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Heat Exchangers and Heat Pipes

Greg F. NatererUniversity of Ontario Institute of Technology, Oshawa, Ontario, Canada

Abstract

This entry provides an overview of the design and opertion of heat exchangers and heat pipes. Different

types of heat exchangers are discussed, including concentric-tube, cross-flow, and shell-and-tube heat

exchangers. Methods of analysis are briefly discussed, with correction and geometrical factors for complex

configurations. Condensers and evaporators are described in more detail. Heat pipes are additional types of

heat exchange devices that use a porous wick material in a tube structure. The performance and operation of

heat pipes are discussed. Limitations of wicking, entrainment, sonic, and boiling conditions are outlined,

with respect to their effects on heat pipe performance.

INTRODUCTION

Heat exchangers are devices allowing energy exchange

between fluid streams at different temperatures. They are

commonly used in many applications, including power

generation, energy storage, air conditioning systems,

materials processing, and various others. Some common

configurations include concentric-tube, cross-flow, and

shell-and-tube heat exchangers (see Figs. 1 and 2).

Another widely used device for heat exchange is a heat

pipe, for applications such as spacecraft thermal control

and thermal energy management in microelectronic

assemblies. This entry explains the fundamental operating

principles of heat exchangers and heat pipes.In a concentric-tube heat exchanger, an internal fluid

flows through the inner tube, and an external flow passes

through the annular region between the inner and outer

tubes. In a parallel-flow configuration, the outer fluid flows

in the same direction as the inner flow. Otherwise, if the

outer fluid flows in a direction opposite to the inner flow,

then it is called a counter-flow heat exchanger. Analysis of

heat exchangers usually requires empirical or advanced

computer simulation techniques.

A cross-flow heat exchanger consists of an outer flow

passing across tubes carrying fluid that flows in a direction

perpendicular to the cross-flow. An example of this type of

heat exchanger is found in a car radiator, where the outer

and inner flows consist of air and water, respectively. The

tubes are often covered with fins or other annular

attachments to enhance the rate of heat transfer between

the different fluid streams. For systems having fluid

streams separated from one another by fins or baffles, the

configuration is called unmixed, whereas a mixed

configuration permits complete mixing of the fluid streams

in the external cross-flow.Another common type of heat exchanger is a shell-and-

tube heat exchanger. In this case, the configuration

consists of an outer shell pipe where fluid enters through

one end, passes across internal tubes carrying a fluid at a

different temperature, and exits through the other end.

Baffles are often placed perpendicular to the inner tubes to

enhance mixing and turbulence of the outer fluid stream.

Baffles refer to perforated plates that obstruct some region

of the outer flow while directing the flow around the

remaining uncovered sections. Condensers in power plants

are common examples of shell-and-tube heat exchangers.

In these condensers, the outer flow is steam that condensesand leaves as water following heat exchange with the inner

tubes carrying cold water.

Heat transfer occurs between fluids at different

temperatures or phases. In the case of heat exchange

between fluids of the same phase, but at different

temperatures, the heat gained by the colder fluid stream

balances heat lost by the hotter fluid stream, minus any

external heat losses to the surroundings (often assumed

negligible). Spacing and packing of tubes within heat

exchangers varies with different applications. The surface

area density of surfaces characterizes this packing, based

on the number and diameter of tubes within the heatexchanger. The packing is often expressed in terms of a

hydraulic diameter of tubes, Dh. A typical range is

0.8 cm!Dh!5 cm for shell-and-tube heat exchangers,

while 0.2 cm!Dh!0.5 cm for automobile radiators and

0.05 cm!Dh!0.1 cm for gas turbine regenerators. For

heat exchange in biological systems (such as human

lungs), the range is typically 0.01 cm!Dh!0.02 cm.

HEAT EXCHANGER ANALYSIS

Heat exchange between two fluid streams in a concentric-

tube heat exchanger depends on the overall heat transfer

801

Keywords: Tubular heat exchanger; Cross-flow heat exchanger; Shell-

and-tube heat exchanger; Condensers and evaporators; Heat pipe;

Wicking limit; Entrainment limit; Sonic limit.

Heat

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coefficient between both streams, including thermal

resistances due to convection, fouling (due to fluid

impurities such as rust formation), and conduction through

the pipe wall. Frequent cleaning of the heat exchanger

surfaces is needed to reduce and minimize the adverse

effects of fouling, such as an increased pressure drop and

reduced heat transfer effectiveness. Finned surfaces

produce additional thermal resistances in a heat exchanger.

These effects are often modeled based on the surface

efficiency of a finned surface, which includes the

efficiency for heat exchange through the fin, as well as

heat transfer through the base surface (between the fins).

