CHEMICAL ENGINEERING

152 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Outside:hoD 0 .8kW/m^2 K

and hence the clean overall coefficient is given by:

1 /UcD 1 /hioC 1 /hoD 1 .75 m^2 K/kW orUcD 0 .572 kW/m^2 K

Thus allowing for scale and the wall:

UDD 0. 572

100  20 / 100 D 0 .457 kW/m^2 K

Area

In equation 9.1: ADQ/UmD 393. 8 /
0. 457 ð 44. 3 D 19 .45 m^2

Outside areaD

$ð 0. 025 ð 1. 0 D 0 .0785 m^2 /m

and hence total length of pipingD
19. 45 / 0. 0785 D 247 .6m.

4 .71 kg/s water
4. 71 / 1000 D 0 .00471 m^3 /s

and hence cross-sectional area/pass to give a velocity of 0.6 m/s

D 

0. 00471 / 0. 6 D 0 .00785 m^2

Cross-sectional area of one tubeD

$/

 0. 0202 D 0 .000314 m^2.

Therefore number of tubes/passD 

0. 00785 / 0. 000314 D 25.

Thus:
with 1 tube pass, total tubesD25 and tube lengthD
247. 6 / 25 D 9 .90 m

with 2 tube passes, total tubesD50 and tube lengthD
247. 6 / 50 D 4 .95 m

with 4 tube passes, total tubesD100 and tube lengthD
247. 6 / 100 D 2 .48 m

A tube length of 2.48 m is perhaps the most practical proposition.

PROBLEM 9.20

An organic vapour is being condensed at 350 K on the outside of a bundle of pipes through
which water flows at 0.6 m/s; its inlet temperature being 290 K. The outer and inner diam-
eters of the pipes are 19 mm and 15 mm respectively, although a layer of scale, 0.25 mm
thick and of thermal conductivity 2.0 W/m K, has formed on the inside of the pipes.
If the coefficients of heat transfer on the vapour and water sides are 1.7 and
3 .2kW/m^2 K respectively and it is required to condense 0.025 kg/s of vapour on each of
the pipes, how long should these be, and what will be the outlet temperature of water?

The latent heat of condensation is 330 kJ/kg.

Neglect any resistance to heat transfer in the pipe walls.

Solution

For a total ofnpipes, mass flow of vapour condensedD 25 nð 10 ^3 kg/s and hence load,
QD
0. 025 nð 330 D 8. 25 nkW.