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 (p = 7830 kg/m³, c = 550 J/kg ∙ K, k = 48 W/m ∙ K), which is initially at a uniform temperature of T_j = 200°C and is to be heated to a minimum temperature of 550°C. Heating is effected in a gas-fired furnace, where products of combustion at T_∞ = 800°C maintain a convection coefficient of h = 250 W/m₂ ∙ K on both surfaces of the plate. How long the plate should be left in the furnace?