## Steel bar to make a hard surface, Mathematics

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Take the carburizing of a steel bar to make a hard surface. To obtain the desired hardness, we require to control the diffusion of carbon into the surface and the phases obtained during heat treatment and cooling. The base steel has a composition of 0.2 wt%C. For mathematical simplicity we took an infinitely thick bar and a diffusivity that does not vary with concentration. All concentrations are in weight percent.

A) Use the graph you have make to estimate the times needed for a diffusion depth of 600 microns (i.e. 0.6 mm) for each of the three temperatures.

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