Effects of localised and global convection on thermal explosion in a parallel-plate geometry

Abstract

During an exothermic reaction in a fluid, convection may ensue on a local scale and then develop to the scale of the entire vessel. In this work, we study the effects of both localised and global convection on thermal explosions occurring between parallel plates. Analytical relations are derived for the various transitions in regimes of convective and thermal behaviours. We show that these relations agree well with previous numerical work and with new simulations in the present investigation. We also determine analytically the time for onset of convection, as well as the temperature increase at that time, for stable and explosive systems. The effects of the Prandtl number of the fluid on the transitions between regimes are noted.