CHEMICAL ENGINEERING

158 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Overall

TakingkwD 15 .9W/mKandRoandRias 0.0004 and 0.0002 m^2 K/W respectively, then
in equation 9.201:

1 /UoD 

1 / 805. 5 C 

0. 0015 / 15. 9

0. 025 / 0. 0235 C 

1 / 5490

0. 025 / 0. 022 C 0. 0004

C 0. 0002

0. 025 / 0. 022

D 

0. 00124 C 0. 00010 C 0. 00021 C 0. 00040 C 0. 00023 D 0 .00218 m^2 K/W

and: UoD 458 .7W/m^2 K

PROBLEM 9.26

7.5 kg/s of pure iso-butane is to be condensed at a temperature of 331.7 K in a horizontal
tubular exchanger using a water inlet temperature of 301 K. It is proposed to use 19 mm
outside diameter tubes of 1.6 mm wall arranged on a 25 mm triangular pitch. Under these
conditions the resistance of the scale may be taken as 0.0005 m^2 K/W. Determine the
number and arrangement of the tubes in the shell.

Solution

The latent heat of vaporisation of isobutane is 286 kJ/kg and hence the heat load:

QD 

7. 5 ð 286 D2145 kW

The cooling water outlet should not exceed 320 K and a value of 315 K will be used.
The mass flow of water is then:

2145 /[4. 18

315  301 ]D 36 .7 kg/s

In order to obtain an approximate size of the unit, a value of 500 W/m^2 K will be
assumed for the overall coefficient based on the outside area of the tubes.

 1 D 

331. 7  301 D 30 .7deg K, 2 D 

331. 7  315 D 16 .7deg K

and from equation 9.9:mD
30. 7  16. 7 /ln
30. 7 / 16. 7 D 23 .0deg K.
Thus, the approximate areaD
2145 ð 103 /
500 ð 23. 0 D 186 .5m^2.
The outside area of 0.019 m diameter tubesD
$ð 0. 019 ð 1. 0 D 0 .0597 m^2 /mand
hence the total length of tubingD
186. 5 / 0. 0597 D3125 m.
Adopting a standard tube length of 4.88 m, number of tubesD
3125 / 4. 88 D640.
With the large flow of water involved, a four tube-side pass unit is proposed, and for this
arrangement 678 tubes can be accommodated on 25 mm triangular pitch in a 0.78 m i.d.
shell. Using this layout, the film coefficients are now estimated and the assumed value of
Uis checked.

Inside

Water flow through each tubeD 36. 7

/

678 / 4 D 0 .217 kg/s.