Numerical exploration and thermal criticality of a dual exothermic reaction with radiative heat loss in co-axial cylinder configurations

Due to their enormous importance, efficient and optimal performance in industrial applications heavily rely on the proper handling, maintenance, and management of reacting systems, particularly exothermic reactions. This study aims to quantitatively analyze the impact of thermal characteristics on temperature in a dual exothermic reaction with radiative cooling within co-axial cylinders, employing three distinct boundary conditions. Appropriate similarity variables were employed to transform the dimensional equation in a cylindrical coordinate system into dimensionless differential equation. The problem is solved using the iterative analytical method, which relies on the principle of weighted residuals. The approach's validity is demonstrated by observing the convergence of results and comparing it with that of the Runge-Kutta method in Maple mathematical software. An in-depth investigation and discussion were conducted on the impact of significant thermal parameters and critical conditions on temperature. The physical features have a similar effect on the temperature for all three boundaries, although with varying degrees of impact: increase in the initiation rate (ρ), Frank-Kamenetskii (α), second step (β)and reaction kinetics ( n ) parameters enhanced the temperature profile of the reacting system, while a fall in the temperature was observed with an increase in the radiation parameter. Furthermore, conditions that could trigger an uncontrollable reaction are discovered and it was observed that an increase in the activation energy parameter (δ)delayed possible explosion within the system, on the other hand an increase in β hasten possible explosion in the system. Therefore, engineers should be aware of sensitive thermal factors and take proper cognizance during design. They should also include a mechanism that considers the cooling of the system.