Chapter 5, Problem 5.49P

Annealing is a process by which steel is reheated and then cooled to make it less brittle. Consider the reheat stage for a 100-mm-thick steel plate $\left(\rho =7830{\text{kg/m}}^{\text{3}},c=550\text{J/kg}\cdot \text{K,}k=48\text{W/m}\cdot \text{K}\right),$ which is initially at a uniform temperature of $T_i=200°\text{C}$ and is to be heated to a minimum temperature of $550°\text{C}\text{.}$ Heating is effected in a gas-tired furnace, where products of combustion at $T_{\infty }=800°\text{C}$ maintain a convection coefficient of $h=250{\text{W/m}}^{\text{2}}\cdot \text{K}$ on both surfaces of the plate. How long should the plate be left in the furnace?