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 T_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 = 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.

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Air Te, h Plastic coating (k, α, Τ) Wood panel