a mild steel component in a form of a finite slab with a thickness of 2L=2.5 mm is to be hardened by packing it in a carbonaceous material in a furnace for a predetermined time. the uniform initial carbon concentration of the slab is 0.15 percent by mass. the component is now packed in carbonaceous material on both sides and is placed in a high temperature furnace. the diffusion coefficient of carbon in steel at the furnace temperature is given to be constant at 4.8x10^-10 m^2/s, and the equilibrium concentration of carbon in the iron at the interface is determined from the equilibrium data to be 1.2 percent by mass.
if the component is kept in the furnace for 30 minutes, determine the mass concentration of carbon 0.5 mm below the surface.