3。Overall actual heat transfer coefficient is then calculated and compared with the assumed values of U。 

4。If the difference between assumed and ac- tual values is within 0。5%, then algorithm goes to the next step。 Otherwise it assigns new Uassumed = Ucalc and iterates the step 2 until the Uassumed and Ucalc values are within 0。5% agreement。 

5。The computed values of flow velocities and  the constructive details of the exchanger structure are then used to evaluate the cost objective function。 The optimization algorithm, based on the value of the ob- jective function, updates the trial values of the optimi- zation variables which are then passed on to the de- sign routine to define a new architecture of the heat exchanger。 The process is iterated until a minimum of the objective function is found or a prescribed conver- gence criterion is met。 

Heat exchanger design procedure 

This section describes step by step calculation  procedure to evaluate heat exchanger area, tube side 

Figure 1。 Flowchart for heat exchanger design using SA algorithm。 

and shell side pressure drop and total cost of heat exchanger。 Equations (1) to (28) can be found from  Kern [14], Sinnot [15], Caputo et al。 [6]  as  well as Patel and Rao [9]。 

The logarithmic mean temperature difference (LMTD) is determined by: 

LMTD (Thi    Tco ) (Tho   Tci  )                                   (1) 

ln T   hi  Tco  

 T   

Tho ci  

For sensible heat transfer, the heat transfer rate is given by: 

Table 1。 Search optimization variables and their options 

Variable name Corresponding options 

The correction factor, F, for the flow configuration involved is found as a function of dimensionless tem- perature ratio for most flow configurations of: 

The Darcy friction factor ft is calculated as fol- lows: 

f   (1。82log 10Ret    1。64)2 

where the correction coefficient R is given by:      (4) 

Tco Tci

Efficiency P is given by: 

where Ret is the tube side Reynolds number  and given by: 

where di is the inside diameter of tube and for sim- plicity kept constant as di  = 0。8d0  in this work。    How-

ever, for more rigorous calculations, instead of keep- ing it constant, variable pipe thickness can be used 

Assuming the overall heat transfer coefficient  Uassumed, the heat exchanger surface S is   computed  by: 

from tables of tube manufacturers: schedules 40 or 80 or standard tubing gages: B。W。G。 and Stub’s gage。 

Prt is the tube side Prandtl number given by: 

Tube side calculations。 Number of tubes, Nt, and tube bundle diameter, Db, are calculated as follows: 

According to flow regime, the tube side heat transfer coefficient (ht) is computed from following correlation for Ret 10000: 

where K1 and n1 are coefficients that take values ac- cording to flow arrangement and number of passes as 

per table given by Sinnot [15]。 

Velocity through tubes is found by: 

Shell side calculation 

Clearance between tube bundle diameter and  shell diameter is calculated from the figure given by  Sinnot [15] for different head types as follows: