Abstract
When any exothermic reaction proceeds in an unstirred vessel, natural convection may develop. The presence of this flow may alter the balance between heat generation and heat removal in the vessel, which ultimately governs whether the system will explode. Classical theories of thermal explosion have largely neglected the potentially important role that buoyant convection can play. More recently, numerical investigations of the effects of natural convection on thermal explosion have considered reactors where the temperature of the wall of the vessel is held constant. Thus, there is a physically unrealistic, infinitely fast heat transfer between the wall and the surrounding environment. In reality, there will be heat transfer resistances associated with conduction through the wall of the vessel and due to convective transfer from the surface arising from the local environmental conditions. These additional modes of heat transfer have the potential to fundamentally alter the rate of heat transfer from the hot zone in the vessel, to the cooler environment. This work presents a numerical study of thermal explosion in a spherical reactor under the influence of natural convection and external heat transfer, which neglects the effects of consumption of reactant. Simulations were performed to examine the changing behaviour of the system as the intensity of convection, as characterised by the Rayleigh number, and the importance of external heat transfer, as characterised by the Biot number, were varied. It was shown that the temporal development of the maximum temperature in the vessel was qualitatively similar as the Rayleigh and Biot numbers were varied. It has been shown that the maximum dimensionless temperature achieved in a non-explosive reaction on the explosion boundary increases from 1 in the well mixed limit to its constant wall temperature value asymptotically. For Bi < ~ 10, the maximum temperature varies little with Rayleigh number, but interestingly is lower for higher values of Ra. This is in contrast to what is observed at higher Bi where more intense natural convection means that higher temperatures can be sustained in non-explosive cases. Importantly, this variation in maximum temperature achieved in stable systems means that explosion criteria based on the maximum temperature achieved in the reactor may be inappropriate for systems with significant external heat transfer. Additionally, regions of parameter space where explosions occurred were identified. It was shown that reducing the Biot number increases the likelihood of explosion and reduces the stabilising effect of natural convection. The effects of varying important process parameters, such as the size of the vessel and the initial temperature and pressure of the gas on the tendency to explode are also shown. Finally, the results of the simulations were shown to compare favourably with analytical predictions in the classical limits of Semenov and Frank-Kamenetskii. Name of conference Hazards 26