The gas flow in the gravity field through the porous objects with heat sources, which may arise from natural or man-caused disasters, is investigated when the object's outlet is partially closed. The mathematical model and original numerical method, based on the combination of explicit and implicit finite difference schemes, are developed for researching the time-dependent regimes of the gas flow through two-dimensional porous objects with heat sources. The influence of partial closure of the object's outlet on the cooling process of the axisymmetric porous objects with a non-uniform distribution of heat sources is analyzed by means of computational experiment. (C) 2014 Elsevier Ltd. All rights reserved.