A steel is hardened using a high temperature carburising process.

The evolution of the carbon concentration with depth d and time t

is given by the erf function:

cs-cd/cs-co = erf ( d/2 SQRT Dt)

Where, C, Cd and C, respectively represent the concentrations

of the diffusing species at the surface, deep d after time t and in

the bulk. The erf function has the following values:

x erfx

0.3 0.329

0.35 0.379

0.4 0.428

0.45 0.475

0.5 0.520

Consider an initial carbon concentration of 0.15 wt%, if the surface

concentration is suddenly brought to 0.9 wt%, how long will it take

to achieve a 0.6 wt% at a position d=0.2 mm inside the metal?

(Assume a diffusion coefficient of carbon into steel of

2x10^-7 cm^2/s).