface area for more effective air (convective) cooling. The maxiGRIP heat sink attach-ment system features a plastic frame clip and a stainless steel spring clip that runs through the heat sink’s fin field, fastens securely to the plastic frame and applies steady, even pressure to the component throughout the product lifecycle.

Every heat sink in the Kit comes with a high quality ther-mal interface material to enhance cooling performance and allow immediate qualification testing. An enclosed catalog provides each heat sink’s part number, dimen-sions (base and fin tip to fin tip) and cooling performance in both ducted and unducted airflow conditions.

All parts in the kit are RoHS compliant.

Individual orders of maxiFLOW heat sinks with maxiGRIP frame and spring clip assemblies, including replacements for the Kits, are available exclusively from Digi-Key, and can be ordered at digikey.com. Tools that aid in the instal-lation and removal of the assemblies are also available and can be ordered from Digi-Key or ATS.

For further technical information, please contact Advanced Thermal Solutions, Inc. at 1-781-769-2800 or www.qats.com

» 96 Heat Sink AssembliesEach includes a heat sink, with pre-applied phase-changing thermal interface material, plastic frame clip and stainless steel spring clip

» Ideal for Prototyping & Testing Allows engineers to have the best cooling solution avail-able for nearly every applica-tion

» Parts Available from Digi-Key Additional samples and replacement parts are conveniently available from Digi-Key and can be ordered at www.digikey.com

» maxiFLOWTM Heat Sinks maxiFLOW heat sinks reduce device junction temperatures (TJ) by more than 20 percent, compared with other heat sinks of comparable volume

» maxiGRIPTM Attachment Provides secure heat sink at-tachment and applies steady, even pressure to the compo-nent throughout the product lifecyle

» Meets Shock & Vibration StandardsmaxiGRIP assemblies are certified to meet Telcordia, ETSI and MIL-STD vibration and shock test standards

» Detailed Performance Data An enclosed catalog provides each heat sink’s part number, dimensions (base and fin tip to fin tip) and cooling perfor-mance in both ducted and unducted airflow conditions.

» RoHS Compliant

89-27 ACCESS roAd, norWood, mA 02062 USA | t: 781.769. 2800 f: 781.769.9979 | WWW.QAtS.Com

Thermal Management Design KitAtS-tmdK-96

COMPONENT SIZES: 17 mm x 17 mm19 mm x 19 mm21 mm x 21 mm23 mm x 23 mm25 mm x 25 mm27 mm x 27 mm29 mm x 29 mm30 mm x 30 mm31 mm x 31 mm32.5 mm x 32.5 mm33 mm x 33 mm35 mm x 35 mm37.5 mm 37.5 mm40 mm x 40 mm42.5 mm x 42.5 mm45 mm x 45 mm

COMPONENT HEIGHTS: Standard - 3 mm to 4.5 mmLow Profile - 1.5 mm to 2.99 mm

HEAT SINK HEIGHTS:STD LP7.5 mm 9.5 mm12.5 mm 14.5 mm17.5 mm 19.5 mm

Page 5: IN THIS ISSUE · along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing

�January 2009 |Qpedia

Why does LED thermal management matter? Excess heat directly affects both short-term and long-term LED performance. The short-term effects are color shift and reduced light output while the long-term effect is accelerated lumen depreciation and thus diminished lifespan.

Advanced Thermal Solutions, Inc. (ATS), an industry leader in electronics cooling, also offers comprehensive LED/Lighting thermal management analysis and design services tailored to help bring LED products to market faster, ensure their reliability and reduce development costs.

SERVICESEvaluationAnalysisDesignTesting Manufacturing

PRODUCTSHeat SinksComponentsAssembliesInterface MaterialsTest Instruments

High Performance Thermal Management Solutions for LED Applications

More information about ATS thermal design and testing services can be found on the Advanced Thermal Solutions website, www.qats.com, or by calling 781-769-2800.

Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | USAT: 781.769.2800 | F: 769.769.2800 |www.qats.com

Page 6: IN THIS ISSUE · along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing

��

Cooling ATCA and PICMG chassis with ambient air refrigeration

Refrigeration is a use-ful cooling method. A coolant (air or liquid) can be chilled to sub-ambient conditions, and a sub-cooled plate can reduce the tem-perature of a compo-nent, PCB or chassis. The concept of refrigeration for electronics was discussed in a previous Qpedia issue. [1] In this article, we present the salient features that are readily observed when using refrigeration for electronics cooling. Among the most important are these:

A 0.05oC/W thermal performance level can be obtainedSub-ambient temperatures are provided – either as di-rect-die attach or for lowering the device ambient tem-peratureSystem size may be reduced by space savings on air/liq-uid cooling sizes.

A number of challenges must also be resolved to gain the benefits of sub-ambient cooling:

It is a more complex deployment than liquid coolingThere can be a problem with condensation, especially when the cooling system is incorporated into the electron-ics.High pressure liquids must be used for the required com-pression.

••

••

Thermal cycling. Most elec-tronics go through some power cycling. With high-er temperature gradients on the device as the result of refrigeration, the impact of thermal cycling may be negatively amplified.Power consumption. More power is required to oper-

ate the refrigeration system. Vibration can be an issue due to the compressor’s opera-tional cycle.The space needed for refrigeration components can vary from 15 to 30% of the system volume. The percentage of total system cost devoted to cooling hardware can vary. Large systems tend to be at the lower end of the spectrum, while workstations are at the upper end [2].

