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Search name	Searched On	Run search
[Keyword: Blow-up] AND [All Categories: Nanotechnology & Nanoscience] (2)	27 Mar 2025	Run
[Keyword: Implant] AND [All Categories: Ear, Nose & Throat] (1)	27 Mar 2025	Run
[Keyword: Blow-up] AND [All Categories: Statistical Physics, Complexity and Nonline... (2)	27 Mar 2025	Run
[Keyword: Elastic] AND [All Categories: Mechanical Engineering] (1)	27 Mar 2025	Run
[Keyword: Implant] AND [All Categories: Innovation / Technology / Knowledge / Infor... (3)	27 Mar 2025	Run

articleNo Access
A THERMAL EXPLOSION IN A CYLINDRICAL VESSEL: A NON-CLASSICAL SYMMETRY APPROACH
- E. MOMONIAT
International Journal of Modern Physics B10 Jun 2009
Preview Abstract
New solutions to the Frank-Kamenetskii partial differential equation modeling a thermal explosion in a cylindrical vessel are obtained. The classical Lie group method is used to determine an approximate solution valid in a small interval around the axis of the cylinder. Non-classical symmetries are used to determine solutions valid after blow-up. These solutions have multiple singularities. Solutions are plotted and analyzed.
articleNo Access
STEADY STATE SOLUTIONS FOR A THERMAL EXPLOSION IN A CYLINDRICAL VESSEL
- C. HARLEY and
- E. MOMONIAT
Modern Physics Letters B10 Jun 2007
Preview 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.

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