CHEMICAL ENGINEERING

208 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The pipe is then lagged with a 50 mm thickness of lagging of thermal conductivity
0.1 W/m K. If the outside heat transfer coefficient is given by the same equation as for
the bare pipe, by what factor is the heat loss reduced?

Solution

For 1 m length of pipe: surface areaD$dlD$
25 / 1000 ð 1. 0 D 0 .0785 m^2

With a negligible temperature drop through the wall, the wall is at the steam temperature,
403 K, andTD
403  293 D110 deg K.

Thus, the coefficient of heat transfer from the pipe to the surroundings is:

hD 1 .22[110/

 25 / 1000 ]^0.^25 D 9 .94 W/m^2 K.

and the heat loss:QDhA
TwTs

D 

9. 94 ð 0. 0785

403  293 D 85 .8W/m

With the lagging:

QDk

 2 $rml

T 1 T 2 /

r 2 r 1 (equation 9.22)

In this case:kD 0 .1W/mK,T 1 D403 K andT 2 is the temperature at the surface of the
lagging.

r 1 D 

25 / 1000 / 2 D 0 .0125 m

r 2 D 0. 0125 C 

50 / 1000 D 0 .0625 m

and:rmD
0. 0625  0. 0125 /ln
0. 0625 / 0. 0125 D 0 .0311 m

Thus:QD
0. 1 ð 2 $ð 0. 0311 ð 1
403 T 2 /
0. 0625  0. 0125 D 0. 391
403 T 2 (i)

But: QD 1 .22[
T 2  293 /
2 ð 0. 0625 ]^0.^25
$ð 2 ð 0. 0625 ð 1 
T 2  293

D 0. 806 

T 2  2931.^25 (ii)

From (i) and (ii):
0. 391
403 T 2 D 0. 806
T 2  2931.^25

Solving by trial and error:T 2 D 313 .5K

and hence:

QD 0. 39 /

 403  313. 5 D 35 .0W/m,

a reduction of:
85. 8  35. 0 D 50 .8W/m

or:
50. 8 ð 100 / 85. 8 D 59 .2%

PROBLEM 9.77

A vessel contains 1 tonne of liquid of specific heat capacity 4.0 kJ/kg K. It is heated
by steam at 393 K which is fed to a coil immersed in the liquid and heat is lost to the