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6* Heat Transfer Enhancement

6* Heat Transfer Enhancement

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eliminate any increase in the heat transfer coefficient achieved by enhancement of a

clean surface. Nevertheless, in the present-day concerns of sustainable energy utilization and the need for conservation, the benefits of using enhancement techniques in

most heat exchange systems cannot be overstated.



8.6.1 Applications

There is a very large, rapidly growing body of literature on the subject of heat transfer enhancement. Manglik and Bergles [23] have documented the latest cataloging

of technical papers and reports on the subject and have discussed the status of recent

advancements as well as the prospects of future developments in enhanced heat

transfer technology. The taxonomy that has been developed [21–22] for the classification of the various enhancement techniques and their applications essentially considers the fluid flow condition (single-phase natural convection, single-phase forced

convection, pool boiling, flow boiling, condensation, etc.) and the type of enhancement technique (rough surface, extended surface, displaced enhancement devices,

swirl flow, fluid additives, vibration, etc.).

Table 8.3 shows how each enhancement technique applies to the different

types of flow according to Bergles et al. [24]. Extended surfaces or fins are probably the most common heat transfer enhancement technique, and examples of different types of fins are shown in Fig. 8.24. The fin was discussed in Chapter 2 as an

extended surface with primary application in gas-side heat transfer. The effectiveness of the fin in this application is based on the poor thermal conductivity of the

gas relative to that of the fin material. Thus, while the temperature drop along the

fin reduces its effectiveness somewhat, overall an increase in surface area and thus

in heat transfer performance is realized. Several manufacturers have recently made

available tubing with integral internal fins, and the prediction of the associated convective heat transfer coefficient has been highlighted in Chapter 6. Extended surfaces may also take the form of interrupted fins where the objective is to force the

redevelopment of boundary layers. As discussed in Section 8.2, compact heat

exchangers [10, 12] use extended surfaces to give a required heat transfer surface

area in as small a volume as possible, and representative examples of such fins are

shown in Fig. 8.24. This type of heat exchanger is important in applications such as



TABLE 8.3



Application of enhancement techniques to different types of flowsa



Extended surfaces

Rough surfaces

Displaced enhancement devices

Swirl flow devices

Treated surfaces



Single-Phase

Natural

Convection



Single-Phase

Forced

Convection



Pool

Boiling



Flow

Boiling



Condensation



c

o

n

n

n



c

c

o

c

c



c

o

n

n

c



o

c

o

c

o



c

c

n

o

c



c ϭ commonly practiced, o ϭ occasionally practiced, n ϭ not practiced.



a



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Chapter 8 Heat Exchangers



FIGURE 8.24 Examples of different types of finned tubes and plate fins used in

tubular and compact tube-fin and plate-fin heat exchangers.

Source: Courtesy of Dr. Ralph Webb.



automobile radiators and gas turbine regenerators, where the overall size of the heat

exchanger is of major concern.

Rough surfaces refer to small roughness elements approximately the height of

the boundary layer thickness. In recent years, a variety of structured roughness elements of different geometries and surface distributions have been considered in the

literature [21–22]. These roughness elements do not provide any significant

increase in surface area; if there is an increase in area, then such surface modifications are classified as extended surfaces. Their effectiveness is based on promoting

early transition to turbulent flow or promoting mixing between the bulk flow and

the viscous sublayer in fully developed turbulent flow. The roughness elements

may be randomly shaped, such as on a sand-grained surface, or regular, such as

machined grooves or pyramids. Rough surfaces are primarily used to promote heat

transfer in single-phase forced convection.

Displaced enhancement devices are inserted into the flow channel to improve

mixing between the bulk flow and the heat transfer surface. A common example

is the static mixer that is in the form of a series of corrugated sheets meant to promote bulk flow mixing. These devices are used most often in single-phase forced

convection particularly in thermal processing of viscous media in the chemical

industry so as to promote both fluid mixing and enhanced heat or mass transfer.

