The spontaneous ignition of coal stockpiles is a serious economic and safety problem. This phenomenon is analyzed using the approach of modern reaction engineering, which is made challenging by the nonlinear interactions of chemical reaction, heat transfer, and buoyancy-driven flows within and around the stockpile. A model developed represents reaction and transport within a realistically-shaped stockpile and transport and flow in the surrounding air. A new methodology based on the Galerkin finite-element method (Salinger, 1993b) allows for efficient solution of flows in both porous and open domains. Bifurcation analysis is used to track steady-state model solutions of relevant parameters, such as the Damkohler number (dimensionless reaction rate), Rayleigh number (dimensionless driving force for buoyant flow), and dimensionless permeability of the stockpile. The solutions provide an understanding of the roles of various transport mechanisms on the ignition behavior and nonlinear coupling between these mechanisms. Results clearly demonstrate the need for incorporating realistic descriptions of flow and transport in the surrounding air into the model.