$4-94$ Refractory bricks are used as linings for furnaces, and they generally have low thermal conductivity to minimize heat loss Page $306$ through the furnace walls. Consider a thick furnace wall lined with refractory bricks $(k=1\mathrm{.}0\frac{W}{m}*K$ and

$=5\mathrm{.}08{10}^{-7}\frac{m^2}{s}),$ where initially the wall has a uniform temperature of $15C.$ If the wall surface is subjected to uniform heat flux of $20k\frac{W}{m^2},$ determine the temperature at the depth of $10$ cm from the surface after an hour of heating time.