The critical conditions for thermal explosion in a system heated at a constant rate

We have analyzed the condition needed for thermal explosion to occur in a solid sample when the temperature of the vessel walls is raised at a constant rate. We have developed a dimensionless model that allows its direct comparison with an isoperibolic system (constant vessel wall temperature). We have obtained an analytical expression for the critical condition as a function of the system parameters. Our solution takes into account reactant consumption and covers different geometries: thin film, finite and infinite cylinder. The critical condition has been validated with numerical simulations and experiments. We show that, compared to the isoperibolic system, thermal explosion is a little bit more difficult to achieve under constant heating conditions. Besides, we show that thermal explosion on submicrometric films is nearly impossible.