CHEMICAL ENGINEERING

166 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

∴ tD

(

48. 6 ð 0. 50 ð 103



0. 78 ð 0. 225 ð 5. 67 ð 10 ^8

)(

1

4 ð 14003

)

ð

(

ln

1400 CT

1400 T

C2tan^1

T

1400

) 600

290

D200 s

PROBLEM 9.34

A wall is made of brick, of thermal conductivity 1.0 W/m K, 230 mm thick, lined on the
inner face with plaster of thermal conductivity 0.4 W/m K and of thickness 10 mm. If
a temperature difference of 30 K is maintained between the two outer faces, what is the
heat flow per unit area of wall?

Solution

Foranareaof1m^2 ,

thermal resistance of the brick:
x 1 /k 1 AD 0. 230 /

1. 0 ð 1. 0 D 0 .230 K/W

thermal resistance of the plaster:
x 2 /k 2 AD 0. 010 /
0. 4 ð 1. 0 D 0 .0025 K/W

and in equation 9.18: 30D
230 C 0. 0025 QorQD129 W

PROBLEM 9.35

A 50 mm diameter pipe of circular cross-section and with walls 3 mm thick is covered
with two concentric layers of lagging, the inner layer having a thickness of 25 mm and
a thermal conductivity of 0.08 W/m K, and the outer layer a thickness of 40 mm and a
thermal conductivity of 0.04 W/m K. What is the rate of heat loss per metre length of
pipe if the temperature inside the pipe is 550 K and the outside surface temperature is
330 K?

Solution

From equation 9.22, the thermal resistance of each component is:
r 2 r 1 /k
2 $rml

Thusfor the wall: r 2 D 

0. 050 / 2 C 0. 003 D 0 .028 m

r 1 D 

0. 050 / 2 D 0 .025 m

and: rmD
0. 028  0. 025 /
ln 0. 028 / 0. 025 D 0 .0265 m.

TakingkD45 W/m K andlD 1 .0 m the thermal resistance is:

D 

0. 028  0. 025 /

 45 ð 2 $ð 0. 0265 ð 1. 0 D 0 .00040 K/W.