The total discounted operating cost related to pumping power to overcome friction losses is com- puted from the following equation: 

C0  PCeH                                                              (31) 

ny

Constraints 

Though the lowest cost exchanger is the main selection criterion for STHEs, this is not the only cri- terion for commercial plants。 The concept of a good design involves aspects that cannot be easily des- cribed in a single economic objective function e。g。 fouling suppression, maintenance ease, mechanical  resistance, simplicity, flow distribution, potential tube  vibration etc。 These criteria, though subjective, have a profound effect on exchanger performance in com- mercial plants。 These criteria are sometimes expres- sed as geometric and hydraulic and service cons- traints [17]。 

C  C0

                                                       (32) 

Geometric constraints 

x 1 (1 i)

where pumping power P is computed from: 

The STHE candidate must respect a series of geometric constraints, involving the  following rules: the ratio between tube length and shell diameter must 

P 1

(  mt  ΔP   ms  ΔP )                                    (33) 

be between 3 and 15, the ratio between baffle spa-

t s

Based on all above calculations, total cost is computed from Eq。 (29) for case studies 1 and 2。 The cost objective function is kept exactly same as case  study by GA approach by Caputo et al。 [6] to enable  the performance comparison of SA approach and GA approach。 

However, for case study 3 the authors did not 

cing and shell diameter must be between 0。2 and    1; 

the baffle spacing cannot be lower than 50 mm; the  baffle spacing must obey the maximum unsupported  span。 These constraints can be represented by the  following mathematical expressions: 

3 L / Ds   5                                                            (37) 

0。2 Rbs  1                                                             (38) 

use same cost function in their case studies。 Some of 

0。050D

/ R

0。5Lmax   / D                                    (39) 

the authors [16] use total annual cost slightly diffe- rently as follows: the total cost consists of five com- ponents: the capital cost of the exchanger, the capital costs for two pumps, and the operating (power) costs of the pumps。 The expression for the total annual cost is of the form: 

s bs b s

Velocity constraints 

These constraints represent fluid velocity  limits in order to reduce fouling and erosion problems。 The tube and shell side velocity must obey lower and up- per bounds: