Self-heating is commonly observed when organic materials such as biosolids, coal, food grains and compost are stockpiled. A convection-diffusion model is presented that accounts for the roles of advection and the transport of oxygen in the self-heating process, as well as the development of an empirical correlation between dimensionless Darcy number, Frank-Kamenetskii parameter and pile aspect ratio, to predict the critical permeability above which thermal runaway can be avoided. It is apparent that the permeability of the stockpile determines the likelihood of the thermal runaway. However, the solids that form a stockpile are poly-disperse and it is essential to determine an effective permeability. This has been achieved using experimental data on biosolids obtained from a wastewater treatment plant in Australia. With this method the model is used to demonstrate how the permeability of a stockpile might be adjusted to reduce the incidence of thermal runaway. (C) 2015 Elsevier Ltd. All rights reserved.