Using analytical methods for basic parallel-flow

configurations of heat exchangers, the total heat transfer

from a hot fluid stream to a cold stream between an inlet

(1) and outlet (2) can be readily determined based on given

(or measured) temperature differences, DT1 and DT2. A

similar analysis can be derived for both parallel and

counter-flow heat exchangers. In a parallel-flow heat

exchanger, the highest temperature difference is encoun-

tered between the two incoming fluid streams. In the

streamwise direction, heat transfer from the hot stream to

the cold stream reduces the temperature difference

between the fluids. But in a counter-flow heat exchanger,

the temperature difference increases in the flow direction,

since the temperature of the incoming cold fluid stream

increases due to heat transfer from the hot stream flowing

in the opposite direction. A counter-flow heat exchanger is

generally considered to be more effective, since a smaller

surface area is required to achieve the same heat transfer

rate (assuming equivalent heat transfer coefficients

between the fluid streams).

Predicted results for parallel-flow and counter-flow

heat exchangers can be extended to more complicated

geometrical configurations, such as cross-flow and shell-

and-tube heat exchangers, after multiplying the heat

transfer rate by a correction factor, F, which is usually

based on experimental data to account for baffles and

other geometrical parameters. The value of F depends on

the type of heat exchanger. For example, FZ1 for a one-

shell-pass, one-tube-pass heat exchanger. For more

complex arrangements, values of F are usually tabulated

Fig. 1 Types of heat exchangers.

Fig. 2 Shell-and-tube heat exchanger.

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and graphically depicted. For example, results of

correction factors for a variety of heat exchanger

configurations have been presented and graphically

illustrated by Bowman et al.[1] Incropera and Dewitt,[5]

and others. The Standards of the Tubular Exchange

Manufacturers Association (6th edition, New York, 1978)

provides additional results in terms of algebraic

expressions or graphical representations.

The competing influences of pressure drop and heat

exchange are important considerations in heat exchanger

design. Larger rates of heat transfer can usually be

achieved by increasing the packing of tubes within the

heat exchanger or using baffles or other heat enhancement

devices. But this comes at the expense of an increased

pressure drop, which is disadvantageous due to additional

pumping power required to move the fluid through the

system at a specified mass flow rate. On the other hand,

fewer heat exchange tubes can lead to a smaller pressure

drop, but often at the expense of lower heat transfer, in

comparison to a design with a high surface area density.

Thus, optimization serves to provide an effective balance

between the heat exchange and pressure losses. Empirical

correlations are often used to predict the pressure drop in

heat exchangers, in terms of additional parameters such as

fluid velocity, the ratio of the free-flow area of the finned

passages to the frontal area of the heat exchanger, friction

factor, flow length, and flow passage hydraulic radius

(total heat exchanger volume divided by the total heat

transfer surface area). Values of friction factors have been

documented extensively by Kays and London[6] for a

variety of heat exchangers, including finned and various

tubular configurations.

Plate-to-fin heat exchangers are commonly used in

applications involving heat exchange between gas-to-gas

streams. For example, air-to-air heat exchangers are

typically based on plate-to-fin arrangements. These fins

are classified into various types, such as plain fins, strip

fins, pin fins, perforated fins, and others. Detailed design

data involving these types of heat exchangers are outlined

in Kays and London.[6]

CONDENSERS AND EVAPORATORS

Other common types of heat exchangers are condensers

and evaporators, which are two-phase heat exchangers

used in various engineering systems, such as power-

generation and refrigeration systems. When a fluid stream

evaporates or condenses within a heat exchanger and

experiences a change of phase, then it is usually more

useful to evaluate enthalpy (rather than temperature) in

energy balances for heat exchanger analysis. The fluid

temperature can remain nearly constant during the phase

change, even though heat is transferred between the fluid

streams. When calculating an enthalpy difference, the heat

transfer analysis would include both the latent and sensible

heat portions of the energy transfer between different fluid

streams in the heat exchanger.

Unlike previously discussed heat exchangers involving

single phase flows, a main difficulty in the analysis of

condensers and evaporators is the range of phase-change

regimes experienced by the fluid stream. The heat transfer

coefficient depends on the local phase fraction, which

varies throughout the flow path, so the heat transfer

coefficient becomes position dependent. Unfortunately,

the phase distribution is generally unknown until the flow

field solution is obtained. Thus, a systematic procedure is

needed to analyze heat transfer processes in condensers

and evaporators.

