Criticality and Thermal Distribution of Combustion-Reaction in a Concentric Cylinder with Heat Loss and Bimolecular Kinetics

In contrast to existing studies on thermal criticality, which are limited to single-cylinder configurations, this study examines bimolecular exothermic reactions in finite concentric cylinders subject to asymmetric and Neumann boundary conditions. The nonlinear energy equation is first nondimensionalised and then solved using the Weighted Residual Collocation Method (WRCM) with a six-term polynomial trial function implemented in Maple. The accuracy and convergence of the WRCM are verified by comparison with the classical fourth-order Runge–Kutta (RK4) method, yielding errors below 10−7 throughout the computational domain. The results indicate that an increase in the Frank– Kamenetskii parameter causes a rapid rise in temperature, leading to eventual thermal runaway at criticality values of 0.780 for asymmetric conditions and 1.650 for Neumann conditions. Higher heat-loss parameters improve thermal stability by enhancing boundary heat dissipation, whereas the initiation parameter significantly influences reaction sensitivity and temperature gradients near the core. Furthermore, asymmetric boundary conditions generate higher peak temperatures than Neumann conditions, owing to reduced heat removal. These findings provide useful design insights for combustion chambers, catalytic reactors, and energy storage systems, highlighting how appropriate control of heat dissipation can mitigate thermal runaway and improve operational safety.