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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.
We study a mathematical model for laser-induced thermotherapy,
a minimally invasive cancer treatment. The model consists of a
diffusion approximation of the radiation transport equation
coupled to a bio-heat equation and a model to describe the
evolution of the coagulated zone. Special emphasis is laid on
a refined model of the applicator device, accounting for the
effect of coolant flow inside. Comparisons between experiment
and simulations show that the model is able to predict the
experimentally achieved temperatures reasonably well.