The above features clearly highlight the benefits and challeng-es of refrigeration cooling. A cooling system that can provide 0.05oC/W thermal resistance is a dream come true. However, as shown, deploying such a system is not a simple pursuit; there is significant cost associated with such an endeavor. The traditional question lingers as to how to cool telecom and datacom chassis (e.g., ATCA or PICMG platforms). Their power dissipation is on the continuous rise, and air cooling is by far the most sought after thermal management option.Consider the following table that shows four standard 4.5 inch fans. [3] Fan number 3 is hypothetical since, no such a fan

Page 7: IN THIS ISSUE · along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing

� March 2009 |Qpedia

with the stated performance is available at this juncture.

Table 1. Three Available Air Movers (Fans) and a Hypothetical One (Fan No. 3).

Fan#MaxPressurePa

(H2O”)MaxVolumetricFlow

m3/min(CFM)

0 222 (0.89) 5.7 (200)1 445 (1.78) 8.2 (290)2 667 (2.67) 9.9 (350)3 890 (3.56) 14.2 (500)

Let us assume we have applied these fans to a standard five slot ATCA chassis in a push-pull situation, as shown in Figure 1.

Figure 1. A Five Slot ATCA Chassis with Fans in a Push-Pull Sys-tem

Let’s then consider four PCB-level power dissipations as shown in Table 2:

Table 2. PCB and System Power Dissipations for Four Configura-tions.

No. PCBPower(W) SystemPower(W)1 200 1,0002 300 1,5003 400 2,0004 500 2,500

To determine if refrigeration is a suitable option, and compare its performance with other cooling methods, we must estab-

lish some thermal design rules to gauge the quality of the so-lution. The industry falsely uses the fluid temperature rise in a PCB channel as a measure of performance. We adhere, to this practice only for the sake of clarity. Otherwise, such a gauge is perhaps the most ambiguous criterion for measur-ing whether a cooling solution is acceptable. (The misstep in gauging the fluid temperature rise in a PCB channel resides in the huge temperature and velocity gradients that exist in the PCB channel and the change of flow distribution on the PCB as the inlet boundary condition changes, i.e., fluid velocity. The best gauge is the device junction temperature, whether calculated or measured.) Here, we follow the industry practice and set 10, 15 and 20oC as the three temperature rises that we want our cooling solution deliver for the PCB-level power dissipations shown in Table 2.

This gauge states that, if the fluid temperature rise is within the set limit (10, 15 and 20oC,) the given cooling solution is ac-ceptable and the system will meet the required thermal crite-rion. In the stated three conditions, 10oC represents the most stringent and 20oC the most relaxed criteria. Considering the system in Figure 1, the volumetric flow rates for the four fans are given in Figure 2.

Figure 2. System Volumetric Flow Rate for the Four Fans Consid-ered [3].

Based on the above flow rates we can calculate the tempera-ture rise in the PCB channel and see whether the criterion

Pres

sure

(Pa)

Volumetric Flow Rate m3/s

hf0(G1)

hf1(G1)

hf2(G1)

hf3(G1)

R1(G1)

0 1 2 3 4 5 6 7 8

0

20 0

40 0

60 0

80 0

G1

Fan curves System

curve

Page 8: IN THIS ISSUE · along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing

FuTure coolING

Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | USAT: 781.769.2800 | F: 769.769.2800 |www.qats.com

Advanced Thermal Solutions, Inc. (ATS) has published Qpedia Thermal eMagazine, Volume 1, Issues 1-12, a hardbound, full-color book that compiles all of the electronics thermal management articles that first appeared in its online emagazine, Qpedia. In all, the book contains 46 technically comprehensive articles offering expert-level coverage on a wide range of heat management issues that impact virtually all of today’s electronic devices. Topics range from spot cooling hot areas on silicon dies to enhancing airflow over PCBs and inside chassis and cabinets.

All articles are written and edited at the engineer-level by the thermal and mechanical engineers from Advanced Thermal Solutions, including Kaveh Azar, Ph.D., the company’s president and CEO; and Bahman Tavassoli, Ph.D., its chief technologist. Both Azar and Tavassoli are internationally recognized experts in the thermal management of electronics.

Qpedia Thermal eMagazine, Volume 1, Issues 1-12, ISBN-978-0-615-23660-5, the hardbound, full color book can be ordered for $94.95 (USD) by calling 781-769-2800 or by email [email protected].

Volume discounts for organizations and academic institutions are also available. Contact ATS or visit www.qats.com for details.

First Volume of Qpedia Thermal eMagazine Articles Now Available in Hardcover Book

$94.95On Sale Now!

Visit www.qats.com, email [email protected] or call 781-769-2800 to place your order!

Page 9: IN THIS ISSUE · along with thermal design consulting services and training. Each article within Qpedia is meticulously researched and written by ATS’ engineering staff and contributing

Hence, the traditional design criterion of 10oC was not met as the PCB power dissipation increased. Now even, with a super-hypothetical fan, the higher power PCBs are not ther-mally managed, and a higher capacity cooling system with a different thermal transport capability, like jet impingement, is required.

There are many different cooling options – let’s explore device junction temperature as applied to the conditions we have stated above. Figure 5 shows the result of different cooling systems as applied to the ATCA chassis shown in Figure 1. It is clear that a conventional cooling system will not meet the criterion of 55oC temperature rise over ambient for a device that dissipates 100 W. (The two air-cooling technologies, fan-assisted air jet, with and without a heat sink, are noteworthy and will be discussed in future articles.)

