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1CHSLT - Center for Holographic Studies and Laser micro-mechaTronics

Mechanical Engineering Department/NEST - NanoEngineering, Science, and Technology 1

ME-4429Thermofluid applications and design

C’2014M, 3 March 2014

Prof. Ryszard J. PryputniewiczProf. Ryszard J. PryputniewiczNEST - NanoEngineering, Science, and Technology

CHSLT - Center for Holographic Studies and Laser micro-mechaTronicsMechanical Engineering Department

School of EngineeringWorcester Polytechnic Institute

Worcester, MA 01609

Lecture 23Lecture 23Heat exchangers (HEXs).Heat exchangers (HEXs).

The overall heat transfer coefficient.The overall heat transfer coefficient.Analysis of HEXs. The LMTD method. Analysis of HEXs. The LMTD method.

The effectiveness-NTU method. Microchannel heat sinks.The effectiveness-NTU method. Microchannel heat sinks.



Interim discussion of Topical Projects

The D-Day is on Thursday, March 63 days from today

ANY QUESTIONS, CHALLENGES, etc.???



Consultations this week and …• Consultation hours will be as scheduled

• Should you have any questions relating either to Exam II scheduled for Friday, March 7, or anything else relating to the course, please see me ASAP

• There will be QAR addressing Exam III tomorrow, Tuesday, March 5, therefore prepare questions

• Wednesday is Conference No. 5

• Plan your week taking the above items into consideration



Last Wednesday of C-term…

Conference C07, no new material covered

Prepare questions, good time to start review for Exam III, which will be on Friday, March 7


Mechanical Engineering Department/NEST - NanoEngineering, Science, and Technology

Chapter 22HEAT EXCHANGES

Fundamentals of Thermal-Fluid Sciences 4th Edition

Yunus A. Cengel, John M. Cimbala, Robert H. TurnerMcGraw-Hill, 2012



Objectives

• Recognize numerous types of heat exchangers, and classify them

• Develop an awareness of fouling on surfaces, and determine the overall heat transfer coefficient for a heat exchanger

• Perform a general energy analysis on heat exchangers

• Obtain a relation for the logarithmic mean temperature difference for use in the LMTD method, and modify it for different types of heat exchangers using the correction factor

• Develop relations for effectiveness, and analyze heat exchangers when outlet temperatures are not known using the effectiveness-NTU method

• Know the primary considerations in the selection of heat exchangers.

• Introduce the state-of-the-art (SOTA) microchannel HEXs



22-1. TYPES OF HEAT EXCHANGERS

Different flow regimes and associated temperature profiles in a double-pipe heat exchanger.

T-x diagrams

x x, or A



Shell-and-tube heat exchanger: The most common type of heat exchanger in industrial applications.

They contain a large number of tubes (sometimes several hundred) packed in a shell with their axes parallel to that of the shell. Heat transfer takes place as one fluid flows inside the tubes while the other fluid flows outside the tubes through the shell.

Shell-and-tube heat exchangers are further classified according to the number of shell and tube passes involved.



Regenerative heat exchanger: Involves the alternate passage of the hot and cold fluid streams through the same flow area.

Dynamic-type regenerator: Involves a rotating drum and continuous flow of the hot and cold fluid through different portions of the drum so that any portion of the drum passes periodically through the hot stream, storing heat, and then through the cold stream, rejecting this stored heat.

Condenser: One of the fluids is cooled and condenses as it flows through the heat exchanger.

Boiler: One of the fluids absorbs heat and vaporizes.



22-2. THE OVERALL HEAT TRANSFER COEFFICIENT

• A heat exchanger typically involves two flowing fluids separated by a solid wall.

• Heat is first transferred from the hot fluid to the wall by convection, through the wall by conduction, and from the wall to the cold fluid again by convection.

• Any radiation effects are usually included in the convection heat transfer coefficients.

Thermal resistance network associated with heat transfer in a

double-pipe heat exchanger.



U the overall heat transfer coefficient, W/m2C

When

The overall heat transfer coefficient U is dominated by the smaller convection coefficient. When one of the convection coefficients is much smaller than the other (say, hi << ho), we have 1/hi >> 1/ho, and thus U hi. This situation arises frequently when one of the fluids is a gas and the other is a liquid. In such cases, fins are commonly used on the gas side to enhance the product UA and thus the heat transfer on that side.



The overall heat transfer coefficient ranges from about 10 W/m2C for gas-to-gas heat exchangers to about 10,000 W/m2C for heat exchangers that involve phase changes.

