Heat Transfer Handbook part 86 pdf

a The plain fin is characterized by long uninterrupted flow passages and is designated by a numeral that indicates the number offins per inch.. b The louvered fin is characterized by fins tha

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[845],(49)

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Header Air fin

Air fin Tube

Tube

Tube plates ( ) Round tube and fina

( ) Bar and plated

( ) Formed plate fing

( ) Flat tube and finb

( ) Bar and platee

( ) Formed plate finh ( ) Dimpled strut tubei

( ) Tube and centerc

( ) Bar and platef

Tube

Tube plates

Spacer bar

Heating fins

Louvered air fins Header

Header

Side bar

Sidebar Header bar

Louvered air fins

Turbulator strip

Turbulator dimples

Turbulator strip Reinforcement rod

Header bar

Corrugated air fins

Side bar

Figure 11.16 Some compact heat exchanger elements (Courtesy ofHarrison Radiator Division.)

3 Surfaces with ﬂow normal to banks of smooth tubes Unlike the radial low ﬁn

tubes, smooth round tubes are expanded into ﬁns that can accept a number oftube

rows, as shown in Fig 11.16a Holes may be stamped in the ﬁn with a drawn hub or

foot to improve contact resistance or as a spacer between successive fins, as shown, or brazed directly to the fin with or without a hub Other types reduce the flow resistance

outside the tubes by using ﬂattened tubes and brazing, as indicated in Fig 11.16b and c Flat tubing is made from strips similar to the manufacture of welded circular

tubing but is much thinner and is joined by soldering or brazing rather than welding

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[846], (50)

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The designation considers staggered (S) and in-line (I) arrangements oftubes and identiﬁes transverse and longitudinal pitch ratios The sufﬁx (s) indicates data correla-tion from steady-state tests All other data were correlated from a transient technique

Examples include the surface S1.50-1.25(s), which is a staggered arrangement with data obtained via steady-state tests with transverse pitch-to-diameter ratio of1.50 and longitudinal pitch-to-diameter ratio of1.25 The surface I1.25-1.25 has an in-line arrangement with data obtained from transient tests with both transverse and longitudinal pitch-to-diameter ratios of1.25

4 Plate ﬁn surfaces These are shown in Figs 11.16d through i.

(a) The plain ﬁn is characterized by long uninterrupted ﬂow passages and is

designated by a numeral that indicates the number ofﬁns per inch The sufﬁx

T is appended when the passages are ofdeﬁnite triangular shape Examples are the surfaces 19.86, 15.08, and 46.45T

(b) The louvered fin is characterized by fins that are cut and bent into the flow

stream at frequent intervals and is designated by a fraction which indicates the length ofthe fin in the flow direction (inches) followed by a numeral that indicates the number offins per inch For example, the designation

1

2− 6.06

indicates 6.06 1

2-in.-long ﬁns per inch

(c) The strip fin is designated in the same manner as the louvered fin The suffixes

(D) and (T) indicate double and triple stacks The strip ﬁns are frequently

referred to as offset ﬁns because they are offset at frequent intervals and the

exchanger is essentially a series ofplate ﬁns with alternate lengths offset

(d) The wavy ﬁn is characterized by a continuous curvature The change in ﬂow

direction introduced by the waves in the surface tends to interrupt the boundary layer, as in the case oflouvered and strip ﬁns Wavy ﬁn designations are always followed by the letter W For example, the

11.44 −3

8W

is a wavy ﬁn with 11.44 ﬁns per inch and a 38-in wave

(e) The pin ﬁn surface is constructed from small-diameter wires This surface

yields very high heat transfer coefﬁcients because the effective ﬂow length

is very small The designation ofthe pin ﬁn surfaces is nondescriptive

(f) The perforated ﬁn surface has holes cut in the ﬁns to provide boundary layer

interruption These ﬁns are designated by the number ofﬁns per inch followed

by the letter P

5 Finned-tube surfaces Circular tubes with spiral radial ﬁns are designated by

the letters CF followed by one or two numerals The first numeral designates the number offins per inch, and the second (ifone is used) refers to the nominal tube size With circular tubes with continuous fins, no letter prefix is employed and the

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[847],(51)

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two numerals have the same meaning as those used for circular tubes with spiral radial fins For finned flat tubes, no letter prefix is used; the first numeral indicates the fins per inch and the second numeral indicates the largest tube dimension When

CF does not appear in the designation ofthe circular tube with spiral radial ﬁns, the surface may be presumed to have continuous ﬁns