The question is, what role can refrigeration play in an ATCA or PICMC style chassis? Obviously there are several ways to introduce refrigeration into such chassis, including:

Refrigerate the entire chassisUse a refrigerated cold plate to reduce the PCB and sub-sequently device temperatureRefrigerate the air that is coming into the chassis

Of these options, the third appears to involve the lowest cost of operations and deployment, and perhaps the highest ex-

1.2.

3.

�March 2009 |Qpedia

established above can be met. Figure 3 shows PCB fluid tem-perature rise plotted against volumetric, flow rate through each PCB channel for the four PCB power dissipations in Table 2.

Figure 3. Temperature Rise Between the Inlet and Outlet of the ATCA Chassis for Four Operating Points and at Four Different PCB Power Levels [3].

Figure 3 clearly shows that, if the PCB power dissipation is 200 or 300 W the, 10oC fluid temperature rise criterion can be met provided that the air flow inside the chassis is at least 6.8 m3/min (240 CFM) and 9.9 m3/min (350 CFM), respectively. The 10oC criterion cannot be met for higher powers, even using a hypothetical super fan. If we loosen our gauge and consider 15 or 20oC criteria, we see that higher PCB power dissipation is acceptable (400 W per PCB), provided that the volumetric flow rate is 8.5 m3/min (~300 CFM), and at 500 W, the flow rate is 10.6 m3/min (375 CFM). As we can see, creat-ing such a flow in a small chassis is a rather challenging task with many reliability and compliance issues, including acous-tic noise and fan failure.

By considering the device junction temperature (as the right criterion) for typical 30, 50, 70 and 100 W devices, we see a similar conclusion as the above with respect to cooling capa-bility for high power applications. Figure 4 shows the result of such an analysis for the aforementioned devices.

200 WBoard

300 WBoard

deltaT1i

deltaT2i

deltaT3i

deltaT4i

6 7 8 9 10 115

10

15

20

25

30

35

400 WBoard

500 WBoard

Gi

Volumetric Flow Rate (m3/s)

Figure 4. Junction Temperature of Four Different Devices at the Op-erating Point of the Four Different Fans.

2 .5 3 3 .5 4 4 .560

80

10 0

12 0

14 0

16 0

18 0

V 1i

Tj1i

Tj2i

Tj3i

Tj4i

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FuTure coolING

10 11

Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | 02062 | USAT: 781.769.2800 | F: 769.769.9979 |www.qats.com

Boards running hot?LeT THe exPeRTS AT ATS SHoW yoU HoW To eNSURe PRodUCT ReLIABILITy, SPeed TIMe-To-MARkeT ANd RedUCe CoSTS WITH exPeRT THeRMAL MANAGeMeNT ANALySIS ANd deSIGN SeRvICeS.

65

12

19

23

30

35

17

15

4

2

0 10 20 30 40 50 60 70

Junction Temperature (°C)

Conventional cooling

Cold plate (200W brd)

Cold plate (300W brd)

Cold plate (400W brd)

Cold plate (500W brd)

Fan assisted air jet

Fan assisted air jet-Highperformance heat sink

Compressor assisted air jet

Spray cooling

Water Jet

Junction Temperature Rise for Different Cooling Schemes

55°C Limit

Conventional Cooling is not

adequate for high power devices

Figure 5. Device Junction Temperature Rise for Different Cooling Schemes as Applied to 5-Slot ATCA Chassis [3].

Conventional air cooling

is not adequate for high

power devices

Conventional air cooling

is not adequate for high

power devices��oC

Limit

��oC

Limit

55

2

9

13

20

25

7

5

-6

-8

-10 0 10 20 30 40 50 60

Junction Temperature (°C)

Conventional cooling

Cold plate (200W brd)

Cold plate (300W brd)

Cold plate (400W brd)

Cold plate (500W brd)

Fan assisted air jet

Fan assisted air jet-Highperformance heat sink

Compressor assisted air jet

Spray cooling

Water Jet

Junction Temperature for Different Cooling Schemes

All cooling options are satisfactory

and Tj criterion is met with

Figure 6. Device Junction Temperature for a 100 W Device When the Approach Air to the Chassis is Chilled to -10oC [3].

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1111March 2009 |Qpedia

pected reliability. Figure 6 shows the result of such a study on the junction temperature of a 100 W device residing on a PCB in an ATCA chassis, as shown in Figure 1. Figure 6 clearly shows that once the approach air is chilled to the appropriate level, albeit borderline, even conventional air cooling will meet the thermal requirements. Now, even if we consider higher capacity cooling systems such as a fan-assisted air jet (e.g. Therm-Jet™, Advanced Thermal Solutions, Inc. patent pending technology), based on the thermal margin shown in Figure 6, even higher power dissipation can be readily attained at the component and PCB. Further, the data shows that -10oC may not be required and higher temperatures may still work effectively with less environmental impact and lower operation cost. Nevertheless, if power dissipation at the PCB and device levels continues to rise and system packaging follows the past decade’s trend of higher density, refrigeration is inevitable if we want to retain current ATCA and PICMC packaging. Such chassis were never designed for the high levels of power dissipation that the industry is experiencing.

In conclusion, refrigeration will provide higher capacity cooling for PICMG or ATCA like chassis. The question that remains is how effectively and economically can such a system be de-ployed. The energy efficiency, carbon footprint and total cost of deployment (covering acquisition, operation and end-of-life disposal) remain the cornerstones of the decision making pro-cess for the customers who acquire the systems and for the OEMs who fabricate them.

