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from which we obtain

Tw out 280 (0:5)(2090)(25)

(0:201)(4177) 311:1 K (100F)

This result applies to both parallel flow and counterflow. For the counterflow configuration, DTlmis

calculated as

DTlm 70 63:9

ln 70

63:9

66:9 K (120:4F)

and applying equation (22-10), we see that the area required to accomplish this energy transfer is

A 26125W

(250 W/m2 K)(66:9 K) 1:562 m2 (16:81ft2)

Performing similar calculations for the parallel-flow situation, we obtain

DTlm 95 38:9

ln 95

38:

9

62:8 K (113F)

A 26125W

(250 W/m2 K)(62:8 K) 1:66 m2 (17:9 ft2)

The area required to transfer 26,125 W is seen to be lower for the counterflow arrangement by

approximately 7%.

22.3 CROSSFLOW AND SHELL-AND-TUBE HEAT-EXCHANGER ANALYSIS

More complicated flow arrangements than the ones considered in the previous sections aremuch more difficult to treat analytically. Correction factors to be used with equation (22-10)

have been presented in chart form by Bowman, Mueller, and Nagle2

and by the Tubular

Exchanger Manufacturers Association.3

Figures 22.9 and 22.10 present correction factors

for six types of heat-exchanger configurations. The first three are for different shell-and-tube

configurations and the latter three are for different crossflow conditions.

The parameters in Figures 22.9 and 22.10 are evaluated as follows:

YTtout Ttin

Ts in Ttin(22-12)

Z (_mcp)tube

(_mcp)shell Ct

Cs Ts in Ts out

Ttout Ttin(22-13)

where the subscripts s and t refer to the shell-side and tube-side fluids, respectively. The

quantity read on the ordinate of each plot, for given values ofYandZ, is F,the correction

factor to be applied to equation (22-10), and thus these more complicated configurations

2 R. A. Bowman, A. C. Mueller, and W. M. Nagle, Trans. A.S.M.E. 62, 283 (1940).3 Tubular Exchanger Manufacturers Association, Standards, 3rd edition, TEMA, New York, 1952.

22.3 Crossflow and Shell-and-Tube Heat-Exchanger Analysis 343

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CorrectionfactorF

0 0.1 0.2 0.3 0.4

(a)

(b)

Shell fluid

Tube fluid

0.5

Y

0.6 0.7 0.8 0.9 1.00.5

Correction factor plot for exchangerwith one shell pass and two, four,

or any multiple of tube passes

Y

0.6

0.8

Correctionfacto

rF

1.0

0.8

0.9

1.0

0.20.4

0.2

0.4

0.6

0.8

1.02.0

3.0

z= 4.0

1.5

0.60.81.01.52.0z= 4.0

A

TH1

TH2

Tc2

Tc1

B

TH1 TH2

Tc2 Tc1

TH1 TH2

Tc2

Tc1

z =

3.0

0.6

0.7

Correction factor plot for exchanger withtwo shell passes and four, eight, or

any multiple of four tube passes

Y

(c)

0.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.6

0.7

0.9

0.8

Co

rrectionfactor,F

1.0

0.20.40.60.81.01.52.03.0z= 4.0

TH1

TH2

Tc2

Tc1

TH1 TH2Tc2

Tc1z =

Figure 22.9 Correction

factors for three shell-and-

tube heat-exchanger

configurations. (a) One shell

pass and two or a multiple of

two tube passes. (b) One

shell pass and three or amultiple of three tube passes.

(c) Two shell passes and two

or a multiple of two tube

passes.

(From R. A. Bowman, A. C.

Mueller, and W. M. Nagle,

Trans. A.S.M.E.,62,284, 285

(1940). By permission of the

publishers.) Correction

factors,F, based on

counterflow LMTD.

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Y=

(a)

0.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.6

0.7

0.9

0.8

Corre

ctionfactor,F

1.0

0.2

TH1

Tc1 Tc2

TH2

Tc2Tc1

TH1Tc1

0.40.60.81.01.52.03.0z= 4.0

TH1TH2

Tc2Tc1

z =

Y=

(b)

0.50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.6

0.7

0.9

0.8

Correctionfactor,F

1.0

0.20.40.61.0

TH1

Tc1 Tc2

TH2

Tc2Tc1

TH1Tc1

TH1 TH2

Tc2Tc1

z =

0.81.52.03.0z= 4.0

Figure 22.10 Correction factors for three crossflow heat-exchanger configurations. (a) Crossflow,

single-pass, both fluids unmixed. (b) Crossflow, single-pass, one fluid unmixed. (c) Crossflow,

tube passes mixed; fluid flows over first and second passes in series.

(From R. A. Bowman, A. C. Mueller, and W. M. Nagle, Trans. A.S.M.E., 62, 288289 (1940). By

permission of the publishers.)

22.3 Crossflow and Shell-and-Tube Heat-Exchanger Analysis 345

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may be treated in much the same way as the single-pass double-pipe case. The reader is

cautioned to apply equation (22-10), using the factor Fas in equation (22-14).

q UA(FDTlm) (22-14)

with the logarithmic-mean temperature difference calculated on the basis ofcounterflow.

The manner of using Figures 22.9 and 22.10 may be illustrated by referring to the

following example.

EXAMPLE 2 In the oilwater energy transfer described in Example 1, compare the result obtained with the result

that would be obtained if the heat exchanger were

(a) crossflow, water-mixed;

(b) shell-and-tube with four tube-side passes, oil being the tube-side fluid.

For part (a), Figure 22.10(b) must be used. The parameters needed to use this figure are

YTtout Ttin

Ts in Ttin

25

95 0:263

Y

(c)

0.50 0.2 0.4 0.6 0.8 1.0

0.6

0.7

0.8

0.9

Co

rrectionfactor,

F

1.0

Tc2

Tc1

TH2

TH1

TH1TH2

Tc2Tc1

0.2

0.4

0.6

0.8

1.0

1.5

2.0

3.0

z= 4.0

Figure 22.10 Continued

346 Chapter 22 Heat-Transfer Equipment