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11%, provides a reduction in the total annual cost of 22%. It is
important to notice that the film heat transfer coefficients for
Design A are closer to each other than the ones obtained by
Mizutani et al. [9], thus providing a more efficient design. Large
differences in film coefficients are linked to an inefficient use of
pressure drops, which raises the pumping costs needed for the
exchanger.
The GAwas also used for this problemwithout the constraints in
tube length and baffle cut imposed byMizutani et al. [9]. The results
are reported as Design B in Table 2. One can notice a significant
reduction in the total area required by the exchanger. This is the
result of the number of passes being reduced to one, and of smaller
tube diameters being selected. This arrangement produces higher
stream velocities with better heat transfer coefficients, which
provide a smaller area. Another issue worth of mention is that the
relationship Ltt/Ds is higher than for the other two designs. Design B
has a total annual cost 49.88% lower than the one obtained by
Mizutani et al. [9], and 17.13% lower than Design A.
Example 2. This example was previously analyzed by Serna and
Jimenez [7]. A shell-and-tube heat exchanger must be designed
to cool down oil using cooling water. Fig. 4 shows the design data.
The tube wall thermal conductivity was neglected.
The solution was obtained after 90 generations using a CPU
time of 71 s. Table 3 shows a summary of the results obtained with
the proposed algorithm, as well as the design reported by Serna
and Jimenez [7]. Their design was based on gradient methods, and
they did not optimize the geometry of the exchanger; the main
design variables such as baffle and tube characteristics were
specified. From Table 3 it can be seen that the design obtained
using the algorithm proposed in this work meets all the geometric
and operational constraints. On the other hand, the design by Serna
and Jimenez [7] shows a shell-side stream velocity 65% higher than
the maximum recommended value, which can lead to erosion in
the baffles and tube vibrations.
The new design provides the geometric configuration (tubes,
baffles, shell) needed as part of the optimal solution. A proper use
of the pressure drops for each side of the exchanger provides a high
heat transfer coefficient, thus optimizing the area and the cost of
the exchanger. The design obtained using GA has total pumping
costs 10.7% lower than the one reported by Serna and Jimenez [7],
along with reductions in the exchanger area of 10% and in total
annual cost of 6.1%.
Example 3. In this example, the data from Example 2 were taken,
but three major aspects were changed. First, only standard sizes for
the tube length and the shell diameter were considered. Second, a
different economic environment was assumed, in which higher
capital investment is required for heat exchangers. And third, the
economic model involved a more detailed description for the cost
of the exchanger.
The exchanger cost was calculated from the cost of component
parts plus manufacturing costs. The following relations, proposed
by Purohit [11], were used for Eq. (16)
Cts ¼ pqmatC1ðDs þ 2tsÞ
2
tt
3456
ð20Þ
Csh ¼ pqmatC2DsLtots
144
ð21Þ
C0
b ¼ pqmatC1D2
s
Nb
13824
ð22Þ
Ctd ¼ C4Ntt ð23Þ
Ctb ¼ C3A ð24Þ
Cba ¼ C5 ð25Þ
The constants for the cost equations were taken from Purohit [11]:
C1 = 0.5 $/lb, C2 = 1.0 $/lb, C3 =75 (A)
0.4
$/ft
2
, C4 = 2.0 $/tube,
C5 = $30,000. For the exchanger, qmat = 486.954 lb/ft