3. (10%) A steel rod with an initial carbon concentration 0.2% by weight is to be hardened. An equilibrium concentration of carbon in iron at the phase interface of 1.5%. Calculate the time required for the location Imm below the surface to have a carbon mass concentration of 0.8%. The diffusion coefficient of carbon in steel at the process temperature is
. Hints: The similarity variable for this problem is
, and the erfc(x)= 1 - erf(x)