Chapter 5, Problem 5.50P

Consider an acrylic sheet of thickness $L=5\text{mm}$ that is used to coat a hot. isothermal metal substrate at $T_h=300°\text{C}\text{.}$ The properties of the acrylic are $\rho =1990{\text{kg/m}}^{\text{3}},c=1470\text{J/kg}\cdot \text{K,}$ and $k=0.21\text{W/m}\cdot \text{K}\text{.}$ Neglecting the thermal contact resistance between the acrylic and the metal substrate, determine how long it will take for the insulated back side of the acrylic to reach its softening temperature, $T_{\text{soft}}=90°\text{C}\text{.}$ The initial acrylic temperature is $T_i=20°\text{C}\text{.}$