Question $7(5$ Marks$)$

A reheating furnace will be operating at $1150C$ at steady state conditions. The outside temperature should not exceed $75C.$ The furnace walls are to be constructed using:

$20mm$ steel shell: $k=50W{m}^{-1}{K}^{-1}$

$200mm$ alumina bricks: $k=5\mathrm{.}5W{m}^{-1}{K}^{-1}$

$20mm$ glass wool: $k=0\mathrm{.}8W{m}^{-1}{K}^{-1}$

Calculate the interface temperature between the alumina bricks and glass wool.