References:Advanced Thermal Solutions, Inc., Qpedia eMagazine, Refrigeration Cooling for Electronics Thermal Manage-ment, February 2008.Schmidt, R. and Notohardjono, B., High-End Server Low-Temperature Cooling, IBM Journal of Research and Development, Nov 2002.Azar, K., Limits of Air Cooling for ATCA and the Role of Liquid Cooling in Growing Thermal Demands, ATCA Summit, San Jose, CA, 2008.

1.

2.

3.

11

Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | 02062 | USAT: 781.769.2800 | F: 769.769.9979 |www.qats.com

Boards running hot?LeT THe exPeRTS AT ATS SHoW yoU HoW To eNSURe PRodUCT ReLIABILITy, SPeed TIMe-To-MARkeT ANd RedUCe CoSTS WITH exPeRT THeRMAL MANAGeMeNT ANALySIS ANd deSIGN SeRvICeS.

65

12

19

23

30

35

17

15

4

2

0 10 20 30 40 50 60 70

Junction Temperature (°C)

Conventional cooling

Cold plate (200W brd)

Cold plate (300W brd)

Cold plate (400W brd)

Cold plate (500W brd)

Fan assisted air jet

Fan assisted air jet-Highperformance heat sink

Compressor assisted air jet

Spray cooling

Water Jet

Junction Temperature Rise for Different Cooling Schemes

55°C Limit

Conventional Cooling is not

adequate for high power devices

Figure 5. Device Junction Temperature Rise for Different Cooling Schemes as Applied to 5-Slot ATCA Chassis [3].

Conventional air cooling

is not adequate for high

power devices

Conventional air cooling

is not adequate for high

power devices��oC

Limit

��oC

Limit

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The Thermal Performance of Microchannel and Macrochannel cold Plates

1�

In recent years, intense activity has gone into improving the capabilities of cold plates. Specifically, the use of microchannels has provided great improvements in cold plate thermal performance. Regardless of a cold plate’s channel size, the following equations can be used for heat transfer coefficients when determining thermal performance [1].

Where,

= Nusselt number

Dh= hydraulic diameter

= Reynolds number

ν = kinematic viscosityPr= Prandtl number

The pressure drop can also be calculated as:

ΔP=fLρU2/Dh

Where, ρ = densityf= friction factor

In recent years, microchannel cold plates have gained popularity due to their high performance. Webb shows that the best results can be achieved when the channel aspect ratio is about 7.4, and with a fin aspect ratio of 8. [2] Figure 1 shows a Fin-H copper microchannel with a channel hydraulic diameter of 0.49 mm. Due to the small size of the channels, the flow is generally considered to be laminar. The optimization resulted in a 25 mm wide and 20 mm long microchannel cold plate [2]. Webb considered both single-pass and two-pass designs on the water side. The two-pass version was made to determine if there was any mal-distribution of the water from the single-pass case.

Figure 1. Copper Microchannel Fin-H Used in a Cold Plate [2].

Figure 2 shows the thermal resistance of the Fin-H for the 1-pass and 2-pass designs as a function of flow rate.

hhDNu K=

hUDRe =

Nu=1.86( )1/3 otherwiseRe.Pr L Dh

Nu=0.023Re4/5Pr0.4 if Re > 10000

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1�1�March 2009 |Qpedia

Figure 2. Thermal Resistance of a Fin-H Cold Plate as a Function

of the Water Flow Rate [2].

This figure shows that the 1-pass version has a much better thermal resistance than the two-pass model for the same flow rate. It also shows that the flow has been distributed relatively uniformly. Figure 3 shows the pressure drop of the cold plate as a function of flow rate for the Fin-H and the Thermaltake Bigwater 735 cooler [3]. The figure shows the pressure drop of the 1-pass design is only 38% of the 2-pass design.

Figure 3. Pressure Drop of a Fin-H Cold Plate and a Thermaltake

Cooler as a Function of the Water Flow Rate [2].

Figure 4 shows the thermal resistance of the Fin-H cooler in the 1-pass design compared to the Thermaltake cooler [3]. At 2.28 l/min the Thermaltake’s thermal resistance is 0.106 K/W. The balance point of the Fin-H for 1-pass is with a thermal resistance of 0.07 K/W at a flow rate of 0.361 l/min. This is only 16% of the flow rate for the Thermaltake cooler. Referring to Figure 3, the pressure drop is almost the same for both coolers. The major implication is that the microchannel cold plate requires a smaller pump compared to macrochannel cold plates, and provides a 50% increase in thermal performance.

Figure 4. Thermal Resistance of a Fin-H Cold Plate and a Thermaltake Cooler as a Function of the Water Flow Rate [2].

Another innovative approach is the concept of forced-fed boiling (FFB). [4] Figure 5 shows a schematic of this process. It consists of a micro-grooved, thin copper surface with alternating fins and channels. The microgrooves have a hydraulic diameter of 28 microns, an aspect ratio of 15, and a fin density of 236 fins per cm. There are feed channels on top of the micro-grooved surface. The fluid is forced through these channels into the microgrooves, which are located on top of the heated surface. The fluid vaporizes in the microgrooves and moves upward, while the liquid flows beneath the escaping vapor. This keeps the surface wet, resulting in an increase of the critical heat flux (CHF)

Figure 5. A Force-Fed Boiling Cold Plate [4]

Figure 6 shows the heat transfer as a function of the temperature difference between the inlet fluid and the surface for various values of the flow rate for R245fa, a non-aqueous fluid for low pressure refrigeration applications. The figure shows that for heat fluxes of about 200 W/cm2 or less, heat transfer is independent of the flow rate, but this is not the case at higher heat fluxes. It also shows that the slope of the heat flux decreases with increasing temperature difference.