For short fins of high thermal conductivity, we can use this total area in the convection resistance relation Rconv = 1/hAs

To account for fin efficiency

When the tube is finned on one side to enhance heat transfer, the total heat transfer surface area on

the finned side is



Fouling FactorThe performance of heat exchangers usually deteriorates with time as a result of accumulation of deposits on heat transfer surfaces. The layer of deposits represents additional resistance to heat transfer. This is represented by a fouling factor Rf.

The fouling factor increases with the operating temperature and the length of service and decreases with the velocity of the fluids.



22-3. ANALYSIS OF HEAT EXCHANGERSAn engineer often finds himself or herself in a position 1. To select a heat exchanger that will achieve a specified temperature

change in a fluid stream of known mass flow rate - the log mean temperature difference (or LMTD) method.

2. To predict the outlet temperatures of the hot and cold fluid streams in a specified heat exchanger - the effectiveness–NTU method.

The rate of heat transfer in heat exchanger (HE is insulated):

heat capacity rate

Two fluid streams that

have the same capacity rates

experience the same

temperature change in a well-

insulated heat exchanger.



Variation of fluid temperatures in a heat exchanger when one of the fluids condenses or boils.

is the rate of evaporation or condensation of the fluid

hfg is the enthalpy of vaporization of the fluid at the specified temperature or pressure.

The heat capacity rate of a fluid during a phase-change process must approach infinity since the temperature change is practically zero.

Tm an appropriate mean (average) temperature difference between the two fluids



22-4. THE LOG MEAN TEMPERATURE DIFFERENCE METHOD

Variation of the fluid temperatures in a parallel-flow double-pipe heat exchanger.

log mean temperature difference



The arithmetic mean temperature difference

The logarithmic mean temperature difference Tlm is an exact representation of the average temperature difference between the hot and cold fluids.

Note that Tlm is always less than Tam. Therefore, using Tam in calculations instead of Tlm will overestimate the rate of heat transfer in a heat exchanger between the two fluids.

When T1 differs from T2 by no more than 40 percent, the error in using the arithmetic mean temperature difference is less than 1 percent. But the error increases to undesirable levels when T1 differs from T2 by greater amounts.



Counter-Flow Heat ExchangersIn the limiting case, the cold fluid will be heated to the inlet temperature of the hot fluid.

However, the outlet temperature of the cold fluid can never exceed the inlet temperature of the hot fluid.

For specified inlet and outlet temperatures, Tlm a counter-flow heat exchanger is always greater than that for a parallel-flow heat exchanger.

That is, Tlm, CF > Tlm, PF, and thus a smaller surface area (and thus a smaller heat exchanger) is needed to achieve a specified heat transfer rate in a counter-flow heat exchanger.

When the heat capacity rates of the two fluids are equal



Multipass and Cross-Flow Heat Exchangers: Use of a Correction Factor

F correction factor depends on the geometry of the heat exchanger and the inlet and outlet temperatures of the hot and cold fluid streams.

F for common cross-flow and shell-and-tube heat exchanger configurations is given in the figure versus two temperature ratios P and R defined as

1 and 2 inlet and outletT and t shell- and tube-side temperatures

F = 1 for a condenser or boiler



Correction factor F charts for common shell-and-tube heat exchangers.



The LMTD method is very suitable for determining the size of a heat exchanger to realize prescribed outlet temperatures when the mass flow rates and the inlet and outlet temperatures of the hot and cold fluids are specified.

With the LMTD method, the task is to select a heat exchanger that will meet the prescribed heat transfer requirements. The procedure to be followed by the selection process is:

1. Select the type of heat exchanger suitable for the application.

2. Determine any unknown inlet or outlet temperature and the heat transfer rate using an energy balance.

3. Calculate the log mean temperature difference Tlm and the correction factor F, if necessary.

4. Obtain (select or calculate) the value of the overall heat transfer coefficient U.

5. Calculate the heat transfer surface area As .

The task is completed by selecting a heat exchanger that has a heat transfer surface area equal to or larger than As.



22-5. THE EFFECTIVENESS–NTU METHODA second kind of problem encountered in heat exchanger analysis is the determination of the heat transfer rate and the outlet temperatures of the hot and cold fluids for prescribed fluid mass flow rates and inlet temperatures when the type and size of the heat exchanger are specified.

Heat transfer effectiveness

the maximum possible heat transfer rate

Cmin is the smaller of Ch and Cc



Effectiveness relations of the heat exchangers typically involve the dimensionless group UAs /Cmin.

