Question

A composite wall is composed of 10 cm of structural firebrick with k = 1.4 W/m-K in the inside of a furnace and 10 cm of insulating firebrick with k = 0.5 W/m-K on the outside. The inside temperature of the furnace is 1225oC and the heat flux is 5 kW/m2. What is the temperature at the interface the two types of brick?

Answer 1

`T_(m)=868\°C`

Step-by-step explanation:

The rate of heat transfer through the wall is given by:

`q=(Ak)/(L)dT`

`(q)/(A)=(k)/(L)dT`

Assumptions:

1) the system is at equilibrium

2) the heat transfer from structural firebrick side to interface and interface to insulating firebrick side is equal. There is no heat retention at any point

3) the external surface of the wall (insulating firebrick side) is large enough that all heat is dissipated and there is no increase in temperature of the air on that side

Details available in the question:

`(q)/(A)=5 kW/m^(2) = 5000 W/m^(2)`

`{k_(sf)= 1.4 W/m.K`

`{L_(sf)= 10 cm = 0.1 m`

`{T_(sf)= 1225 \°C`

`{T_(m)= ? \°C =` temperature at the interface

Solving for
`{T_(m)` will give the temperature at the interface:

`(q)/(A)=(k_(sf) )/(L_(sf) )(T_(sf) -T_(m))`

`5000=(1.4)/(0.1)(1225-T_(m)})`

`1225 - T_(m) = 357`

`T_(m)=868`