A plastic coating is applied to wood panels by first depositing molten polymer on a panel and then cooling the surface of the polymer by subjecting it to airflow at 25∘C. As first approximations, the heat of reaction associated with solidification of the polymer may be neglected and the polymer/wood interface may be assumed to be adiabatic. If the thickness of the coating is L=2 mm and it has an initial uniform temperature of Ti=200∘CT i =200 ∘ C, how long will it take for the surface to achieve a safe-to-touch temperature of 42∘C if the convection coefficient is h=200W/m2⋅Kh=200W/m 2⋅K? What is the corresponding value of the interface temperature? The thermal conductivity and diffusivity of the plastic are k=0.25W/m⋅Kk=0.25W/m⋅K and α=1.20×10−7m2/s m 2/s, respectively.