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programming methods have been used for design optimization of heat exchangers in
the last decade [10-14]. Although accurate and fast, these approaches rely strictly on
the initial starting point, the topology of the feasible region and the surface associated
with the objective function. In other words, a good starting point is crucial for these
methods to function successfully. These drawbacks therefore decrease the effective-
ness of these methods in thermal system design applications where the problems are
usually non-convex and have a large amount of discrete design variables. Stochastic
methods perform well for global searching and have the capability of quickly exploring
and finding high performance regions in the search space. These methods are able to
handle complex problems without being limited by the nonlinearities, the non-
convexities and the discontinuities of the objective function [15]. Due to these capabili-
ties, there has been a trend recently among researchers to implement these methods to
heat exchanger design optimization problems. Simulated annealing [16] and genetic
algorithms (GAs) [17-22] are the most frequently used methods among this certain
class of optimization methods.
2.2.1 Problem Formulation for Design of ACHEs
The objective is to find the optimal design of an ACHE which is capable of accom-
plishing the prescribed thermal duty with minimum total cost. The overall cost associ-
ated with a heat exchanger may be categorized as the capital and operating costs. The
capital cost includes the cost associated with design, materials, manufacturing, test-
ing, shipping and installation, which is usually estimated based on empirical formulas
expressed in terms of tube surface area. On the other hand, the operating cost consists
of the expense associated with electrical power consumed by fans.
There are many thermal/mechanical/practical limitations which should be
considered in a practical design. Each design parameter has a specified/recommended
range of variation. Besides this, other constraints such as energy balance, mass con-
servation, and maximum allowable pressure drop and fluid velocity in tubes should be
satisfied in the optimization process.
2.2.2 Example of ACHE Design
As an illustrative example, a refrigeration air-cooled condenser is considered here.
Process condition used for this problem is given in [23]. To show the performance of
the HS its results are validated by means of comparison with GA as shown in Table 2.
Table 2.
Cost comparison for ACHE design example
Algorithms Total Cost CPU time (sec.)
GA $2627.0 11.43
HS $2620.9 2.14
It can be seen that HS shows better performance than GA in this case. Although the
cost of the ACHEs obtained by GA and HS are close to each other, the geometries ob-
tained by these algorithms are completely different. Also, the computational time
elapsed in HS method is comparatively less than that of GA approach.
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