CHEMICAL ENGINEERING

136 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

In calculatingNu,Pr,andRe, the thermal conductivity of the oil may be taken as
0.14 W/m K and the specific heat as 2.1 kJ/kg K, irrespective of temperature. The viscosity
is to be taken at the mean oil temperature. Viscosity of the oil at 319 and 373 K is 154
and 19.2mNs/m^2 respectively.

Solution

Heat load

QD 

0. 5 ð 2. 1

327  311 D 16 .8kW

Logarithmic mean driving force

 1 D 

373  311 D62 deg K, 2 D 

373  327 D46 deg K

∴in equation 9.9, mD
62  46 /ln
62 / 46 D 53 .6deg K

A preliminary estimate of the overall heat transfer coefficient may now be obtained
from Table 9.18.
For condensing steam,hoD 10 ,000 W/m^2 K and for oil,hiD250 W/m^2 K (say). Thus
1 /UD 1 /hoC 1 /hiD 0 .0041,UD244 W/m^2 K and from equation 9.1, the preliminary
area:

AD 

16. 8 ð 103 /

 244 ð 53. 6 D 1 .29 m^2

The area/unit length of tube is

$ð 19. 0 ð 10 ^3 ð 1. 0 D 

5. 97 ð 10 ^2 m^2 /m

and: total length of tubingD 1. 29 /
5. 97 ð 10 ^2 D 21 .5m

Thus: number of tubesD
21. 5 / 1. 5 D 14. 3 , say 14 tubes

Film coefficients

The inside coefficient is controlling and hence this must be checked to ascertain if the
preliminary estimate is valid.

The Reynolds number,ReDdiG^0 /D 

19. 0 ð 10 ^3 G^0 /

At a mean oil temperature of 0. 5

327 C 311 D319 K,D 154 ð 10 ^3 Ns/m^2.

Area for flow per tubeD

$/ 4

19. 0 ð 10 ^32 D 2. 835 ð 10 ^4 m^2.

∴ total area for flowD
14 ð 2. 835 ð 10 ^4 D 3. 969 ð 10 ^3 m^2

and hence: G^0 D 0. 5 /
3. 969 ð 10 ^3 D 1. 260 ð 102 kg/m^2 s

Thus: ReD
19. 0 ð 10 ^3 ð 1. 260 ð 102 /
154 ð 10 ^3 D 15. 5

That is, the flow is streamline and hence:

hidi/k

s/^0.^14 D 2. 01 

GCp/kl^0.^33 (equation 9.85)

At a mean wall temperature of 0. 5

373 C 319 D346 K,sD 87. 0 ð 10 ^3 Ns/m^2.