Harmony Search Applications in Mechanical, Chemical and Electrical Engineering - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 71

the surface area of tubes using experimental formulas and pumping cost are calculated
based on electricity fees and pressure drop of fluids in the exchanger. Calculation of
the required surface area and pressure drop of fluids is a very complex process which
can be found in much detail in heat transfer textbooks [5-7].
There is a major design constraint which should be satisfied in a practical design.
The STHE should be capable of accomplishing the prescribed heat load. Also, there
are many other thermal/mechanical/practical limitations which should be considered.
For example when designing the tubes, it is practical to ensure that the tube pitch is
not less than 1.25 times the tubes' outside diameter, the baffle cut which is the ratio of
the baffle window height to the shell diameter should be greater than 15%, and baffles
should not be spaced closer than about one-fifth of the shell diameter. Furthermore,
because of fouling problems and mechanical cleaning limitations, tube diameters
should be greater than a specified value.
2.1.2 Example of STHE Design
This example taken from Fesanghary et al. [8] is concerned with the design of a shell
and tube oil-cooler. The light oil enters the exchanger at 102°C and is to be cooled
down to 64°C by water entering at 21°C. The objective is to find the most economic
design which can satisfy the heat load of the exchanger together with pressure drop
limitations.
To show the ability of the HS method, its performance is compared with a genetic
algorithm (GA). Although both GA and HS have proven their abilities in finding near
global solutions within a reasonable amount of time, they are comparatively ineffi-
cient in finding the precise optimum solution. To evaluate the accuracy of the ob-
tained results, the global optimum solution is also calculated considering all possible
exchanger geometries. Thus, first the continuous variables are divided to 100 equal
sections in their range of variations. Considering discrete variables, a total number of
67,797,000,000 combinations are obtained. Then all the candidate solutions are exam-
ined to find the optimal solution. Table 1 lists the comparative performances for the
exchanger cost and average central processing unit (CPU) times for HS and GA.
Table 1. Cost comparison for STHE design example
Algorithms Total Cost CPU time (sec.)
GA $10630.5 13.12
HS $10572.0 8.38
Global optimum [8] $10553.4 591,453
Results reveal that both HS and GA can converge to near optimal solutions in a
reasonable amount of time. The difference between the global optimum solution and
those obtained using HS is 0.2 percent. This difference becomes 0.7 percent for GA.
Note that to find the global optimal solution, the time elapsed through evaluating all
possible combinations was about 164 hours while it took only a few seconds for HS to
find a good near optimal solution.