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Steady state solutions for a thermal explosion in a cylindrical vessel. (English) Zbl 1115.80005

Summary: Steady state solutions of a heat balance equation modeling a thermal explosion in a cylindrical vessel are obtained. The heat balance equation reduces to a Lane-Emden equation of the second-kind when steady state solutions are investigated. Analytical solutions to this Lane-Emden equation of the second-kind are obtained by implementation of the Lie group method. The classical Lie group method is used to obtain the well-known solution of Frank-Kamenetskii for the temperature distribution in a cylindrical vessel. Using an extension of the classical Lie group method a non-local symmetry is obtained and a new solution describing the temperature distribution after blow-up is obtained.

MSC:

80A25 Combustion
35K55 Nonlinear parabolic equations
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References:

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