Volume 15, Issue Supplement 1, August 2008, Pages 69 - 76
Alternate Derivation of the Critical Value of the Frank-Kamenetskii Parameter in Cylindrical Geometry
Authors
Charis Harely, Ebrahim Momoniat
Corresponding Author
Charis Harely
Available Online 1 August 2008.
- DOI
- 10.2991/jnmp.2008.15.s1.6How to use a DOI?
- 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, ? = 2, is obtained in a very natural way.
- Copyright
- © 2008, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Charis Harely AU - Ebrahim Momoniat PY - 2008 DA - 2008/08/01 TI - Alternate Derivation of the Critical Value of the Frank-Kamenetskii Parameter in Cylindrical Geometry JO - Journal of Nonlinear Mathematical Physics SP - 69 EP - 76 VL - 15 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2008.15.s1.6 DO - 10.2991/jnmp.2008.15.s1.6 ID - Harely2008 ER -