Chapter 5, Problem 5.59P

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 $25°\text{C}\text{.}$ 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 $L=2\text{mm}$ and it has an initial uniform temperature of $T_i=200°\text{C,}$ how long will it take for the surface to achieve a safe-to-touch temperature of $42°\text{C}$ if the convection coefficient is $h=200{\text{W/m}}^{\text{2}}\cdot \text{K?}$ What is the corresponding value of the interface temperature? The thermal conductivity and diffusivity of the plastic are $k=0.25\text{W/m}\cdot \text{K}$ and $\alpha =1.20\times {10}^{-7}{\text{m}}^{\text{2}}\text{/s},$ respectively.