Chapter 5, Problem 5.52P

Steel is sequentially heated and cooled (annealed) to relieve stresses and to make it less brittle. Consider a 100-mm-thick plate $\left(k=45\text{W/m}\cdot \text{K,}\rho =7800{\text{kg/m}}^{\text{3}},c_p=500\text{J/kg}\cdot \text{K}\right)$ that is initially at a uniform temperature of $300°\text{C}$ and is heated (on both sides) in a gas-fired furnace for which $T_{\infty }=700°\text{C}$ and $h=500{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ How long Will it take for a minimum temperature of $550°\text{C}$ to be reached in the plate?