Thermal explosions are often influenced by the complex interaction between transport and reaction phenomena. In particular, reactant consumption can promote safer, non-explosive operation conditions of combustion systems. However, in liquids or gases, the presence of forced convection can affect the behaviour of a system, instigating oscillations in the temperature, reactant concentration and velocity fields. This work describes the effect of reactant consumption on a simple, one-step, exothermic reaction occurring in a spherical reactor with both forced and natural convection, by means of numerical simulations. Regime diagrams characterised by ratios of timescales for each transport and reaction phenomena are presented and the explosion boundary is represented for several forced convection and reaction consumption intensities. Special attention is given to the oscillatory behaviour observed for moderate forced convection and oscillatory regions are represented on the regime diagrams. Parametric conditions for this new oscillatory regime are identified by extending the criticality condition developed by Frank-Kamenetskii for the effect of reactant consumption in diffusive systems to include the effects of both natural and forced convection.