$($b$)$ A furnace wall comprises of three layers: $13\mathrm{.}5$ cm thick inside layer of fire brick, $7\mathrm{.}5$ cm

thick middle layer of insulating brick and $11\mathrm{.}5$ cm thick outside layer of red brick. The furnace

operates at $860C$ and it is anticipated that the outside of this composite wall can be maintained

at $30C$ by the circulation of air. The area of the furnace wall is $10m^2.$ Assuming close bonding

of layers at their interfaces, find the rate of heat loss from the furnace and the wall interface

temperatures.

$[$Note: Thermal conductivities of fire, insulating and red bricks are $1\mathrm{.}2\frac{W}{m}C,0\mathrm{.}14\frac{W}{m}C$

and $0\mathrm{.}85\frac{W}{m}C$ respectively.$]$