CHEMICAL ENGINEERING

HEAT TRANSFER 183

Solution

Preliminary calculation

At 101.3kN/m^2 , benzene condenses at 353 K at which the latent heatD394 kJ/kg.

∴ heat load:QD

1. 25 ð 394 D492 kW

The maximum water outlet temperature to minimise scaling is 320 K and a value of
300 K will be selected. Thus the water flow is given by:

492 DGð 4. 18

300  295

or: GD 23 .5 kg/s [or
23. 5 / 1000 D 0 .0235 m^3 /s]

∴ area required for a velocity of 1.05 m/sD
0. 0235 / 1. 05 D 0 .0224 m^2

The cross-sectional area of a tube of 

25  2 ð 1. 6 D 21 .8mmi.d.is:

$/ 4 ð 0. 02182 D 0 .000373 m^2

and hence number of tubes requiredD
0. 0224 / 0. 000373 D60 tubes.

The outside areaD
$ð 0. 025 ð 2. 5 ð 60 D 11 .78 m^2

 1 D 

353  295 D58 deg K, 2 D 

353  300 D53 deg K

and in equation 9.9: mD
58  53 /ln
58 / 53 D 55 .5degK

∴ UD 492 /
55. 5 ð 11. 78 D 0 .753 kW/m^2 K

This is quite reasonable as it falls in the middle of the range for condensing organics
as shown in Table 9.17. It remains to check whether the required overall coefficient will
be attained with this geometry.

Overall coefficient

Inside:
The simplified equation for water in tubes may be used:

hiD 4280

0. 00488 T 1 u^0.^8 /d^0 i.^2 W/m^2 K. (equation 9.221)

where TD 0. 5
300 C 295 D 297 .5K

uD105 m/s anddiD 0 .0218 m

∴ hiD 4280
0. 00488 ð 297. 5  11. 050.^8 / 0. 2180.^2 D4322 W/m^2 Kor4.32 kW/m^2 K

Based on the outside diameter:

hioD 

4. 32 ð 0. 218 / 0. 025 D 3 .77 kW/m^2 K

Wall:
For steel,kD45 W/m K,xD 0 .0016 m and hence:
x/kD
0. 0016 / 45 D 0 .000036 m^2 K/Wor0.036 m^2 K/kW