300

200

Arithmetic

Error

100

Geometric

Error (abs.)

0

3

2

1

0

10

10

10

10

Approach Factor

logarithmic mean temperature difference is always negative. Thus, the predicted

heat transfer using this approximation would always be conservative; i.e., it would

under-predict the actual heat transfer. We also note from Table 2 that, as we had

shown analytically, the error resulting from the use of the geometric mean approxi-

mation approaches 100% in magnitude as *AF *goes to zero and approaches zero as

The ratio of the error from using the arithmetic mean and geometric mean

approximations is also given in Table 2. Because the error from the arithmetic mean

approximation becomes infinite and the error from the geometric mean approxima-

tion approaches 100% as the approach factor *AF *goes to zero, their ratio approaches

zero at that point. Thus, the geometric mean approximation is infinitely better than

the arithmetic mean approximation at that point. Since neither approximation is

acceptable near that point, this observation is of little use. However, it is of interest

to note that the ratio of errors approaches 1/2 as *AF *approaches unity. Although this

εa(%)

εg(%)

εg/εa

AF

+∞

0.0

100.0

0.00

0.0001

361.0

90.8

0.25

0.001

246.0

78.1

0.32

0.01

135.0

53.4

0.40

0.1

40.7

19.1

0.47

0.2

20.7

10.0

0.48

0.3

11.8

5.79

0.49

0.4

6.90

3.41

0.495

0.5

3.97

1.97

0.497

0.6

2.17

1.08

0.498

0.7

1.058

0.528

0.4992

0.8

0.415

0.207

0.4997

0.9

0.0925

0.0462

0.4999

→ 0.500...

1.0

0.0

0.0

22

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