Maximum spacing is given by B = 74d00。75。 

Most failures occur when unsupported tube length greater than 80% TEMA maximum due to de- signer trying to limit shell side pressure drop。 

Thumb rule 8。 Preferably use  baffle  spacing from 0。2 to 1。0 shell diameters。 The  smaller  the  number of baffle, the easier is the construction。 

Shell and tube fluid velocities 

High velocities will give high heat transfer coeffi- cients but also a high pressure drop。  The  velocity must be high enough to prevent any suspended so- lids settling, but not so high as to cause erosion。 High velocities will reduce fouling。 Typical design velocities are given in section 2。3。 

Pressure drop 

In many applications the pressure drop available to drive the fluids through the exchanger will be set by the process conditions, and the available  pressure drop will vary from a few mbars in vacuum service to several bars in pressure systems。 When the  designer is free to select the pressure drop an economic ana- lysis can be made to determine the exchanger design which gives the lowest operating costs, taking into  consideration both capital and pumping costs。 How- ever, a full economic analysis will only be justified for very large, expensive, exchangers。 Typical values for pressure drop constraints are given in section 2。3。 When a high-pressure drop is utilized, care must be  taken to ensure that the resulting high fluid velocity  does not cause erosion or flow-induced tube vibration。 

CONCLUSIONS 

Heat exchanger design can be a complex task  and advanced optimization tools are useful to identify the best and cheapest heat exchanger for a specific duty。 The present study has demonstrated successful application of SA technique for the optimal design of STHE from economic  point  of  view。  The presented SA technique is simple in concept, few in parameters and easy for implementations。 These features boost the applicability of the SA particularly in thermal sys- tem design, where the problems are usually complex and have a large number of variables and disconti- nuity in the objective function。 Furthermore, the SA 

algorithm allows for rapid solutions of the design pro- blems (as compare to exhaustive search of solution space by conventional design method) and enables to examine a number of alternative solutions of good  quality, giving the designer more degrees of  freedom in the final choice with respect to traditional methods。 Important additional constraints, like geometric, velo- city and pressure drop constraints, usually ignored in previous optimization schemes, are included in  order  to approximate the solution to  the  design practice。  The solutions to case studies taken from literature show that cost of heat exchangers of previously re- ported designs can be improved through the use of the approach presented in this work。 

Nomenclature 

a1 = numerical constant ($) 

a2 = numerical constant ($/m2) a3 = numerical constant 

Nf = tubes number 

ny = equipment life (yr) P = pumping power (W) 

Prs = Prandtl number (shell side) Prt = Prandtl number (tube side) Pt = tube pitch (m) 

Ptype = Pitch type 

ΔPs = shellside pressure drop (Pa) ΔPt = tubeside pressure drop (Pa) Q = heat duty (W) 

Rb = Baffle Spacing / Shell Diameter Ratio Res = Reynolds number (shell side) 

Ret = Reynolds number (tube side) 

Rfs = conductive fouling resistance shell side (m2K/W) Rft  = conductive fouling resistance tube side (m2K/W)  S = heat exchange surface area (m2) 

Sa = Cross-sectional area normal to flow direction Thi  = inlet fluid temperature shell side (K)