T2
400- F
120- F
280- F
T1
500- F
310- F
190- F
Tlm
( T2
T1)
ln
T2
T1
(280- F
190- F)
ln
280- F
190- F
232- F
Q
m h
m
Q
m cp T
m
HEAT EXCHANGERS
Heat Transfer
HT-02
Page 36
Rev. 0
chimney effect of the warm humid air in the tower or by fans at the bottom (forced draft) or at
the top (induced flow) of the tower. Mechanical draft towers are more economical to construct
and smaller in size than natural-convection towers of the same cooling capacity.
Log Mean Temperature Difference Application To Heat Exchangers
In order to solve certain heat exchanger problems, a log mean temperature difference (LMTD
or T ) must be evaluated before the heat removal from the heat exchanger is determined. The
lm
following example demonstrates such a calculation.
Example:
A liquid-to-liquid counterflow heat exchanger is used as part of an auxiliary system at
a nuclear facility. The heat exchanger is used to heat a cold fluid from 120- F to 310- F.
Assuming that the hot fluid enters at 500- F and leaves at 400- F, calculate the LMTD
for the exchanger.
Solution:
The solution to the heat exchanger problem may be simple enough to be represented by a
straight-forward overall balance or may be so detailed as to require integral calculus. A steam
generator, for example, can be analyzed by an overall energy balance from the feedwater inlet
to the steam outlet in which the amount of heat transferred can be expressed simply as
, where
is the mass flow rate of the secondary coolant and h is the change in
enthalpy of the fluid. The same steam generator can also be analyzed by an energy balance on
the primary flow stream with the equation
, where
, c , and T are the mass
p
flow rate, specific heat capacity, and temperature change of the primary coolant. The heat
