The study of heat transfer in a stockpile of reactive materials, modeled in a cylindrical domain, is carried out in this article. The reactive cylinder is assumed to lose heat to the surrounding environment by convection and radiation. The complicated combustion process results with nonlinear interactions, and therefore, the ordinary differential equation (ODE) governing the problem cannot be solved exactly, but numerically. The Runge-Kutta-Fehlberg (RKF45) numerical method is applied to solve the ODE. The solutions are expressed graphically and discussed accordingly. The results generally show that the reaction rate parameter increases the temperature of the system, whereas the radiation parameter reduces the temperature profiles thereof. © Published under licence by IOP Publishing Ltd.