This quantity is called the number of transfer units NTU.

For specified values of U and Cmin, the value of NTU is a measure of the surface area As. Thus, the larger the NTU, the larger the heat exchanger.

capacity ratio

The effectiveness of a heat exchanger is a function of the number of transfer units NTU and the capacity ratio c.



MicrochannelsUsed to accommodate fluid flow for cooling in the IC substrate

Characteristic dimensions of microchannels (cross-section) is on the order of 200 µm



Schematic view of a microchannel heat sink



Thin layer to be patterned

Si Substrate

Fabrication of Si microchannelsPhotolithography: overview

The process used in this illustration is known as Sacrificial Surface Micromachining (SSM)

Deposition of thin layer to be patterned



Un-patterned photoresistUV-Sensitive layer

Photoresist Layer

Si Substrate

Deposition of photoresist





Si Substrate

Photoresist Layer

Mask

UV radiation



Lithographically patterned photoresist

Si Substrate

Removal of exposed photoresist




Patterning of thin layer

Si Substrate


Deposition of thin layer to be patterned




Removal of remaining photoresist

Patterned thin layer

Si Substrate



Fabrication of Si microchannels



Fabricated triangular channel80 µm deep channel



Fundamental relationshipsMC-HEX. MICROCHANNEL HEAT EXCHANGERS AND MINIATURE POWER

DEVICES Continued miniaturization of components (especially those that need/use energy for operation) depends on their efficient thermal management. Thus thermal management is a topic of ever increasing interest because of emerging technologies (ETs). The thermal management, in turn, depends on availability of reliable heat exchangers (HEXs). As components decrease in size, with the advancement of ETs, so do the HEXs that are used to keep them cool. In fact, very recently, a temperature control subsystem (the smallest and one of the most intricate HEX developed heretofore) was demonstrated as a part of one of the research programs conducted at WPI-ME/CHSLT-NEST laboratories. This intricate HEX is virtually built into an IC chip, which also contains very advanced (micromechatronics) MEMS sensors that require extremely uniform and stable thermal environment in order to satisfy their extreme performance requirements. This Chapter introduces microchannel (and other ultraminiature) heat sinks. Synonymous with these advances in technology of HEXs are also breakthroughs in miniature power devices and trends in their development. A prominent place in this development is taken by heat pipes. Heat pipes (not to be confused with heat pumps) evolved over the last several years from laboratory curiosities to serious applications where, now, only heat pipes can provide thermofluids solution to a given problem. Today, heat pipes are used to heat and cool homes, classrooms, factories, and in devices/systems where physical space is at a premium and thermofluid devices of high performance to volume/weight ratios (provided by heat pipes) can be effectively used as, e.g., in avionics, spacecraft, and most notable in compact microelectronics where heat pipes effectively provide thermal management. This Chapter also exposes the reader to rudimentary principles of heat pipes and illustrates them with representative examples. In addition, emerging nonconventional miniature power devices, characterized by a “postage-stamp-size” are being introduced as a preview of where energy-delivery and control may be heading as we venture into the future.

MC-HEX.1. Fundamental relationships As a coolant passes through a heat sink (aka HEX), viscous forces cause the fluids mechanical energy (pressure) convert into fluid enthalpy rise (temperature). As a result, the coolant experiences a pressure drop across a HEX. The magnitude of the pressure drop depends on Re, the channel geometry, and whether or not the flow is fully developed at the channel exit. The pressure drop between the inlet and outlet coolant plenums can be determined using

∆𝑃=ቈ൬𝐴𝑐𝐴𝑝൰2ሺ2𝐾90ሻ+ሺ𝐾𝑖 + 𝐾𝑒ሻ+ቀ4𝑓𝑎𝑝𝑝 𝐿𝐷ℎቁ 𝑉2𝜌𝑓2𝑔𝑐 , (MC-1)



Fundamental relationships, cont’d where, (Ac/ Ap)=AR which is the area ratio, K’s designate various losses, Dh is the hydraulic diameter, ρf is the density of (coolant) fluid, gc is the gravitational conversion constant, and fapp is the apparent friction factor defined as 𝑓𝑎𝑝𝑝 = 𝐴𝑅𝑒𝐵 , (MC-2) where Re is the Reynolds number while the constants A and B should be determined using 𝐴= 0.09290+ 1.01612 𝑥𝐷ℎ , (MC-3)

and

𝐵= −0.26800− 0.31930𝐷ℎ𝑥 , (MC-4)

respectively, with x designating the length/distance. Viscous dissipation represents conversion of mechanical energy (pressure) into heat. As the coolant flows through a channel it experiences a pressure drop due to friction. This pressure drop is converted to thermal energy that results in a temperature rise as

∆𝑇𝑣𝑖𝑠𝑐 = ∆𝑃𝜌𝑓𝑐𝑝𝑓 , (MC-5)

where cpf is the specific heat at constant pressure of the coolant/fluid while other parameters are as defined above.



