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Log
Mean Temperature Difference Application to Heat Exchangers - Heat Transfer
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[ Heat
Transfer Table of Contents]
In order to solve certain heat exchanger
problems, a log mean temperature difference (LMTD or
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 deg F
to 310 deg F.
Assuming that the hot fluid enters at 500
deg F and leaves at 400
deg F, calculate the LMTD
for the exchanger.
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 
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 , 
, and 
are the mass p
flow rate, specific heat
capacity, and temperature change of the primary coolant. The
heat transfer rate of the steam generator can also be
determined by comparing the temperatures on the
primary and secondary sides with the heat transfer
characteristics of the steam generator using
the equation 
Condensers are also examples of components
found in nuclear facilities where the concept of LMTD
is needed to address certain problems. When the steam enters
the condenser, it gives up its
latent heat of vaporization to the circulating water and
changes phase to a liquid. Because condensation
is taking place, it is appropriate to term this the latent
heat of condensation. After the
steam condenses, the saturated liquid will continue to
transfer some heat to the circulating water
system as it continues to fall to the bottom (hotwell) of the
condenser. This continued cooling
is called subcooling and is necessary to prevent cavitation
in the condensate pumps.
The solution to condenser problems is
approached in the same manner as those for steam generators,
as shown in the following example.
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