Strongly exothermic explosions in a cylindrical pipe: a case study of series summation technique

In this paper, the steady state solutions for the strongly exothermic decomposition of a combustible material uniformly distributed in a heated cylindrical pipe under Bimolecular, Arrhenius and Sensitised reaction rates, neglecting the consumption of the material are examined. Analytical solutions are constructed for the governing nonlinear boundary-value problem using perturbation technique together with a special type of Hermite-Padé approximants and important properties of the temperature field including bifurcations and thermal criticality are discussed.