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The heat distribution and branched-chain thermal criticality for a combustible exothermic reaction is examined in this study. The reactive diffusion occurs in a cylinder with pre-exponential variable factor, and the ambient heat exchange is less than the system heat exchange. With material consumption, the reaction is stimulated by initiation rate, branched-chain steps, generalized Arrhenius reaction rate, and molecular diffusion. The mathematical model of this reaction results in a highly nonlinear ordinary differential equation with boundary conditions at the cylinder surface. An approximate solution to the transformed dimensionless nonlinear equation is provided using Collocation Weighted Residual Method (CWRM) and compared with numerical method. The results for the temperature distribution and criticality for dependent parameters are presented graphically. The results from this study will assist in understanding the correlation between the thermal/ignition branched-chain and traditional theory of thermal explosion.

On Criticality for a Branched-chain Thermal Reactive-Diffusion in a Cylinder