A furnace wall consists of three layers $($i$)$ a layer of heat$-$resistance or refractory brick, $($ii$)$ a layer of insulating brick, and $($iii$)$ a steel plate, $0\mathrm{.}25$ in$.$ thick, for mechanical protection. Calculate the thickness of each layer of brick if the heat loss through the wall is $5000Bt\frac{u}{f}{t}^2*hr,$ assuming that the layers are in excellent thermal contact. The inside wall temperature of the furnace is $2500F,$ the temperature between refractory brick and insulating brick is $2000F$ and the outside temperature of the steel is $100F.$ The thermal conductivities of refractory brick, insulating brick and steel are $3\mathrm{.}85,1\mathrm{.}35$ and $26\mathrm{.}1Bt\frac{u}{f}t*hr*F.$

$10\%$

$T_0$:$2500F$

$T_1$:$2000F$

$T_3$:$100F$