Chapter 13

HEAT EXCHANGERS
The LMTD method is very suitable for determining the size of a heat
exchanger to realize prescribed outlet temperatures when the mass flow
rates and the inlet and outlet temperatures of the hot and cold fluids are
specified.
With the LMTD method, the task is to select a heat exchanger that will
meet the prescribed heat transfer requirements. The procedure to be
followed by the selection process is:
1. Select the type of heat exchanger suitable for the application.
2. Determine any unknown inlet or outlet temperature and the heat
transfer rate using an energy balance.
3. Calculate the log mean temperature difference ΔTlm and the correction
factor F, if necessary.
4. Obtain (select or calculate) the value of the overall heat transfer
coefficient U.
5. Calculate the heat transfer surface area As .
The task is completed by selecting a heat exchanger that has a heat
transfer surface area equal to or larger than As.

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 THE EFFECTIVENESS–NTU METHOD
A second kind of problem encountered in heat exchanger analysis is the
determination of the heat transfer rate and the outlet temperatures of the hot and
cold fluids for prescribed fluid mass flow rates and inlet temperatures when the type
and size of the heat exchanger are specified.

Heat transfer effectiveness

the maximum possible heat transfer rate

Cmin is the smaller of Ch and Cc
3
Actual heat transfer rate

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The effectiveness of a
heat exchanger depends
on the geometry of the
heat exchanger as well
as the flow arrangement.
Therefore, different types
of heat exchangers have
different effectiveness
relations.
We illustrate the
development of the
effectiveness relation for
the double-pipe
parallel-flow heat
exchanger.

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Effectiveness relations of the heat exchangers typically involve the
dimensionless group UAs /Cmin.
This quantity is called the number of transfer units NTU.

For specified values of U and Cmin, the value

of NTU is a measure of the surface area As.
Thus, the larger the NTU, the larger the heat
exchanger.
capacity ratio

The effectiveness of a heat exchanger is a function of the number of

transfer units NTU and the capacity ratio c.

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7
Effectiveness
for heat
exchangers.

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When all the inlet and outlet temperatures are specified, the size of the heat
exchanger can easily be determined using the LMTD method. Alternatively,
it can be determined from the effectiveness–NTU method by first evaluating
the effectiveness from its definition and then the NTU from the appropriate
NTU relation. 10
(e.g., boiler, condenser)

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Observations from the effectiveness relations and charts
• The value of the effectiveness ranges from 0 to 1. It increases rapidly with
NTU for small values (up to about NTU = 1.5) but rather slowly for larger
values. Therefore, the use of a heat exchanger with a large NTU (usually
larger than 3) and thus a large size cannot be justified economically, since
a large increase in NTU in this case corresponds to a small increase in
effectiveness.
• For a given NTU and capacity ratio c = Cmin /Cmax, the counter-flow heat
exchanger has the highest effectiveness, followed closely by the
cross-flow heat exchangers with both fluids unmixed. The lowest
effectiveness values are encountered in parallel-flow heat exchangers.
• The effectiveness of a heat exchanger is independent of the capacity ratio
c for NTU values of less than about 0.3.
• The value of the capacity ratio c ranges between 0 and 1. For a given
NTU, the effectiveness becomes a maximum for c = 0 (e.g., boiler,
condenser) and a minimum for c = 1 (when the heat capacity rates of the
two fluids are equal).

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SELECTION OF HEAT EXCHANGERS
• The uncertainty in the predicted value of U can exceed 30 percent. Thus, it
is natural to tend to overdesign the heat exchangers.
• Heat transfer enhancement in heat exchangers is usually accompanied by
increased pressure drop, and thus higher pumping power.
• Therefore, any gain from the enhancement in heat transfer should be
weighed against the cost of the accompanying pressure drop.
• Usually, the more viscous fluid is more suitable for the shell side (larger
passage area and thus lower pressure drop) and the fluid with the higher
pressure for the tube side.
The proper selection of
a heat exchanger depends
The rate of heat transfer in the
on several factors:
prospective heat exchanger
• Heat Transfer Rate
• Cost
• Pumping Power
The annual cost of electricity associated with
• Size and Weight
the operation of the pumps and fans
• Type
• Materials

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 Summary
• Types of Heat Exchangers
• The Overall Heat Transfer Coefficient
– Fouling factor
• Analysis of Heat Exchangers
• The Log Mean Temperature Difference Method
– Counter-Flow Heat Exchangers
– Multipass and Cross-Flow Heat Exchangers: Use of a
Correction Factor
• The Effectiveness–NTU Method
• Selection of Heat Exchangers

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