The most prominent and frequently used example of a swirl flow device is a

twisted-tape insert, and its typical usage inside tubes of a shell-and-tube heat

exchanger and the concomitant prediction of single-phase convective heat transfer

coefficients have been considered in Chapter 6. Another example is an oval tube that

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is helically twisted about its axis, as shown in Fig. 8.25. Enhancement primarily

arises due to secondary or helical swirl flows generated by the twisted flow geometry, and increased flow path length in the tube. Swirl flow devices are used for single-phase forced flow and in flow boiling [25].

Treated surfaces are used primarily in pool boiling and condensing applications. They consist of very small surface structures such as surface inclusions which

promote nucleate boiling by providing bubble nucleation sites. Condensation can

be enhanced by promoting the formation of droplets, rather than a film, on the condensing surface. This can be accomplished by coating the surface with a material

that leaves the surface nonwetting. Boiling and condensation will be discussed in

Chapter 10.

Figure 8.26 on the next page compares the performance of four enhancement

techniques for single-phase forced convection in a tube with that for a smooth tube

[26]. The basis of comparison is the heat transfer (Nusselt number) and pressure

drop (friction factor) plotted as a function of the Reynolds number. One can see that

at a given Reynolds number, all four enhancement techniques provide an increased

Nusselt number relative to the smooth tube but at the expense of an even greater

increase in the friction factor.



8.6.2 Analysis of Enhancement Techniques

We have previously noted the need for a comprehensive analysis of any candidate

enhancement technique to determine its potential benefits. Since heat transfer

enhancement can be used to accomplish several goals, no general procedure that

would allow one to compare different enhancement techniques exists. A comparison

such as that given in Fig. 8.26, which is limited to the thermal and hydraulic performance of the heat exchange surface, is often a useful starting point. Other factors

that must be included in the analysis are the hydraulic diameter, the length of the



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Chapter 8 Heat Exchangers

1. Wall protuberances

2. Axially supported discs

3. Twisted tape with axial core

4. Twisted tape

1,000



1.0

1



Smooth tube 3

4

2

10

1

1

102



Nu = 0.023 Re0.8

Pr0.4



103



104



105



3



2



0.1



2LG2



ΔPDρ



100



f=



Nu/ Pr0.4



520



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0.01



f=



0.001

102



Re

(a)



16

4

Re

Smooth tube

0.046

f = 0.2

Re

103



104



105



Re

(b)



FIGURE 8.26 Typical data for turbulence promoters inserted inside

tubes. (a) Heat transfer data, (b) friction data [26].

flow passages, and the flow arrangement (cross-flow, counterflow, etc.). In addition

to these geometric variables, the flow rate per passage or Reynolds number and the

LMTD can be varied or can be constrained for a given application. The factors that

can be varied must be adjusted in the analysis to produce the desired goal, e.g.,

increased heat duty, minimum surface area, or reduced pressure drop. Table 8.4 lists

the variables that should be considered in a complete analysis.



TABLE 8.4

Symbol

1. —

2. Nu(ReDH)

3. f(ReDH)

4. ReDH

5. DH



Variables in the analysis of heat transfer enhancement

Description

Type of enhancement technique

Thermal performance of the

enhancement technique

Hydraulic performance of the

enhancement technique

Flow Reynolds number



6. L



Flow passage hydraulic

diameter

Flow passage length



7. —



Flow arrangement



8. LMTD



Terminal flow temperatures



9. Q

10. As

11. ⌬p



Heat duty

Heat transfer surface area

Pressure drop



Comments

Determined by choice of

technique

Determined by choice of

technique

Probably an independent

variable

May be determined by choice

of technique

Generally an independent

variable with limits

May be determined by choice

of technique

May be determined by the

application

Probably a dependent variable

Probably a dependent variable

Probably a dependent variable



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Fortunately, many applications constrain one or more of these variables,

thereby simplifying the analysis. As an example, consider an existing shell-andtube heat exchanger being used to condense a hydrocarbon vapor on the shell side

with chilled water pumped through the tube side. It may be possible to increase the

flow of vapor by increasing the water-side heat transfer since the vapor-side

thermal resistance is probably negligible. Suppose the pressure drop on the water

side is fixed due to pump constraints, and assume that it is necessary to keep the

heat exchanger size and configuration the same to simplify installation costs. The

water-side heat transfer could be increased by placing any of several devices such

as swirl tapes or twisted-tape inserts inside the tubes, or wire-coil inserts to create

structured [21–22] roughness on the tube inner surface. Assuming that thermal and

hydraulic performance data are available for each enhancement technique to be

considered, then items 1, 2, and 3 in Table 8.4, as well as 5, 6, 7, and 10, are known.

