Question

A furnace wall is to be built of 20-cm firebrick and building (structural) brick of same thickness. The thermal conductivities of fire brick and building brick are 1.6 and 0.7 W/m.K , respectively. The inner surface of the firebrick is at 980 °C, the outer surface of the structural brick is at 30 °C. The heat flux and the temperature of the brick interface are..

Answer 1

q=2313.04
`W/m^2`

T=690.86°C

Step-by-step explanation:

Given that

Thickness t= 20 cm

Thermal conductivity of firebrick= 1.6 W/m.K

Thermal conductivity of structural brick= 0.7 W/m.K

Inner temperature of firebrick=980°C

Outer temperature of structural brick =30°C

We know that thermal resistance

`R=(t)/(KA)`

These are connect in series

`R=\left((t)/(KA)\right)_(fire)+\left((t)/(KA)\right)_(struc)`

`R=(0.2)/(1.6A)+(0.2)/(0.7A)\ K/W`

`R=(23)/(56A)\ K/W`

Heat transfer

`Q=(\Delta T)/(R)`

`Q=56A* (980-30)/(23)\ W`

So heat flux

q=2313.04
`W/m^2`

Lets temperature between interface is T

Now by equating heat in both bricks

`(980-T)/((0.2)/(1.6A))=(T-30)/((0.2)/(0.7A))`

So T=690.86°C