CHEMICAL ENGINEERING

HEAT TRANSFER 155

Case (b)

Again,mD 37 .4 K. In equation 9.212:

XD

 2  1 /

T 1  1 D 

320  300 /

 360  300 D 0. 33

YD

T 1 T 2 /

 2  1 D 

360  335 /

 320  300 D 1. 25

Hence, from Fig. 9.71,FD 0. 94

and in equation 9.212:

AD 2090 /

 2. 0 ð 0. 94 ð 374 D 29 .73 m^2

PROBLEM 9.22

Find the heat loss per unit area of surface through a brick wall 0.5 m thick when the
inner surface is at 400 K and the outside at 310 K. The thermal conductivity of the brick
may be taken as 0.7 W/m K.

Solution

QDkA

T 1 T 2 /x (equation 9.12)

D 0. 7 ð 1. 0

400  310 / 0. 5 D126 W/m^2

PROBLEM 9.23

A furnace is constructed with 225 mm of firebrick, 120 mm of insulating brick, and
225 mm of building brick. The inside temperature is 1200 K and the outside temperature
330 K. If the thermal conductivities are 1.4, 0.2, and 0.7 W/m K, find the heat loss per
unit area and the temperature at the junction of the firebrick and insulating brick.

Solution

IfT 1 KandT 2 K are the temperatures at the firebrick/insulating brick and the insulating
brick/building brick junctions respectively, then in equation 9.12, for conduction through
the firebrick:

QD 1. 4 ð 1. 0

1200 T 1 / 0. 255 D 6. 22

1200 T 1 W/m^2 (i)

For conduction through the insulating brick:

QD 0. 2 ð 1. 0 

T 1 T 2 / 0. 120 D 1. 67 

T 1 T 2 W/m^2 (ii)

and for conduction through the building brick:

QD 0. 7 ð 1. 0 

T 2  330 / 0. 225 D 3. 11 

T 2  330 W/m^2 (iii)