A mathematical model for the case hardening of steel is presented. Carbon is dissolved in the surface layer of a low-carbon steel part at a temperature sufficient to
render the steel austenitic, followed by quenching to form
a martensitic microstructure. The model consists of a nonlinear evolution equation for the temperature, coupled
with a nonlinear evolution equation for the carbon concentration, both coupled with two ordinary differential equations to describe the evolution of phase fractions.
We investigate questions of existence and uniqueness of a solution and finally present some numerical simulations.