A mathematical model relating heat and mass transfer in compost pile disposal in field is presented. The unsteady non linear mathematical diffusion model is solved through the finite volume method. The volumetric heat generation caused by the action of aerobic bacteria and by oxidation of cellulose in a porous media is incorporated as a function of the means moisture by a source term. Field studies in compost pile exposed to atmospheric conditions were made trying to reproduce the conditions in which self-heating and combustion may take place. Inside a compost pile made of solid residues obtained after municipal waste water treatment, temperature changes, oxygen contents and moisture were measured in time and depth. The mathematical model and numerical simulations in two dimensions, describe the internal changes of heat, oxygen and moisture observed in fields conditions and with this quantify the effects of the moisture in the temperature and oxygen concentration. (C) 2011 Elsevier Ltd. All rights reserved.