00.020.040.060.080.1

0.5 0.7 0.9 1.1 1.3 1.5

Water Flow Rate (l/min)

Rto

t (K/W

)

Fin-H, 2-Pass-116W Fin-H, 1-Pass-110W

0

4

8

12

16

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Flow Rate (l/min)

Pre

ssur

e D

rop

(kP

a)

Fin-H (2-Pass)Fin-H 1-Pass)Thermaltake

0

0.05

0.1

0.15

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Water Flow Rate (l/min)

Rto

t (K/W

)

Thermaltake Fin-H, 1-Pass Operating point

Vapor Flow Feed Channels Liquid Flow

MicrogroovedSurface

Heated Surface

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Feel like you are always battling heat problems?

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Advanced Thermal Solutions, Inc. (ATS), a leading electronics cooling provider, offers comprehensive thermal management analysis and design services tailored to help bring telecommunications, networking, embedded computing and other high performance electronic products to market faster, ensure their reliability and reduce development costs.

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SERVICESEvaluationAnalysisDesignTesting Manufacturing

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Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | 02062 | USAT: 781.769.2800 | F: 769.769.9979 |www.qats.com

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Figure 6. Heat Flux as a Function of the Temperature Difference for the FFB Cold Plate [4]

Figure 7 shows an interesting trend for the heat transfer coefficient as a function of heat flux for the same fluid. At first, the heat transfer coefficient increases with the increase in heat flux. This indicates that by increasing the heat flux, a phase change process takes place which changes the single-phase flow to two-phase heat transfer. After reaching an impressive peak at 300 KW/m2.K, the heat transfer coefficient starts to decrease. This is attributed to local dryouts from bubble generation, which also blocks the microchannels.

While advances in cold plate performance have been incremental, their technology is still evolving. Improvements in microchannel manufacturing will open more opportunities in this field. Microchannel cold plates provide tremendous heat transfer coefficient capacities, but limitations prevent their broad deployment. Fouling, dryout, and fabrication issues have been major negating factors for microchannel deployment in the broader market. Microchannel cold plates may have particular value in such applications as military, space, and high capacity computing, where service and maintenance are part of the deployment. However, from the design and problem-solution standpoint, microchannel cold plates can be an effective part of a closed loop liquid cooling

system.

References:Dittus, F. and Boelter, L., Publications on Engineering, University of California at Berkley, 1930.Webb, R., High-Performance, Low-Cost Liquid Micro-Channel Cooler, Thermal Challenges in Next Generation Electronic Systems II, Millpress Science Publishers, Rotterdam, The Netherlands, 2007.Thermaltake Company, 2006.Cetegen, E., Dessiatoun, S., and Ohadi, M., Force Fed Boiling and Condensation for High Heat Flux Applications, VII Minsk International Seminar: Heat Pipes, Heat Pumps, Refrigerators, Power Sources, Minsk, Belarus, 2008.

1.

2.

3.4.

Tsurface - Tfluid_in0 10 20 30 40 50

q" -

Hea

t Flu

x [W

/cm

2 ]

0

100

200

300

400

500

580 kg/m2-s774 kg/m2-s968 kg/m2-s

q" - Heat Flux [W/cm2]

0 100 200 300 400 500

h - H

eat T

r. C

oeff.

[kW

/m2 -K

]

50

100

150

200

250

300

350

580 kg/m2-s

774 kg/m2-s

968 kg/m2-s

Figure 7. Heat Transfer Coefficient as a Function of Heat Flux for the FFB Cold Plate [4].

Qpedia Thermal eMagazine Articles Now Available in Hardcover Book!

Qpedia Thermal eMagazine, Volume 1, Issues 1-12, ISBN-978-0-615-23660-5, the hardbound, full color book can be ordered for $94.95 (USD) by calling 781-769-2800 or by email [email protected]. Contact ATS or visit www.qats.com for details.

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1�

Thermosyphons: how They Work and Their Practical limitations

IntroductionIn electronics cooling, heat pipes are used to transfer heat dissipated from devices into the environment. Thermosyphons follow the same principal as heat pipes and are widely used in energy systems. [1] In fact, thermosyphon technology was proposed for thermally managing the nuclear core of the Pebble Bed Modular Reactor. [2] But, unlike heat pipes, thermosyphons are not widely used in the electronics industry. This article helps explain why this is so by discussing their operation. It looks at the working fluid and compatible tube materials available for use in thermosyphons, and then reviews some thermosyphon configurations.

PrincipalofOperationA heat pipe is a tube lined with a wicking structure in which a small amount of working fluid is present. It is divided into an evaporator (heat addition) section and a condenser (heat rejection) section. When heat is added to the evaporator section, the working fluid in the wicking structure vaporizes and flows to the cooler section where it condenses and gives up its latent heat of vaporization. The capillary forces in the wicking structure then pump the liquid back to the evaporator. [3]

Two-phase closed thermosyphons, on the other hand, are essentially heat pipes without the wicking structure. Unlike a heat pipe, the thermosyphon uses gravity to assist the transfer of heat from a heat source that is located below the cold sink. As a result, the evaporator section must be situated below the condenser section. The working fluid evaporates, condenses in the condenser section, and then flows back to

the evaporator section under the influence of gravity. It has been shown that in the presence of gravity, thermosyphons are preferred to heat pipes because the wicks in heat pipes produce an additional resistance to the flow of condensate. [4] Figure 1 illustrates the principal difference between the

heat pipe and the thermosyphon.

Figure 1. Principal difference between a heat pipe (a) and a thermosyphon (b) [1]

In the electronics industry, especially consumer electronics, the orientation of a product in use can’t be guaranteed, which is why thermosyphons are not frequently used in electronics cooling applications.

