Alternate derivation of the critical value of the frank-kamenetskii parameter in cylindrical geometry

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Abstract

Noether's theorem is used to determine first integrals admitted by a generalised Lane-Emden equation of the second kind modelling a thermal explosion. These first integrals exist for rectangular and cylindrical geometry. For rectangular geometry the first integrals show the symmetry of the temperature gradients at the rectangular walls. For a cylindrical geometry the first integrals show the dependence of the critical parameter on the temperature gradient at the cylinder wall. The well known critical value for the Frank-Kamenetskii parameter, δ = 2, is obtained in a very natural way.

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Harley, C., & Momoniat, E. (2008). Alternate derivation of the critical value of the frank-kamenetskii parameter in cylindrical geometry. In Journal of Nonlinear Mathematical Physics (Vol. 15, pp. 69–76). https://doi.org/10.2991/jnmp.2008.15.s1.6

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