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