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T
G
1
T
G
2
∆
T
2
∆
T
1
T
L
2
T
L
1
(A) Concurrent flow
T
G
1
∆
T
1
T
L
2
T
G
2
∆
T
2
T
L
1
(B) Countercurrent flow
T
G
1
T
G
2
∆
T
2
∆
T
1
T
L
2
T
L
2
Length of Exchanger
(C) Isothermal condensation w/countercurrent flow
FIGURE 16.19
Temperature profiles in a heat exchanger. (From USEPA,
APTI Course 415: Control of
Gaseous Emissions
, EPA 450/2-81-005, U.S. Environmental Protection Agency Air Pollution Training
Institute, Washington, DC, 1981, p. 6-13.)
In a surface heat exchanger, the temperature difference between the hot vapor and the coolant
usually varies throughout the length of the exchanger. Therefore, a mean temperature difference
(∆
T
m
) must be used. The log mean temperature difference can be used for the special cases when the
flow of both streams is completely co-current, the flow of both streams is completely countercur-
rent, or the temperature of the fluids remains constant (as is the case in condensing a pure liquid).
The temperature profiles for these three conditions are illustrated in Figure 16.19. The log mean
temperature for countercurrent flow can be expressed as shown in Equation 16.23.
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