CHEMICAL ENGINEERING

156 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The thermal resistances of each material, (x/kA), are: firebrickD
1 / 6. 22 D 0 .161;
insulating brickD
1 / 1. 67 D 0 .60; building brickD
1 / 3. 11 D 0 .322 K/Wm^2 ;andin
equation 9.18:

1200  330 D 

0. 161 C 0. 60 C 0. 322 Q

or: QD 803 .3W/m^2

Tfirebrick/TD
x/kAfirebrick/
x/kA

∴
1200 T 1 /
1200  330 D 0. 161 /
0. 161 C 0. 60 C 0. 322 D
0. 161 / 1. 083

and: T 1 D1071 K

Similarly for the insulating brick:



1071 T 2 /

 1200  330 D 

0. 60 / 1. 083

and: T 2 D589 K

PROBLEM 9.24

Calculate the total heat loss by radiation and convection from an unlagged horizontal
steam pipe of 50 mm outside diameter at 415 K to air at 290 K.

Solution

Outside area per unit length of pipeD
$ð 0. 050 ð 1. 0 D 0 .157 m^2 /m.

Convection

For natural convection from a horizontal pipe to air, the simplified form of
equation 9.102 may be used:

hcD 1. 18 

T/do 0.^25

In this case:TD 

415  290 D125 deg K anddoD 0 .050 m.

∴ hcD 1. 18
125 / 0. 0500.^25 D 8 .34 W/m^2 K

Thus, heat loss by convection:qcDhcA

T 1 T 2

D 8. 34 ð 0. 157

415  290 D 163 .7W/m

Radiation

An extension of equation 9.118 may be used. Taking the emissivity of the pipe as 0.9:

qrD 

5. 67 ð 10 ^8 ð 0. 9

4154  2904 ð 0. 157 D 181 .0W/m

and the total loss is 344.7W/mlength of pipe.