A plastic coating is applied to wood panel by first depositing molten polymer on a panel and then cooling the surface of the polymer by subjecting it to air flow at 25oC. The heat of reaction associated with solidification of polymer may be neglected and the plastic/wood interface may be assumed to be adiabatic. If the thickness of the coating is 2 mm and it has an initial uniform temperature of 200oC; (a) how long will it take for the surface to achieve a safe-to-touch temperature of 42oC if the convection coefficient is h = 200 W/m2-K? (b) What is the corresponding temperature at the plastic/wood interface? The thermal conductivity and diffusivity of the plastic are 0.25 W/m-K and 1.20 x 10-7 m2/s, respectively.