## 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 language | English |
---|---|

Pages (from-to) | 831-841 |

Number of pages | 11 |

Journal | Modern Physics Letters B |

Volume | 21 |

Issue number | 14 |

DOIs | |

Publication status | Published - 10 Jun 2007 |

Externally published | Yes |

## Keywords

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

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Condensed Matter Physics