Criticality branched-chain of thermal reaction with harmonically varying time-periodic surface heating and heat loss

This study examines the thermal ignition characteristics of a branched-chain diffusion-reaction subjected to boundary surface periodic time heating. The model focuses on a slab of combustible species in which the heat generation is influenced by a branched-chain exothermic reaction autocatalytic, characterized by reaction kinetics and higher temperature sensitivity, capable of thermal explosion. An unsteady nonlinear heat conductive equation with Arrhenius-type source term is developed, and the periodic heating effects for the thermal runaway onset are analysed. Temperature distribution and criticality conditions are investigated through a finite semi-implicit difference method on the non-dimensional partial derivative equation. Key dimensionless terms are studied to describe safe and explosive regimes, and the results depict that periodic heating enhances thermal instability due to thermal wave amplitude and phase. It is noticed that high frequencies stabilize the system, boosting Frank-Kamenetskii’s critical term, while large amplitude heating prompts premature ignition. Thermal runaway is caused by exothermic heat generation and the dominance of heat diffusion in branched-chain autocatalytic kinetics. These findings are critical for the development of safety protocols in systems exposed to periodic heating, including catalytic reactors, solar-thermal absorbers, and energy-storage devices.