On the crossing of intermediate unstable steady state solutions for thermal ignition in a sphere

R. O. Weber, G. C. Wake, H. S. Sidhu, G. N. Mercer, B. R. Gray, W. Derrick, E. Balakrishnan

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Abstract

Steady state solutions for spontaneous thermal ignition in a unit sphere are considered. The multiplicity of unstable, intermediate, steady state, temperature profiles is calculated and shown for selected parameter values. The crossing of the temperature profiles corresponding to the unstable, intermediate, steady states is exhibited in a particular case and is proven in general using elementary ideas from analysis. Estimates of the location of crossing points are given.

Original languageEnglish
Pages (from-to)77-85
Number of pages9
JournalANZIAM Journal
Volume43
Issue number1
Publication statusPublished - 2001

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ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Weber, R. O., Wake, G. C., Sidhu, H. S., Mercer, G. N., Gray, B. R., Derrick, W., & Balakrishnan, E. (2001). On the crossing of intermediate unstable steady state solutions for thermal ignition in a sphere. ANZIAM Journal, 43(1), 77-85.