The energy balances involve enthalpy to accommodate

the latent heat of phase change, as well as sensible heat

portions of the heat exchange. The fluid possibly under-

goes various phase-change regimes, so the tube length is

usually subdivided into discrete elements, and energy

balances are applied individually over each element. After

the enthalpy in a particular element is computed, its value

may exceed the saturated vapor value of enthalpy at the

flow pressure. In this case, the fluid enthalpy can be used to

calculate the temperature of the superheated vapor based

on thermodynamic property tables or computer-generated

tabulation of the superheated property values. Alterna-

tively, the specific heat of the fluid can be used to predict

the temperature change corresponding to the enthalpy

difference. This approach assumes a locally constant value

of the specific heat, which requires a sufficiently small

temperature change between elements. This method can be

used when the fluid exists entirely as a superheated vapor,

as the vapor specific heat at the mean temperature can be

used.

However, if the enthalpy is computed to be less than the

saturated vapor enthalpy, then the quality (mass fraction of

vapor in the element) is needed. An updated estimate of

the convection coefficient can be calculated based on the

phase fraction and corresponding flow regime. Additional

empirical factors (such as a transition factor) are often

used to identify the flow regime and appropriate

correlation for heat transfer. Then an updated overall

heat transfer coefficient can be determined from the phase

fraction and flow regimes.

A typical numerical procedure for analyzing two-phase

heat exchangers can be summarized as follows: a boundary

condition is first applied within the initial element of the

tube. Then, a suitable forced convection correlation is used

up to the element in which phase change is first realized. An

appropriate heat transfercorrelation can thenbe selectedfor

that phase change regime. Near the points of saturated

vapor or saturated liquid, a suitablesingle-phase correlation

can be used with property values along the saturated liquid

and vapor lines. Then, this procedure can be repeated for

each element in the domain. For either condensing or

boiling problems,a similar procedure can be adopted. In the

latter case (boiling), a two-phase flow map would typically

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be utilized to identify the flow regime based on the

computed phase fraction. This mapping would distinguish

between flow regimes, such as the wavy, annular, and slug

flow regimes.

Various design features and aspects of maintenance are

important in terms of the effective performance of

condensers and evaporators. Tubes should be readily

cleanable on a regular basis, either through removable

water heads or other means. Larger flow rates within the

heat exchanger can reduce fouling (buildup of scale and

dirt on the walls), reduce service, and extend the life of the

heat exchanger. Furthermore, higher operating efficiencies

can be achieved by placement of tubes in stacks with

metal-to-metal contact between fins to permit better

drainage of the condensate. Less thermal resistance occurs

when less liquid accumulates on the fins, thereby

improving the thermal efficiency of heat exchange. Also,

a light and compact design is beneficial, as it requires less

space and reduces difficulties in installation and moving,

while often reducing costs associated with maintenance.

Another important factor in proper operation of

condensers and evaporators is safety. For systems

operating at pressures different from the surrounding

ambient (atmospheric) pressure, leakage can occur. In

maintenance procedures, the specific points of leakage can

be detected and repaired by a basic method of soap or

detergent brushed onto the surfaces where leakage is

suspected, thereby generating bubbles to indicate leakage

points. Alternatively, pressurizing the system and record-

ing changes in pressure over time can indicate the

tightness of a system (but not necessarily the location of

leakage). Certain chemical leaks can be detected indivi-

dually. For instance, sulfur dioxide can be detected by the

white smoke forming when ammonia is brought into close

contact with the leakage point.

Operating materials must be properly selected in

conjunction with the working fluids. Most refrigerants

can be used well under normal conditions with most

metals (such as steel, aluminum, and iron), but some

materials and liquids should never be used together. An

example is methyl chloride fluid with aluminum shells and

tubes, which can produce flammable gas byproducts. Also,

the tensile strength, hardness, and other properties of

exposed materials must be fully considered under all

operating conditions. Effects of certain plastic materials on

refrigerant liquids can often be difficult to predict,

particularly due to the rapid rise in the number and types

of polymer materials. An effective overall design of

condensers and evaporators requires a thorough investi-

gation of both thermal and materials engineering aspects.

HEAT PIPES

A heat pipe is a closed device containing a liquid that

transfers heat under isothermal conditions. It operates

through vaporization of liquid in an evaporator, transport

and condensation of the vapor, and return flow of liquid by

capillary action through a wick structure back to an

evaporator. Due to geometrical requirements, the adiabatic

section is designed to fit within spacing limitations of the

heat pipe. Adiabatic implies zero heat transfer, as in a

well-insulated section. Thermal energy from the external

source is transferred to the working fluid in the heat pipe at

the evaporator section. At the end of the heat pipe, a buffer

volume may be constructed to enclose a non-condensable

gas (such as helium or argon) for controlling the operating

temperature, based on control of pressure within the inert

gas. Flow of vapor occurs through the core interior region

of the heat pipe at high velocities to the condensing section

(up to 500 MPH in some cases).