Two-Phase Closed Thermosyphon Heat Pipe

Wick

Th

Tc

inQ.

outQ.

Liquid Flow

Vapor Flow

outQ. Tc

Th inQ.

Vapor Flow

Liquid Flow

Working Fluid

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Thermosyphons: how They Work and Their Practical limitations

1�1�March 2009 |Qpedia

WorkingFluidsAndCompatibleTubeMaterialsSome working fluids for thermosyphons are listed in Table 1. A working fluid is evaluated based on its minimum and maximum operational temperatures, compatibility with the thermosyphon tube material and the maximum heat transfer rate. Table 1 shows that for high temperature applications, metals in liquid/vapour phase are commonly used.

Table 1. The Useful Operating Temperature Range of Some Thermosyphon Working Fluids/Mediums [3].

Work fluid/medium Usefultemperaturerange[ºC]

Helium -271 to -269

Nitrogen -203 to -160

Ammonia -60 to 100

Pentane -20 to 120

Acetone 0 to 120

Methanol 10 to 130

Ethanol 0 to 130

Water 30 to 200

Mercury 250 to 650

Cesium 450 to 900

Potassium 500 to 1000

Sodium 600 to 1200

Lithium 1000 to 1800

Silver 1800 to 2300

When an incompatible fluid is used, two major issues are corrosion and the generation of non-condensable gas. [3] If the wall material is soluble in the working fluid, mass transfer is likely to occur with solid material being deposited in the evaporator. This will result in local hot spots or, in the case of heat pipes, blocking of the pores of the wick material. Non-condensable gas generation is probably the most common

indication of heat pipe failure. In thermosyphons, non-condensable gasses accumulate in the condenser, which will gradually become blocked. This decreases the area available for condensing the working fluid and the performance of the thermosyphon decreases. Table 2 shows some compatible materials for working fluids at low temperatures.

Table 2. Compatibilty And Useful Operating Temperature Range Data. For Some Low Temperature Working Fluids [3].

Tubematerials

Working fluid

Water Acetone Ammonia Methanol

Copper RU RU NR RU

Aluminum GNC RL RU NR

Stainless steel GNT PC RU GNT

Nickel PC PC RU RL

Useful temperature range [ºC]

30 - 200 0 – 120 -60 – 120 10 – 130

Abbreviations:RU: Recommended by past successful usageRL: Recommended by literatureNR: Not recommendedPC: Probably compatibleGNT: Generation of gas at all temperaturesGNC: Generation of gas at elevated temperatures

The figure of merit (FOM) can be used to evaluate the maximum heat transfer rate for a working fluid. FOM is defined as ρlσhfg/μ and is usually expressed in kW/cm². Figure 2 shows that R-134a has a lower FOM than butane, and that water has the highest. Therefore, under the same parameters, e..g. orientation and design, a water-filled thermosyphon will be able to transfer more heat than an R-134a-filled thermosyphon. However, the FOM does not indicate a thermosyphon’s thermal performance; this must be experimentally determined.

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Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | USAT: 781.769.2800 | F: 769.769.2800 |www.qats.com

Advanced Thermal Solutions, Inc. (ATS) has published Qpedia Thermal eMagazine, Volume 1, Issues 1-12, a hardbound, full-color book that compiles all of the electronics thermal management articles that first appeared in its online emagazine, Qpedia. In all, the book contains 46 technically comprehensive articles offering expert-level coverage on a wide range of heat management issues that impact virtually all of today’s electronic devices. Topics range from spot cooling hot areas on silicon dies to enhancing airflow over PCBs and inside chassis and cabinets.

All articles are written and edited at the engineer-level by the thermal and mechanical engineers from Advanced Thermal Solutions, including Kaveh Azar, Ph.D., the company’s president and CEO; and Bahman Tavassoli, Ph.D., its chief technologist. Both Azar and Tavassoli are internationally recognized experts in the thermal management of electronics.

Qpedia Thermal eMagazine, Volume 1, Issues 1-12, ISBN-978-0-615-23660-5, the hardbound, full color book can be ordered for $94.95 (USD) by calling 781-769-2800 or by email [email protected].

Volume discounts for organizations and academic institutions are also available. Contact ATS or visit www.qats.com for details.

First Volume of Qpedia Thermal eMagazine Articles Now Available in Hardcover Book

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Figure 2. Figure of Merit (FOM) for a Number of Heat Pipe and

Thermosyphon Fluids. Data Used Is From [5], [6] and [7].

Thermosyphon ConfigurationsA closed loop thermosyphon consists of a tube loop, while a straight thermosyphon is a straight tube. The closed loop design uses thermally induced density gradients to circulate the working fluid, providing heat transfer from the evaporator to the condenser. This natural circulation eliminates the need for any mechanical moving parts, such as pumps and pump controls. Closed loop thermosyphons are thus particularly suitable for cooling applications where reliability and safety are of paramount importance, such as in nuclear reactor technology. [2]

Closed loop thermosyphons are often configured so that the evaporator and condenser are parallel to each other, with the evaporator normally below the condenser. Data has been published for a top-heat mode loop thermosyphon, i.e., with the evaporator above the condenser [8]. There is also available data for a closed loop thermosyphon where the evaporator is horizontal and positioned below the vertical condenser, as shown in Figures 3 and 4. [9] In this latter case, the working fluids evaluated were R-134a, butane, and water in a copper tube of 6, 9 and 12.5 mm.

