We present a high-level overview of a modeling approach based on a non-equilibrium, multicomponent, thermodynamic formulation, we have dubbed the Gibbs formulation, and discuss its application to this complex problem of aluminum combustion in an oxidizing atmosphere. The Gibbs formulation can be thought of as a generalization of the classical non-equilibrium formulations used in gaseous, multicomponent combustion theory, but expanded to mixtures with simultaneously present concentrations of solids, liquids and gases. We present an example of this approach applied to the ignition and burning of a nano-sized aluminum slab coated by a thin alumina layer. The model considers up to six components: solid, liquid and gaseous aluminum, solid and liquid aluminum oxide (alumina), and oxygen. We discuss the many different behaviors and possible regimes of combustion, that depend on what is assumed for the various diffusion and reaction rates.