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 air flow 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°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 = 200 W/m2 · K? What is the corresponding value of the interface temperature? The thermal conductivity and diffusivity of the plastic are k = 0.25 W/m · K and a = 1.20 X 10-7 m2/s, respectively.