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, andTD
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