Page 41 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

2.6 Design overview for recuperators 37

Considering C to be the product of flow rate and specific heat capacity of either of the fluids, the
effectiveness is defined as follows:

C max ð T h;in T h;out Þ
(2.10a)
ε ¼
C min ð T h;in T c;in Þ
for the cold fluid as the fluid with minimum C. If the hot fluid is the minimum C fluid, the effectiveness
is defined as follows:

C max ð T c;out T c;in Þ
(2.10b)
ε ¼
C min ð T h;in T c;in Þ
This defines the heat transfer rate as

Q ¼ εC min T h;in T c;in (2.11)
Thus, the heat exchanger effectiveness term depends upon whether the hot fluid or cold fluid
has the lower capacity coefficient Cð¼ mC p Þ. It is related to the number of transfer units (NTU)or,
ε ¼ fðNTU; C r Þ where C r ¼ C min /C max and the value of NTUis defined as follows:
NTU ¼ UA=C min (2.12)
Expressions relating ε, NTU and C r for different configuration of exchangers are available and the
same for the common configurations are provided in Table 2.3.
With sufficient other data known about a heat exchange process, an unknown outlet temperature
can be found by this method directly without any trial calculation as required in the F T method.
The ε-NTU method is used for design of compact heat exchangers, while the LMTD method
is more established and is commonly used for tubular (double-pipe, shell and tube) exchangers.
However, both methods yield identical results within the specified convergence tolerances. It may be
noted that the ε-NTU approach is not valid if the overall heat transfer coefficient varies over the
exchanger length.
The overall heat transfer coefficient U is calculated from the individual thermal resistances per unit
area of either the hot ðA h Þ or the cold fluid ðA c Þ side using
the following expressions.
1 1 1
Overall Heat Transfer Coefficient
¼ þ R w A h þ (2.13a)
U h A h h h A h h c A c
or
1 1 1
(2.13b)
¼ þ R w A c þ
U h A c h h A h h c A c
where 1 and 1 are the overall thermal resistances based on the hot surface and cold surface. h h and h c
U h U c
are the heat transfer coefficients for the hot and cold fluid, respectively, and R w is the wall thermal
resistance. Areas A c and A h are defined in Chapter 3 for double-pipe exchanger.
For (external) finned tube exchangers, the heat transfer area should be based on total outside tube
and fin surface and the heat transfer coefficient h needs to take into account the effective tube wall and