We will adjust ReDH, which will affect the water outlet temperature or LMTD, Q,

and ¢p. Since the LMTD is not important (within reason), we can determine which

surface provides the largest Q (and hence vapor flow) at a fixed ⌬p.

Several performance evaluation methods have been proposed in the literature

[21–22], which are based on a variety of figures of merit that are applicable to different heat exchanger applications. Among these, Soland et al. [27] have outlined a

useful performance ranking methodology that incorporates the thermal/hydraulic

behavior of the heat transfer surface with the flow parameters and the geometric

parameters for the heat exchanger. For each heat exchanger surface the method plots

the fluid pumping power per unit volume of heat exchanger versus heat exchanger

NTU per unit volume. These parameters are:

f Re3DH

pumping power

r

=

V

volume

D4H

j ReDH

NTU

NTU

r

=

V

volume

D2H



Pp



(8.30)

(8.31)



Given the friction factor f(Re), the heat transfer performance Nu(Re) or j(Re) for the

heat exchanger surface, and the flow passage hydraulic diameter DH, one can easily

construct a plot of the two parameters P/V and NTU/V.

In Eqs. (8.30) and (8.31) the Reynolds number is based on the flow area Af,

which ignores any enhancement:

GDH

m

#

m

G =

Af



ReDH =



(8.32)



#

where m is the mass flow rate in the flow passage of area Af.

The friction factor is

¢p

f =



4(L/DH)(G2/2rgc)



where ⌬p is the frictional pressure drop in the core.

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(8.33)



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Chapter 8 Heat Exchangers

The j or Colburn factor is defined as

j =



qhc

Pr2/3

Gcp



(8.34)



where hqc is the heat transfer coefficient based on the bare (without enhancement)

surface area Ab. The hydraulic diameter is defined as in Chapter 6 but can be written more conveniently in the form

DH =



4V

Ab



(8.35)



Using these definitions, a smooth tube of inside diameter D and a tube of inside

diameter D with a twisted tape insert and with the same mass flow rate would

have the same G, ReD, Ab, and D but we would expect f and j to be larger for the

latter tube.

Such a plot is useful for comparing two heat exchange surfaces because it

allows a convenient comparison based on any of the following constraints:

1. Fixed heat exchanger volume and pumping power

2. Fixed pumping power and heat duty

3. Fixed volume and heat duty



These constraints can be visualized in Fig. 8.27, in which the f Re3D> D4 and j ReD> D2

data are plotted for the two surfaces to be compared. From the baseline point labeled

“o” in Fig. 8.27, comparisons based on the three constraints are labeled.



Text not available due to copyright restrictions



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A comparison based on constraint (1) can be made by constructing a vertical line

through the baseline point. Comparing the two ordinate values where the vertical line

intersects the curves allows one to compare the heat duty for each surface. The surface with the highest curve will transfer more heat. Constraint (2) can be visualized

by constructing a line with slope ϩ1. Comparing either the abscissa or ordinate where

the line of slope ϩ1 intersects the curves allows one to compare the heat exchanger

volume required for each surface. The surface with the highest curve will require the

least volume. Constraint (3) can be visualized by constructing a horizontal line.

Comparing the abscissa where the line intersects the curves allows one to compare

the pumping power for each surface. The surface with the highest curve will require

the least pumping power.



EXAMPLE 8.5



Given the data in Fig. 8.26, compare the performance of wall protuberances and a

twisted tape [surfaces (1) and (4) in Fig. 8.26] for a flow of air on the basis of fixed

heat exchanger volume and pumping power. Assume that both surfaces are applied

to the inside of a 1-cm-ID tube of circular cross section.



