Explosions may occur owing to thermal and branching effects in combustion processes. The ignition limits of a system are affected by the presence of natural convection, which develops inevitably in terrestrial systems. This work investigates the explosion criterion, through parametric sensitivity, for systems with a Gray and Yang, three-step, non-isothermal branching reaction scheme with natural convection. Ignition is identified with the maximum sensitivity of the non-dimensional temperature rise (T'(max)) to the ratio of branching and termination reaction rates (tau(b)/tau(t)). The effects of self-heating, branching and natural convection on the time to ignition are analysed. A value of dimensionless temperature rise T' = 5 is found to be an appropriate explosion criterion for this system. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.