In literature, attempts to automate and optimize the heat exchanger design process have been pro- posed for a long time and the subject is still evolving。 The suggested approaches mainly vary in the choice of the objective function, in the number and kind of sizing parameters utilized and in the numerical opti- mization method employed。 In commercial software,  heat exchanger cost function has been recently incor- porated and cost minimization is performed by apply- ing mainly gradient based methods。 Depending upon the degree of non-linearity and initial guess, most of the traditional optimization techniques based on gra- dient methods have the possibility of getting  trapped  at local optimum。 Hence, these traditional  optimiza- tion techniques do not ensure global optimum and also have limited applications。 In the recent past, some ex- pert systems based on natural phenomena (evolu- tionary computation) such as simulated annealing [2]  and genetic algorithms [3,4] have been developed to  overcome this problem。 

Chaudhuri et al。 [1] used simulated annealing for the optimal design of heat exchangers and developed a command procedure, to run the HTRI design pro- gram coupled to the annealing algorithm, iteratively。 They have compared the results of the SA program  with a base case design and concluded that signi- ficant savings in the heat transfer area and hence the STHE cost can be obtained using SA。 Manish et al。 [5] used a genetic algorithm framework to solve this optimal problem of heat exchanger design along with SA and compared the performance of SA and GAs in solving this problem。 They also presented GA strate- gies to improve the performance of the optimization framework。 Recently, Caputo et al。 [6] also used GA  based optimization of heat exchanger design。 Selbas et al。 [7] used genetic algorithm for optimal design of STHEs, in which pressure drop was applied as a con-

straint for achieving optimal design parameters。 All of the above researchers concluded that these algo- rithms result in considerable savings in computational time compared to an exhaustive search, and have an advantage over other methods in obtaining multiple solutions of the same quality, thus providing more fle- xibility to the designer。 Fesanghary et al。 [8] used  global sensitivity analysis to identify the most influen- tial geometrical parameters (like tube diameter, shell diameter, baffle spacing, etc。) that affect total cost of STHEs in order to reduce the size of optimization pro- blem and carried out optimization by applying harmo- nic search。 Recently, Patel and Rao [9] have applied particle swarm optimization technique to design lowest cost heat exchangers。 

In view of the encouraging results found out  by the above researchers, an attempt has been made in the present study to apply a strategy called simulated annealing (SA), to the optimal heat exchanger design problem。 Simulated annealing (SA), a recent optimi- zation technique, is an exceptionally simple evolution strategy that is significantly faster and robust at nu- merical optimization and is more likely to find a func- tion’s true global optimum。 Simulated annealing (SA) algorithms that are members of the stochastic optimi- zation formalisms have been used with a great suc- cess in solving problems involving very large search spaces。 This optimization technique resembles the  cooling process of molten metals through annealing。  The cooling phenomenon is simulated by controlling a temperature like parameter introduced with the con- cept of the Boltzmann probability distribution。 Accord- ing to the Boltzmann probability distribution, a system in thermal equilibrium at a temperature T has its ener- gy  distributed  probabilistically  according  to  P(E)   = 

= exp(–E/kT), where k is the Boltzmann constant。 This 

expression suggests that a system at high tempera- ture has almost uniform probability of being in a high energy state。 Therefore, by controlling the tempera- ture T and assuming that the search process follows the Boltzmann probability distribution, the conver- gence of an algorithm can be controlled。 There are numerous papers in literature discussing   application of SA in various problems。 In a comprehensive  study of SA, Johnson et al。 [10-12] discuss the performance of SA on four problems: the travelling salesman prob- lem (TSP), graph partitioning problem (GPP), graph  coloring problem and number partitioning problem。 In general, the performance of SA was mixed – in some problems, it outperformed the  best  known heuristics  for these problems, and, in other cases, specialized heuristics performed better。