SOLUTION



We must first construct the f (Re) and j (Re) curves for the two surfaces.

Curves (1) and (4) in Fig. 8.26(a) and (b) can be represented by straight lines

with good accuracy. From the data in Fig. 8.26(a) and (b), these straight lines for the

Nusselt numbers are

Nu1/Pr0.4 = 0.054 Re0.805

D

Nu4/Pr0.4 = 0.057 Re0.772

D

where the subscripts 1 and 4 denote surfaces 1 and 4.

-1 -1/3

Since j = St Pr2/3 = NuReD

Pr

we have

-0.195 1/15

j1 = 0.054 ReD

Pr



and

-0.228 1/15

j4 = 0.057 ReD

Pr



For the friction coefficient data we find

f1 = 0.075 Re0.017

D

-0.238

f4 = 0.222 ReD

In comparing the two surfaces we should restrict ourselves to the range

104 Ͻ ReD Ͻ 105

where the data for both surfaces are valid.

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Chapter 8 Heat Exchangers

107

4



106



D2



jReD



(m– 2)



1



105

1019



1020



1021

f



ReD3

D4



1022



(m– 4)



FIGURE 8.28 Comparison of wall protuberances and

twisted tapes based on the method of Soland et al. [27].

Constructing the two comparison parameters, we have

f1 Re3D

D41

f4 Re3D

D44

j1 ReD

D21

j4 ReD

D24



=



0.075 Re3.017

D



=



0.222 Re2.76

D



(0.01)4

(0.01)4



= 7.5 * 106 Re3.017

m-4

D

= 2.22 * 107 Re2.76

m-4

D



=



0.054 Re0.805

Pr1/15

D



=



0.057 Re0.772

Pr1/15

D



(0.01)2

(0.01)2



= 527.8 Re0.805

m-2

D

= 557.1 Re0.772

m-2

D



These parameters are plotted in Fig. 8.28 for the Reynolds number range of interest. According to the specified constraint, a vertical line connecting the curves

labeled (1) and (4) in Fig. 8.26 clearly demonstrates that surface 4, the twisted tape,

is the better of the two surfaces. That is, for a fixed heat exchanger volume and at

constant pumping power, the twisted tape enhancement will transfer more heat.



8.7*



Microscale Heat Exchangers

With advancements in microelectronics and other high heat-flux dissipating devices,

a variety of novel microscale heat exchangers have been developed to meet their

cooling needs. Their structure usually incorporates microscale channels, which essentially exploit the benefits of high convection heat transfer coefficients in flows



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through very small hydraulic-diameter ducts [28]. Applications of such heat exchangers include microchannel heat sinks, micro heat exchangers, and micro heat pipes,

used in microelectronics, avionics, medical devices, space probes, and satellites,

among others [28–30], and a few illustrative examples are depicted in Fig. 8.29.

To understand the implication of microchannels on convection heat transfer,

consider laminar single-phase flows. Because of a very small hydraulic diameter Dh,

which can range from a millimeter to a few microns in size, the flow tends to be fully

developed and hence characterized by a constant Nusselt number. As a result, the

heat transfer coefficient given by

h ϭ Nu a



k

b

Dh



would increase substantially with decreasing hydraulic diameter. This was first

explored by Tuckerman and Pease [30] for microelectronic cooling, and the

exploitation of microchannels with both single- and two-phase flows continues to

attract considerable research attention [28].



8.8



Closing Remarks

In this chapter we have studied the thermal design of heat exchangers in which two

fluids at different temperatures flow in spaces separated by a wall and exchange

heat by convection to and from and conduction through the wall. Such heat

exchangers, sometimes called recuperators, are by far the most common and industrially important heat transfer devices. The most common configuration is the shelland-tube heat exchanger, for which two methods of thermal analysis have been

presented: the LMTD (log mean temperature difference) and the NTU or effectiveness method. The former is most convenient when all the terminal temperatures are



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