Refinement in the Mathematical and Numerical Treatment of the Internal Oxidation of Alloys

When oxygen dissolves from atmosphere and diffuses into an alloy during oxidation, the less noble alloy components may react to form oxide particles within the metal. This process is termed internal oxidation. Classical approaches to describe this phenomenon were derived under many strong simplifications such as constant diffusion coefficients, certain boundary conditions and semi-infinite sample. The presented general approach is based on the finite difference solution of the general diffusion equations coupled through the stoichiometry of reaction between oxygen and the considered element. The main enhancement is the consideration of concentration dependent diffusion coefficients, concentration dependent source terms and arbitrary time-dependent boundary conditions formulated as a concentration, a flux or mixed conditions. Furthermore, finite dimension of the specimen is incorporated. This general treatment also allows for the incorporation of the energy balance.