Temperature Sensor

Heater

Hoya substrate

Si Interposer

SOA

(Bottom)(Top)

Temperature control concept on a chip



Temperature control on a silicon chip



Characteristics of a temperature controller on a chip

Resistance vs. Temperature(Heating of d16ae06)

y = 4.1542x + 1523.7

R2 = 0.9999

1600

1650

1700

1750

1800

1850

0 10 20 30 40 50 60 70 80

TEMPERATURE, °C

RE

SIS

TA

NC

E, O

hm



Thermosyphon

liquid

Liquid condensate

Relies on gravitational force

Heat addition

Evaporator

Heat removal Condenser

Vapor



Heat pipeBasic heat pipe configuration

1. Heat addition in the evaporator causes vapor release

2. Vapor travels to the condenser

3. Heat removal in the condenser causes condensation of vapor

4. Return of condensed liquid through the wick by capillarity action



A heat pipe systems for electronic applications

Heat-pipes to move heat from electronic

components to a cooling area where fins

are used to increase the cooling rate

Fins

Heat-pipes



Heat pipe performance wrt Cu rod

0 10 20 30 40 50 60 700

5

10

15

20

25

3030

0

Cu x( )

HP x( )

700 xPower, W

End to end T, C

0.95 cm diameter solid Cu rod0.95 cm diameter heat pipe

Both configurations of the same dimensions



Heat pipeOperating characteristics



Thermal management



The heat pipe: thermal managementLoop of thermosyphons connecting enclosure to HVAC duct



Thermal management of PCs



Heat pipe based HEX for PCs



The heat pipe: thermal managementModern PC (Dell OptiPlex GX270) using tubular heat pipes and a conventional air-cooled heat sink



Fuel cells for every day use



Futuristic power source:small, unattended, multi-year operation



Nanotechnology:Quantum-dot-based power cell



Future-power will come in smallyet very capable packages



Effective study andoptimization

Experimental

Computational and Analytical

AdvantageStudy of actualconfigurations

Disadvantage Impractical to performparametric investigations

Advantage Parametric investigations

DisadvantageAssumed mechanicalcharacteristics and

boundary conditions

Hybridization

Hybridization of a solution



ACES methodology

Solution methodology exact, closed form

approximate, FEM, BEM, FDM

SOTA fiber laser based OE

A

C

E

S

Analytical Computational Experimental



Summary

• Types of Heat Exchangers

• The Overall Heat Transfer Coefficient Fouling factor

• Analysis of Heat Exchangers

• The Log Mean Temperature Difference Method Counter-Flow Heat Exchangers

Multipass and Cross-Flow Heat Exchangers: Use of a Correction Factor

• The Effectiveness–NTU Method

• Introduced SOTA microchannel HEXs



Example: H23 Problem 22-112/970In a chemical plant, a certain chemical is heated by

hot water supplied by a natural gas furnace. The hot water (cp = 4180 J/kg.K) is then discharged at a

rate of 8 kg/min. The plant operates 8 h a day, 5 days per week, 52 weeks a year. The furnace has

an efficiency of 78 percent, and the cost of the natural gas is $1.00 per therm (1 therm = 105,500

kJ). The average temperature of the cold water entering the furnace throughout the year is 14°C. In order to save energy, it is proposed to install a

water-to-water heat exchanger to preheat the incoming cold water by the drained hot water, Fig.

P22-112. Assuming that the heat exchanger will recover 72 percent of the available heat in the hot

water, determine the heat transfer rating of the heat exchanger that needs to be purchased and suggest

a suitable type. Also, determine the amount of money this heat axchanger will save the company

per year from natural gas savings.

Fig. P22-112.



1–6. PROBLEM-SOLVING TECHNIQUE

• Step 1: Problem Statement

• Step 2: Schematic

• Step 3: Assumptions and Approximations

• Step 4: Physical Laws

• Step 5: Properties

• Step 6: Calculations, SIGNIFICANT DIGITS …

• Step 7: Reasoning, Verification, and DISCUSSION

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