A three dimensional mathematical model that considers the turbulent flow around compost piles disposed in fields is studied. The self-heating and self-ignition that occurs inside the compost pile is produced by biological activity and chemical oxidation that are included as source terms in the mathematical model. The model includes the unsteady solution of the turbulent flow field, the energy transport in the flow and the ensuing heat and mass transfer by convection over piles with several geometrical forms. The piles are treated as a porous medium in which the oxygen depletion and heat generation produced by aerobic bacteria and cellulose oxidation are also included. Turbulence is described with the k-epsilon model. The numerical values are obtained with the finite volume method and are validated through a comparison with studies in two dimensions that can be found in the references. The results also shed light over some new design criteria that are proposed in order to improve the storage capacity in the dump waste piles and to decrease the possibility of auto-ignition as mounds number, height of the pile and volume-area ratio V/A. (C) 2012 Elsevier Ltd. All rights reserved.