A steel billet is to be heat treated by immersion in a molten salt bath. The billet is 5 cm square and 1 m long. Prior to immersion in the bath, the billet is at a uniform temperature of 20°C. The bath is at 600°C and the heat transfer coefficient at the billet surface is 20 W/(m2K). Plot the temperature at the center of the billet as a function of time. How much time is needed to heat the billet center to 500°C? Use an implicit difference scheme with node spacing of 1 cm. The thermal conductivity of the steel is 40 W/(m K) and the thermal diffusivity is 1 \ 10–5 m2/s.
GIVEN
Steel billet undergoing heat treatment