The brickwork of a furnace is built up of layers of fire clay and red brick with the space between them filled with crushed brick. The thickness of the fire clay layer is $120mm,$ that of the filling is $50mm$ and the red brick is $250mm.$ The conductivities are $0\mathrm{.}93,0\mathrm{.}13,0\mathrm{.}7\frac{W}{m}K$ respectively. What should be the thickness of the red brick layer if the Sbricks are laid without filling and the heat transfer rate remains the same?

$[6$ Marks$]$