Plans to build a furnace include a layer of firebrick $($k $=1\mathrm{.}5)$ on the inside, covered with a

$22$ cm layer of insulating brick $($k $=0\mathrm{.}15)$ and $15$ cm exterior of building brick $($k $=1\mathrm{.}0).$ The

furnace interior will be as high as $1100\backslash$deg C$,$ and the exterior should hold at $60\backslash$deg C$.$ Determine

the firebrick thickness needed to keep the insulating brick below $900\backslash$deg C$.$ In that case, what

would be the interior face temperature of the building brick?