The effect of natural convection induced thermal explosion in a cylindrical reactor with temperature-dependent thermal conductivity

This paper examines the stability and effects of thermal explosions in porous, cylindrical reactors that experience natural convection and have temperature-dependent thermal conductivity. The momentum and energy equations are constructed using the Darcy-Brinkman theory and the Boussinesq hypothesis. Using Lie group’s symmetry, the energy and momentum equations are translated into ordinary differential equations and are then solved using the regular perturbation approach. The parameter defining the critical region for thermal explosions, the Frank- Kamenetskii parameter, is calculated. A linear stability analysis is carried out to evaluate the ignition threshold. The details of stability boundary effects of different values of the thermal conductivity and Darcy number of the porous medium are thoroughly studied. It is demonstrated that stability margins are enlarged for high values of the thermal conductivity parameter and the system is unstable for higher Darcy numbers. All the analytical results were found to be in observational agreement in different system limits, further confirmed by TikZ simulations.