Carburization is a heat treatment process where a component is placed in a carbon rich atmosphere, at an elevated temperature. During the process, carbon diffuses into the surface of the component, and the carbon concentration in the component changes with time as carbon continues to diffuse to the interior. The process of carburization is modeled using Fick’s second law of diffusion. The carbon concentration c during carburization depends on position and time as c = c(X,t), where X denotes material coordinates, and t is time. The carbon concentration represents the mass fraction of carbon, and it is thus dimensionless. The carbon concentration is governed by the following equation:

where D is the diffusion coefficient, or diffusivity. The diffusivity can be specified directly, or it can be modeled using an Arrhenius expression of the form

where D0 is a pre-exponential factor, QD is an activation energy, and R is the gas constant.