Clearance Ds Db  mDb c 

where m and c are empirical constants and assume following values for different head type: 

– fixed and U tube (0。01, 0。008), outside packed head (0。0, 0。038), split ring floating head (0。027, 0。0446), pull through floating head (0。009, 0。0862)。 

Baffle spacing is calculated as: 

where coefficients m and c are evaluated from figure given by Sinnot [15] for different baffle cuts, as fol- lows: 15% baffle cut (-6。710-8; 0。100067); 25% baffle cut (-4。510-8; 0。070045); 35% baffle cut (-4。410-8; 0。063044); 45% baffle cut (-3。410-8; 0。050034)。 

The overall heat transfer coefficient is calculated as follows: 

Cross-sectional area normal to flow direction is determined by: 

Compare   and   check   the   absolute   error,%, 

a s between Uassumed and Ucalc as per following: 

t

Uassumed Ucalc

where Pt is tube pitch and given by Pt = 1。25 d0。 

Flow velocity for shell side can be obtained from: 

If error is more than 0。5%, assume new U as 

 and go back to Eq。 (5) and  recalculate 

Reynolds number and Prandtl number for shell  side can be calculated as: 

everything until error reaches less than 0。5%。 

When error is less than 0。5%, i。e。, Uassumed and  Ucalc  is very near to each other proceeding for  further 

calculations as follows: 

The tube side pressure drop includes distributed 

where Des is the shell hydraulic diameter and com- puted as: 

– For triangular pitch: 

pressure drops along the tube length and concen- trated pressure losses in elbows and in the inlet and  outlet nozzles: 

The shell side pressure drop is given by: 

where fs is given by: 

Kern’s  formulation  for  segmental  baffle  shell-

and-tube exchanger is used for computing shell side heat transfer coefficient hs: 

j K Re Pr 0。333

where b0 = 0。72 valid for Res < 40000。 Objective function 

Total cost Ctot  is taken as the objective function, 

which  includes  capital  investment  (Ci),  energy cost 

(Ce), annual operating cost (Co) and total   discounted 

where coefficient jh  is calculated from the figure given 

by Sinnot [15] for different baffle cuts。 

operating cost (Cod

The following approximate equation was used: 

j h  m Rec   

Ctot   Ci  Cod                                                                                   (29) 

Adopting Hall’s correlation, the capital invest- ment (Ci) is computed as a function of the exchanger surface area: 

Ci  a1 a2S a3                                                                                                             (30) 

where a1 = 8000, a2 = 259。2 and a3 = 0。93 for ex- changer made with stainless steel for both shell and tubes。