6 Matrix surfaces These are surfaces that are used in rotating, regenerative

equip-ment such as combustion flue gas–air preheaters for conventional fossil furnaces In this application, metal is deployed for its ability to absorb heat with minimal fluid friction while exposed to hot flue gas and to give up this heat to incoming cold com-bustion air when it is rotated into the incoming cold airstream No designation is employed

11.5.3 Geometrical Factors and Physical Data

Compact heat exchanger surfaces are described in the literature by geometric factors that have been standardized largely through the extensive work ofKays and London (1984) These factors and the relationships between them are essential for application

of the basic heat transfer and ﬂow friction data to a particular design problem They are listed and deﬁned in Table 11.1 Physical data for a number of compact heat exchanger surfaces are given in Table 11.2 Relationships between the geometric factors in Table 11.1 will now be established

Consider an exchanger composed ofn1layers ofone type ofplate ﬁn surface and

n2 layers ofa second type, as shown in Fig 11.13 The separation plate thickness

is established by the pressure differential to which it is exposed or through designer discretion Retaining the subscripts 1 and 2 for the respective types of surface, the overall exchanger heightH is

whereb1 andb2 are separation distances between the plates for the two kinds of surface With the widthW and depth D selected, the overall volume V is

In Fig 11.15, the lengthL1is along the depth ofthe exchanger (L1 = D) and the

lengthL2is along the width (L2= W).

The frontal areas are also established Again referring to Fig 11.13, we have

If the entire exchanger consisted of a single exchanger surface, surface 1 or surface

2, the total surface area would be the product ofthe ratio oftotal surface to total

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TABLE 11.1 Compact Heat Exchanger Geometric Factors

Factor and

overall exchanger width and height or depth and height

at the designer’s discretion

Applies to plate ﬁn surfaces only

the ﬂow length ofa single side ofthe exchanger, although two sides may be

present, and that the ambiguity is avoided with the overall exchanger

dimensions, which are designated width, depth, and height It is therefore

reasonable to have the overall exchanger depth be the length on one side of the exchanger and the overall width the length on the other side

Applies to matrix surfaces only

appended to distinguish between hot- and cold-side surfaces

only

merely the product ofthe overall heat exchanger width, depth, and height

on both sides ofthe exchanger Applies to tubular, plate ﬁn surfaces, and

crossed-rod matrices only

dimensions Applies to plate ﬁn surfaces only

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[849],(53)

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[849],(53)

TABLE 11.2 Surface Geometry of Some Plate Fin Surfaces

volumeβ(m2/m3) and the total volume V However, where there are two surfaces, it

is necessary to employ the factorα, which is the ratio ofthe total surface on one side

to the total surface on both sides ofthe exchanger By taking simple proportions,

b1+ b2+ aβ1 (11.122a)

b1+ b2+ aβ2 (11.122b)

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[850], (54)

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and the total surfaces will be

The hydraulic radius is deﬁned as the ﬂow area divided by the wetted perimeter ofthe passage:

r h= A

AL

and the ratio ofthe ﬂow area to the frontal area is designated asσ:

σ =A A

For all but matrix surfaces, because eq (11.124) leads toA = Sr h /L,

σ = A Sr h

fr L =

Sr h

Thus, the ﬂow areas are given by

11.5.4 Heat Transfer and Flow Friction Data

Heat Transfer Data Heat transfer data for compact heat exchangers are correlated

on an individual surface basis using a Colburn type of representation This represen-tation plots the heat transfer factorj h:

j h= St · Pr2/3=Gc h

p

c pµ

k

2/3

(11.128)

as a function of the Reynolds number, which is obtained by employing the equivalent diameterd e = 4r h:

Re=4rµh G = d eµG (11.129) The Stanton number St is the ratio ofthe Nusselt number Nu to the product ofthe Reynolds and Prandtl numbers, with the speciﬁc heatc taken as the value for constant

pressure,

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[851],(55)

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Fin pitch = 46.45 per in.

Plate spacing, = 0.100 in.

Fin length flow direction = 2.63 in.

Flow passage hydraulic diameter, 4 = 0.002643 ft.

Fin metal thickness = 0.002 in., stainless steel Total heat transfer area/volume between plates,

= 1332.5 ft /ft Fin area/total area = 0.837

b

rh

Fin metal thickness = 0.006 in., aluminum Total heat transfer area/volume between plates,

= 414 ft /ft Fin area/total area = 0.870

b

rh

Fin metal thickness = 0.006 in., aluminum Total transfer area/volume between plate,

b

rh

b

rh

0.18⬙

L r/4 = 20.6h

L r/4 = 83.0h

L r/4 = 65h

L r/4 = 35.0h

0.25⬙

0.0431⬙

0.1326⬙

0.1006⬙

0.25⬙

0.418⬙

( )a

( )c

( )b

( )d

Re =d G e , dimensionless

␮ 0.001

0.01

0.1

hG c

c k

( )c ( ) d

( )b

( )a

46.45T 11.115.08

19.86 0100⬙

Figure 11.17 Heat transfer and ﬂow friction characteristics of some plain plate ﬁn compact heat exchanger surfaces (From Kays and London, 1984.)

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[852], (56)

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Louver spacing = 0.1875 in.

Fin gap = 0.035 in.

Louver gap = 0.055 in.

b

rh

Fin gap = 0.110 in.

Fin metal thickness = 0.006 in., aluminum Total transfer area/volume between plates,

b

rh

Fin gap = 0.05 in.

b

rh

Fin gap = 0.110 in.

b

rh

.25⬙

0.04⬙

0.75⬙

0.05⬙

.035⬙ .055⬙

.1875⬙

.50⬙

0.055⬙

0.25⬙

0.375⬙

3/8-6.06

( )a

( )c

( )b

( )d

␮ 0.001

0.01

0.1

( )c

( )d

( )b

( )a

3/16-11.1 3/4-11.13/8-6.06

1/2-6.06 25⬙

hG c

c k

Figure 11.18 Heat transfer and ﬂow friction characteristics of some louvered ﬁn compact heat exchanger surfaces (From Kays and London, 1984.)

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[853],(57)

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Splitter symmetrically located Fin length flow direction = 0.125 in.

Fin metal thickness = 0.004 in., aluminum Splitter metal thickness = 0.006 in.

Total heat transfer area/volume between plates,

= 698 ft /ft Fin area (including splitter)/total area = 0.843

b

r h

Fin metal thickness = 0.006 in., aluminum Splitter metal thickness = 0.006 in.

b

r h

Fin metal thickness = 0.004 in., nickel Splitter metal thickness = 0.006 in.

b

r h

Fin length = 0.125 in.

Flow passage hydraulic diameter, 4 = 0.00879 ft Fin metal thickness = 0.010 in., aluminum Total heat transfer area/volume between plates,

= 381 ft /ft Fin area/total area = 0.840 Note: The fin surface area on the leading and trailing edges of the fins have not been included

in area computations.

b

r h

.205⬙

.125⬙

.0505⬙

.201⬙

.125⬙

.0499⬙

.125⬙

.072⬙

1–

8⬙ .375⬙

.255⬙

.0625⬙

( )a

( )c

( )b

( )d

␮ 0.001

0.01

0.1

h Gc

c k

( )c ( )d

( )b

( )a

1/8-20.06( )D

1/8-19.82( )D

1/8-16.00( )D1/8-13.95

Figure 11.19 Heat transfer and ﬂow friction characteristics of some strip ﬁn compact heat exchanger surfaces (From Kays and London, 1984.)

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[854], (58)

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Pin diameter = 0.031 in., aluminum Pin pitch parallel to flow = 0.062 in.

Pin pitch perpendicular to flow = 0.062 in.

Flow passage hydraulic diameter, 4 = 0.00536 ft Total heat transfer area/volume between plates,

b

r h

Pin diameter = 0.04 in., copper Pin pitch parallel to flow = 0.125 in.

Pin pitch perpendicular to flow = 0.125 in.

Flow passage hydraulic diameter, 4 = 0.01444 ft Total heat transfer area/volume between plates,

b

r h

= 514 ft /ft Fin area/total area = 0.892 Note: Hydraulic diameter based on free-flow area normal to mean flow direction.

b

r h

= 347 ft /ft Fin area/total area = 0.822 Note: Hydraulic diameter based on free-flow area normal to mean flow direction.

b

rh

.0775 Approx ⬙

.0562⬙

.718⬙

.062⬙

.031⬙

.750⬙

0.125⬙

.24⬙

.04 dia.

Min free flow area 375⬙

.078⬙

.087⬙

( )a

( )c

( )b

( )d

␮ 0.0001

0.001

0.01

h Gc

c k

( )c ( )d

( )b

( )a

11.5-3/8W 17.8-3/8W AP-1

PF-3

Figure 11.20 Heat transfer and ﬂow friction characteristics of some wavy and pin ﬁn compact heat exchanger surfaces (From Kays and London, 1984.)

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