The spontaneous ignition of coal stockpiles is a serious economic and
safety problem. This phenomenon is analyzed using the approach of mode
rn reaction engineering, which is made challenging by the nonlinear in
teractions of chemical reaction, heat transfer, and buoyancy-driven fl
ows within and around the stockpile. A model developed represents reac
tion and transport within a realistically-shaped stockpile and transpo
rt and flow in the surrounding air. A new methodology based on the Gal
erkin finite-element method (Salinger, 1993b) allows for efficient sol
ution of flows in both porous and open domains. Bifurcation analysis i
s used to track steady-state model solutions of relevant parameters, s
uch as the Damkohler number (dimensionless reaction rate), Rayleigh nu
mber (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 demo
nstrate the need for incorporating realistic descriptions of flow and
transport in the surrounding air into the model.