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 plate (r = 7830 kg/m3, Cp = 550 J/kg K, k = 48 W/m K). The plate initially is at 200 oC and is to be heated to a minimum temperature of 550 oC. Heating is effected in a gas-fired furnace where the products of combustion at T[infinity] = 800 oC maintain a convection heat transfer coefficient of h = 250 W/m K on both surfaces of the plate.

(a) Calculate the Biot number for this heat transfer process.
(b) Can the lumped-capacitance approximation be used to analyze this transient heat transfer process?
(c) Assuming that the lowest temperature in the plate is at its midplane, calculate the dimensionless temperature at the midplane of the plate when temperature is 550 oC
(d) Using the one-term approximate solution for convective heat transfer into a semi-infinite medium, calculate the Fourier number required to achieve a temperature of 550 oC in the steel
(e) Calculate the time required to achieve a temperature of 550 oC at the midplane of the plate.