SummaryAlthough thermosyphons are widely used in industrial heat recovery systems, they are seldom employed for electronics

cooling. This is because a thermosyphon’s performance is very dependent on its orientation. For a thermosyphon to work, the cold side (condenser), must be above the hot side (evaporator). This lets the working fluid flow to the evaporator with the aid of gravity. The compatibility of

Heat in Heat

out

m+1

(a) (b)

Figure 3. A Common Closed Loop Thermosyphon Configuration (a), and One with a Horizontally-Positioned Evaporator (b).

a)

b)

Figure 4. Operating Principles of a Straight Thermosyphon (a) and a Closed Loop Thermosyphon Where the Evaporator is Horizontal and the Condenser is Vertical (b) [9].

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�0

working fluids with tube materials must be considered, along with a thermosyphon’s physical configuration.

References:Meyer, A. and Dobson, R., A Heat Pipe Heat Recovery Heat Exchanger for a Mini-Drier, Journal of Energy in Southern Africa, Vol 17 No 1, 2006.Ruppersberg, J. and Dobson, R., Experimental Evaluation of the Flow and Heat Transfer in a Closed Loop Thermosyphon – Part 2, Proceedings of the 14th International Heat Pipe Conference, Florianópolis, Brazil, 2007..Dunn, P. and Reay, D., Heat Pipes, 4th Edition, Pergamon, 1994..Pioro, L. and Pioro, I., Industrial Two-Phase Thermosyphons, Begell House, 1997.Lemmon, E., McLinden, M.., and Friend, D.G., “Thermophysical Properties of Fluid Systems” in

1.

2.

3.

4.

5.

NIST Chemistry WebBook, NIST Standard Reference Database Number 69, 2005, Faghri, A, , Heat Pipe Science and Technology, Taylor & Francis, 1995.Mills, A., Heat Transfer, Prentice Hall, 1998.Ippoushi, S., Tabara, S., Motomatu, K., Muto, A., and Imura, H., Development of a Top-Heat-Mode Loop Thermosyphon, 6th ASME-JSME Thermal Engineering Joint Conference, March 2003.Jeggels, Y, Thermal Management and Temperature Control of a Containerised Rapid Deployment Radar System, Mechanical Engineering Department, Stellenbosch University, 2007.Imura, H. and Ippohshi, S., Heat Transfer Characteristics in Two-Phase Crank-Shaped Closed Loop Thermosyphons, Proceedings of the 6th International Heat Pipe Symposium, Chiang Mai, 2000.

6.

7.8.

9.

10.

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�1March 2009 |Qpedia

Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | USAT: 781.769.2800 | F: 769.769.2800 |www.qats.com

In medicine, diagnosing an illness and determining the correct treatment is often a matter of life or death. Healthcare professionals depend on the quality, accuracy and reliability of their electronic devices in order to treat the injured or sick and save lives. In medical electronics, how effective an engineer is at managing a device’s heat is often the difference between its success and failure.

Advanced Thermal Solutions, Inc. (ATS), an industry leader in electronics cooling, offers comprehensive thermal management analysis and design services tailored to help bring medical electronics to market faster, ensure their reliability and reduce development costs.

ATS’ thermal management analysis and design services encompass both experimental and computational simulations using proprietary tools and computation fluid dynamics software packages such as FLOTHERM and CFdesign. ATS studies the full packaging domain, including components, circuit boards (PCBs), shelves, chassis, and system packaging. The company’s design services include heat sink, board and fan characterization; heat sink and fan tray design and optimization; liquid cooling design; prototyping of heat sinks and complete cooling systems; and wind tunnel testing of components, PCBs, chassis and enclosures.

More information about ATS thermal design and testing services can be found on the Advanced Thermal Solutions website, www.qats.com, or by calling 781-769-2800.

Let AtS DiAgnoSe AnD treAtYour thermAL ProbLemS

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��

What Are Pitot Tubes and how Do They Measure Velocity?

IntroductionPitot tubes are devices for measuring fluid velocity. Applications requiring flow measurement, such as the flow over a wing or through an enclosure, can benefit from the use of Pitot tubes. A Pitot tube is a device in which the pressure differential, based on the energy equation, is translated into velocity. In order to measure velocity with a Pitot tube, two of three variables must be known:

Total Pressure – the sum of static and dynamic pressures.Static Pressure – the pressure of fluid flowing parallel to the tube.Dynamic Pressure – the pressure when a particle of fluid traveling at velocity V comes to a sudden stop.

In a Pitot tube application, total pressure and static pressure are sensed directly. The dynamic pressure is the difference between these two. It is either measured directly with separate instrumentation or determined mathematically.

In commercial applications, Pitot tubes may be used to measure the speed of an aircraft, and for measuring the air velocity in heating and cooling ducts. They are also used in the environmental field for exhaust gas and stack testing, as well as in wind tunnels and in laboratory environments.

TypesofPitotTubesThere are basically two types of Pitot tubes. The most popular type used in the laboratory is also known as a Pitot-static tube or Prandtl tube. This model consists of two stainless steel

1.

2.

3.

tubes - one located concentrically inside the other, along with a stem, a 90-degree bend around a generous radius, and a bullet-nosed tip. A hole is concentrically located in the tip and several smaller holes are located around the outer tube about one-third the distance from the tip to the stem. This type is shown in Figure 1, with a typical application shown in Figure 2. The other Pitot tube type is similar in appearance, but is only a single tube with a hole only in the tip. It just senses total pressure, while a separate tube senses static pressure, as shown in Figure 3.

