A steel plate having a thickness of 100 mm is suddenly exposed to a hot gas at 1000 C in a furnace. One surface of the plate is heated while the other surface of the plate can be approximated to be adiabatic. The initial temperature of the steel plate is 20 C. The thermal conductivity and thermal diffusivity of the steel plate are 34.8 W/m K and 0.555 x 10^-5 m²/s respectively. The convective heat-transfer coefficient is 174 W/m² K.

a) Determine the time necessary to raise the surface temperature of the steel plate to 500 C.

b) Determine the maximum temperature difference in the cross-section of the steel plate at the time evaluated in part a) above.

c) Determine the heat energy transferred to the steel plate per unit wall surface area by the time evaluated in part a) above.