Figure 3。 Cost comparisons。 

ric, velocity and pressure drop constraints。 In earlier  GA approach [6] no such geometric, velocity and pressure drop constraints are imposed。 These cons- traints are very much necessary in industrial scenario and ensure smooth functioning of heat exchanger in actual shop floor。 Also in GA approach by Caputo   et al。 [6] the design variables (tube diameter, shell dia- meter etc。) are considered as continuous variable (as opposed to discrete variable which conforms TEMA  standard considered in present case)  and  thus the  final optimum solution may not conform TEMA stan- dard。 In this respect, the solutions obtained by pre- sent approach are much more preferable than that of GA approach。 However, these limitations can be re- moved from GA approach by following the advanced constraints and corresponding modeling methodology adopted in the present approach。 

It was reported by Caputo et al。 [6] that the  objective function converges within about 15 genera- tions (each generations have 70 function calls as  per 70 population) for this case against 703 function calls by SA algorithm to reach convergence。 This shows for this case study, SA converges faster than GA with less number of function call。 However this observation is limited to this case only and cannot be generalized。 As the execution time is very negligible (1。5 s in Pen- tium 4 processors) in such type of design, the exten- sive exploration of  solution  space  and  goodness of the final solutions (i。e。, least cost design) is more  important here。 

Case 2: 1。44 MW duty, kerosene crude oil exchanger 

The original design as well as the design pro- posed by Caputo et al。 [6] using GA approach as- sumed an exchanger with four tube  side passages  (with square pitch pattern) and one shell  side pas- sage。 The same configuration is not retained in the present approach and number of tube  passes and  pitch pattern are kept as a free optimization variable。 The input parameters for heat exchanger design are given in Table 2 and comparisons of final results by  different algorithm are shown in Table 3。 It is  ob- served that in this case higher tube side flow velocity increases the tube side heat transfer coefficient by  123%。 A 13。69% increment in overall heat transfer coefficient is observed in the present case because of the combined increment in tube side and shell side heat transfer coefficient。 As a result of  high  overall  heat transfer coefficient, a reduction of 15。83% in heat exchanger area and reduction of 43% in heat ex- changer length is observed compared to GA approach considered by Caputo et al。 [6]。 The capital invest- ment is decreased by 7。94% and pumping cost also  reduced by 11。62%。 Reduction of tube passes from  4 to 2 and 43% reduction of tube length reduce the tube side pressure drop by 31。3%。 However higher shell side velocity and lower diameter of shell makes the pressure drop of shell side more than calculated by GA。 Overall 8。43% reduction in total annual cost is observed using this approach as compared to the GA approach considered by Caputo et al。 [6]。 

Case 3: 4。54 MW duty, oil- cooling water exchanger 

To demonstrate the effectiveness of SA tech- nique, one more case study is considered which was originally analyzed by Serna and Jimenez [19], and later on improved by Ponce-Ortega et al。 [16] using GA approach。 The input parameters for heat ex- changer design are given in Table 2 and comparisons of final results by different algorithm are shown in Table 3。 For comparison of the results, cost function  (refer Eq (34)–(36)) and all the values related to cost taken from Ponce-Ortega et al。 [16] are as follows: 

Capital cost of exchanger ($) =