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The aim of this work is to apply the homotopy perturbation method for solving the steady state equations of the exothermic decomposition of a combustible material obeying Arrhenius, Bimolecular, and Sensitised laws of reaction rates. These equations are formulated on some Class A geometries (an infinite cylinder, an infinite slab, and a sphere). We also investigate the effect of Frank-Kamenetskii parameter on bifurcation and thermal criticality by means of the Domb-Sykes graphical method.