Figure 1. Pitot-Static Tube

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��March 2009 |Qpedia

What Are Pitot Tubes and how Do They Measure Velocity?

Figure 2. Pitot-Static Tube in a Fluid Stream.

Figure 3.Separate Pitot and Static Tubes in a Fluid Stream.

ApplicationsAs with all instrumentation, a Pitot tube has several attributes which must be considered in order to determine if it is suited to a given application. Those attributes generally regarded as assets include:

Low cost.No moving parts.Simple to install.Relatively small disturbance to flow and pressure, depending on the aspect ratio between the location of measurement and the Pitot tube size.Single point measurement. This may also be a detriment, depending on the application and knowledge of the user. Average velocity through a duct, for example, must be measured with several Pitot tubes or by traversing a

••••

single Pitot tube to different locations within the cross-sectional area of a duct. A typical sampling array is shown in Figure 4. To measure velocity in a localized spot only, a Pitot tube is one of a few instruments ideally suited to the task.

Figure 4. Traverse on Round and Square Duct Areas.

Those attributes regarded as detriments include:

Susceptibility to clogging. This may be caused by particulate matter or water vapor. Water vapor has been known to form ice blockages on Pitot tubes of aircraft. To counter this problem, electric heating elements are built-in. Special particulate tolerant S-type Pitot tubes have a tip design as shown in Figure 5. Sensitive to misalignment. Some manufacturers advertise a generous degree of acceptable misalignment. Sensitive to vibration.

Figure 5. Particulate Tolerant S-Type Pitot Tube

Mounting/InstallationThere are two challenges to installing a Pitot tube - alignment and rigidity. In a permanent installation, such as on an aircraft, alignment and position can be measured once because the tube will remain that way forever. But in a

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Heat issues have you tangled up? let tHe experts at ats sHow you How to ensure product reliability, speed time-to-market and reduce costs witH expert tHermal management analysis and design services.

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��March 2009 |Qpedia

laboratory environment, relocating the tube to different points within a fluid stream may require constant monitoring of the alignment and position. The port through which the tube enters the fluid stream must not impart additional turbulence or leakage. Through-duct fittings can be improvised, or special fittings made for this purpose may be acquired from the Pitot tube supplier. Some Pitot tubes are manufactured with alignment and depth marks to facilitate their insertion into non-transparent ducts.

LimitationsOne of the main drawbacks of using Pitot tubes is measuring very low flows, for example, in conditions when the fluid velocity is less than 0.5 m/s. In this situation, the pressure created by the fluid motion is so low that even the most sensitive pressure transducers might not accurately measure the flow. The use of a Pitot tube under such circumstances must done with great caution to prevent erroneous measurement. Another drawback, especially in electronics cooling applications, is the aspect ratio. A channel constructed of circuit boards and nested electronic components is typically spatially constrained, and the size of the Pitot tube could create a large amount of disturbance and change of flow direction in the volume being measured. Furthermore, like many other flow measurement sensors, Pitot tubes are flow direction ambiguous. Therefore, in a typical electronics cooling application, the primary flow direction must be known a priori before using a Pitot tube for velocity measurement. This poses a major challenge in the PCB environment.

EquationsThe equations below are derived from Bernoulli’s principle, which states that as fluid velocity increases, pressure decreases. Certain assumptions must be true in order for Bernoulli’s equation to yield accurate results:

Flow must be steady.Flow must be incompressible.Flow must be frictionless.Flow must be in a streamline.

Bernoulli's equation states that:

••••

Constant (1)

Where:V = Velocityp =Pressureρ =Fluid Densityg =Gravitational Accelerationz =Elevation

To simplify this further, g and z may be omitted.

The formula for the pressures found at the Pitot tube is:

(2)

Where:

tp = Total Pressure

sp = Static Pressure

dp = Dynamic Pressure

Another variable is:C = Pitot Tube Coefficient

This variable uses a value supplied by the Pitot tube manufacturer. Typically, the C value is determined experimentally or is assumed to be 1 for a well-designed and manufactured tube.

Applying the above variables and some algebra to the simplified Bernoulli equation, (1), the formula for calculating fluid velocity from a Pitot tube is:

(3)

ReferencesAvallone, E. and Baumeister, T., Marks’ Standard Handbook for Mechanical Engineers, Ninth Edition, McGraw-Hill, 1987.Considine, D. M., Process Instruments and Controls Handbook, Second edition, McGraw-Hill, 1975.Vennard, J. K. and Street, R. L., Elementary Fluid Mechanics, sixth edition, John Wiley & Sons, 1982.

1.

2.

3.

2p Vgz2

+ + =ρ

2p Vgz2

+ + =ρ

t s dp p p= +t s dp p p= +

t s2(p p )V C

−=

ρt s2(p p )

V C−

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��

Getting your company’s message out to over 17,000 engineers and industry professionals has never been easier.

Advertise in Qpedia Today!Qpedia was launched in 2007 as a technology eMagazine focused on the thermal management of electronics. It is designed as a resource to help the engineering community solve the most challenging thermal problems.

The newsletter is published monthly and distributed at no charge to over 17,000 engineers worldwide. Qpedia is also available online or for download at www.qats.com/qpedia.Qpedia’s editorial team includes ATS’ President & CEO Kaveh Azar Ph.D., and Bahman Tavassoli Ph.D., the company’s chief technologist. Both Azar and Tavassoli are internationally recognized experts in the thermalmanagement of electronics.

www.qats.com | 781.769.2800 | 89-27 Access Road Norwood, MA 02062 USA

For more information on how you can generate awareness about your company or products, contace Ray Santos at 782.769.2800.