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Consider a carburization process where carbon is diffused into a steel block at 930 °C. The steel contains 0.1 wt% C initially and the carbon content is raised (Fig. 2) as a result of the carburization process. The carbon concentration is maintained at 1 wt.% at the surface for all time t > 0. Assume carbon diffusivity D = 1.4 x 10-7 cm²/s for all compositions. carburizing gas carbon iron surface Cs Co 0 х Figure 2: Carbon diffusion in iron during a carburization process.
C (10 marks) The solution to the carbon concentration under the surface during carbur- ization is given as Ct = Cs – (Cs – Co)erf - 4Dt where C, and C, are the carbon concentrations at the carburization surface and at a depth of x under the surface. Co is the initial carbon concentration in the steel block. Calculate the time required to achieve 0.9wt.% carbon concentration at a depth of 0.05 cm? You can assume that the steel block is very thick and the error function is tabulated below. 2 0.09879 1/9 erf(2) 0.1 0.5 0.9 0.1124629 0.5205 0.7969