CHEMICAL ENGINEERING

170 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Forconvectionfrom the pipe, the heat loss:

qcDhcA

TsT

D 1. 65

443  2900.^25 ð 1. 131

443  290 D 1. 866

443  2901.^25 D1004 W

and the total lossD2718 W or 2.71 kW

For the insulated pipe

The heat conducted through the laggingqlmust equal the heat lost from the surface

qrCqc.

Mean diameter of the laggingD[ 

0. 060 C 2 ð 0. 050 C 0 .060]/ 2 D 0 .110 m

at which the areaD
$ð 0. 110 ð 6. 0 D 2 .07 m^2

and in equation 9.12:qlD 0. 07 ð 2. 07
443 Ts/ 0. 050 D
1280  2. 90 Ts W

whereTsis the surface temperature.

The outside areaD$

 0. 060 C 2 ð 0. 050 ð 6. 0 D 3 .016 m^2

and from equation 9.119 :qrD
5. 67 ð 10 ^8 ð 0. 85 ð 3. 016
T^4 s 2904

D 1. 456 ð 10 ^7 T^4 sD1030 W

and: qcD 1. 65
Ts 2900.^25 ð 3. 016
Ts 290

D 4. 976 

Ts 2901.^25 W

Making a heat balance:

1280  2. 90 Ts D 

1. 456 ð 10 ^7 T^4 s  1030 C 4. 976 

Ts 2901.^25

or: 4. 976
Ts 2901.^25 C

1. 456 ð 10 ^7 T^4 s C 2. 90 TsD 2310

Solving by trial and error:TsD305 K

and hence the heat lostD
1280  2. 90 ð 305 D396 W.

The heat saved by lagging the pipeD 

2712  396 D2317 W or 2.317 kW.

At 800 kN/m^2 , the latent heat of steam is 2050 kJ/kg

and the reduction in the amount of steam condensedD
2. 317 / 2050 D 0 .00113 kg/s

or:
0. 00113 ð 3600 ð 24 ð 365 D 35 ,643 kg/year

∴ annual savingD
35 , 643 ð 0. 5 / 100 D£178/year

It may be noted that arithmetic mean radius should only be used with thin walled tubes,
which is not the case here. If a logarithmic mean radius is used in applying equation 9.8,
TsD 305 .7 K and the difference is, in this case, negligible.