Heat sterilization of lumber, timbers and pallets is used to kill insects to prevent their transfer between countries in international trade. Consider hot air heating that maintains the surface temperature at $70C.$ The boards are stacked outside and in the winter time they can be considered to be at $0C$ when they are brought in for heating.

$($a$)$ Calculate the time for the slowest heating point to reach sterilization temperature of $56C$ for a $2\mathrm{.}54cm$ thick board.

$($b$)$ Calculate the heating time when four such boards are stacked together. Thermal diffusivity of the wood is $8\mathrm{.}5{10}^{-8}\frac{m^2}{s}.$