Along the inner wall of the container of the heat pipe, a

porous wick material with small, random interconnected

channels is constructed for capillary pumping. The pores

in the wick act as a capillary pump, which acts

analogously to regular pumping action on fluids in pipes

by pumps. The wick provides an effective means of

transporting liquid back to the evaporator through surface

tension forces acting within the wick. Also, it serves as an

effective separator between vapor and liquid phases,

thereby allowing more heat to be carried over greater

distances than other pipe arrangements (Fig. 3).

Various applications utilize heat pipes, including

heating, ventilating, and air conditioning (HVAC) heat

recovery systems; microelectronics cooling; and space-

craft thermal control. Heat pipes in air-to-air HVAC heat

recovery systems allow effective storage of thermal energy

contained in exiting combustion gases. Heat pipes offer

key advantages over conventional techniques, including

low maintenance (no moving parts), long life, and cost

savings. Another example involves microelectronics cool-

ing. Heat pipes can be up to 1000 times more conductive

than copper (at the same weight). Examples include laptop

computers, as well as telecommunications equipment,

which have adopted heat pipes with success in their

thermal designs. Also, heat pipes appear in several

spacecraft thermal control applications. Heat pipes have

been used in satellites to transfer heat generated by

electronic equipment to radiation panels that dissipate heat

into space. Another application is tubing in satellites,

which provides effective control of temperatures required

for reliable performance of electrical components on the

satellite.

In the evaporator section of a heat pipe, heat is

transferred by conduction from the energy source through

the container wall and wick-to-liquid matrix to the vapor-

to-liquid interface. Then, liquid is evaporated at the vapor-

to-liquid interface, and heat transfer occurs by convection

of vapor (laminar or turbulent) from the evaporator to the

condenser. The temperature of the vapor is approximately

the average between the source and sink temperatures at

the ends of the heat pipe. Following condensation of vapor



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on the liquid return flow from the condenser to the

evaporator. It is possible that waves can be generated on

the liquid surface and droplets may be entrained by the

vapor flow, since there would be inadequate restraining

forces of liquid surface tension in the wick.

Another factor is the sonic limitation. During conditions

of startup from near-ambient conditions, a low vapor

pressure within the heat pipe can lead to a high resulting

vapor velocity. If the vapor velocity approaches sonic

speed, a choked condition within the pipe limits the axial

heat flux. This sonic limit and other previous depend on the

fluid operating temperature. Heat flux limits generally

increase with evaporator exit temperature due to the effect

of temperature on the speed of sound in the vapor. For

example, the heat flux limit for sodium increases from

0.6 kW/cm2 at 5008C to 94.2 kW/cm2 at 9008C. For liquid

potassium, the heat flux limit is 0.5 kW/cm2 at 4008C

(evaporator exit temperature), and the limit increases to

36.6 kW/cm2 at 7008C. In high-temperature applications,

lithium can be used. Its heat flux limit ranges between

1.0 kW/cm2 at 8008C and 143.8 kW/cm2 at 13008C.

In contrast to the limitations on the axial heat flux, the

boiling limitation involves the radial heat flux through

the container wall and wick. The onset of boiling within

the wick interferes with and obstructs the liquid return flow

from the condenser. Boiling within the wick may cause a

burnout condition by drying out the evaporator contain-

ment. Recent advances in heat pipe technology are

developing innovative techniques for dealing with this

thermal limitation and enhancing the overall capabilities

of heat pipes. Additional references in the topic of heat

pipe analysis are given by Kreith and Bohn,[7] Hewitt

et al.[4] Dunn and Reay,[3] and Chi.[2]

REFERENCES

1. Bowman, R.A.; Mueller, A.C.; Nagle, W.M. Mean tempera-

ture difference in design. Trans. ASME 1940, 62.

2. Chi, S.W. Heat Pipe Theory and Practice; Hemisphere:

Washington, DC, 1976.

3. Dunn, P.D.; Reay, D.A. Heat Pipes, 3rd Ed.; Pergamon: New

York, 1982.

4. Hewitt, G.F., Shires, G.L., Polezhaev, Y.V., Eds., Inter-

national Encyclopedia of Heat and Mass Transfer, CRCPress: Boca Raton, FL, 1997.

5. Incropera, F.P.; DeWitt, D.P. Fundamentals of Heat and Mass

Transfer, 3rd Ed.; Wiley: New York, 1990.

6. Kays, W.M.; London, A.L. Compact Heat Exchangers, 3rd

Ed.; McGraw-Hill: New York, 1984.

7. Kreith, F.; Bohn, M.S. Principles of Heat Transfer, 6th Ed.;

Brooks/Cole Thomson Learning: Pacific Grove, CA, 2001.


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