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Numerical calculation of critical points for a slab with partial insulation

โœ Scribed by P. Greenway; A. Spence

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
735 KB
Volume
62
Category
Article
ISSN
0010-2180

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โœฆ Synopsis

Numerical solutions of a nonlinear partial differential equation arising in thermal explosion theory are obtained for a finite rectangular strip domain with mixed boundary conditions. Critical points in the solution (marking loss of stability and loss of criticality) are computed directly for the case of a self-heating slab with its upper and lower surfaces partially insulated, retaining the full Arrhenius rate term. For the special case of the Frank-Kamenetskii approximation it is shown numerically that the critical value of the rate parameter satisfies

where he(0) = 0.878 and ~ is the ratio of the insulation width to slab thickness.

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