Steady state solutions for a thermal explosion in a cylindrical vessel

C. Harley, E. Momoniat

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)831-841
Number of pages11
JournalModern Physics Letters B
Volume21
Issue number14
DOIs
Publication statusPublished - 10 Jun 2007
Externally publishedYes

Keywords

  • Blow-up
  • Lane-Emden equation
  • Non-local symmetry

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

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