The influence of initial temperature-excess on critical conditions for thermal explosion

1985 ◽  
Vol 61 (3) ◽  
pp. 227-236 ◽  
Author(s):  
B.F. Gray ◽  
S.K. Scott
Keyword(s):  
Thermal Explosion ◽  
Initial Temperature ◽  
Critical Conditions ◽  
Temperature Excess

Critical Conditions of Thermal Explosion Considering Space-Temporal Nonlocality

2018 ◽  
Vol 61 (2) ◽  
pp. 252-256
Author(s):  
V. A. Kudinov ◽  
A. V. Eremin ◽  
I. V. Kudinov ◽  
V. V. Zhukov
Keyword(s):  
Thermal Explosion ◽  
Critical Conditions

Critical conditions for a thermal explosion in distributed systems with chain reactions

1988 ◽  
Vol 23 (4) ◽  
pp. 436-440
Author(s):  
V. T. Gontkovskaya ◽  
I. S. Gordopolova ◽  
A. N. Peregudov
Keyword(s):  
Distributed Systems ◽  
Thermal Explosion ◽  
Critical Conditions ◽  
Chain Reactions

scholarly journals Newton-variational solution of the Frank–Kamenetskii thermal explosion problem

1989 ◽  
Vol 67 (3) ◽  
pp. 442-445 ◽  
Author(s):  
Avygdor Moise ◽  
Huw O. Pritchard
Keyword(s):  
Thermal Explosion ◽  
Newton Method ◽  
Lower Bounds ◽  
Linear Equations ◽  
Spherical Geometry ◽  
Variational Solution ◽  
Upper And Lower Bounds ◽  
Dimensionless Temperature ◽  
Temperature Excess ◽  
Thermal Explosions

The Newton method was shown by Vatsya to be suitable for solving the generalised elliptic problem, and we show that this approach can be used to treat the Frank–Kamenetskii model of a thermal explosion, by using a variational solution of the sequence of linear equations that are encountered in the Newton method. Convergence to the desired solution is rapid in the case of spherical geometry. The method produces converging upper and lower bounds to the critical value of the dimensionless heat production rate, δc, and lower bounds to the dimensionless temperature excess distribution function θ and its critical form θc. Keywords: thermal explosions, Frank–Kamenetskii model.

scholarly journals Initiation of combustion waves in solids, and the effects of geometry

2001 ◽  
Vol 43 (1) ◽  
pp. 149-163 ◽  
Author(s):  
J. Brindley ◽  
J. F. Griffiths ◽  
A. C. McIntosh ◽  
J. Zhang
Keyword(s):  
Initial Temperature ◽  
Solid Medium ◽  
Boundary Surface ◽  
Critical Conditions ◽  
Main Concern ◽  
Initial Temperature Distribution ◽  
Combustion Waves ◽  
Finite Systems ◽  
The Waves ◽  
Central Sphere

AbstractIn a recent paper Weber et al. [9] examined the propagation of combustion waves in a semi-infinite gaseous or solid medium. Whereas their main concern was the behaviour of waves once they had been initiated, we concentrate here on the initiation of such waves in a solid medium and have not examined in detail the steadiness or otherwise of the waves subsequent to their formation. The investigation includes calculations for finite systems. The results for a slab, cylinder and sphere are compared.Critical conditions for initiation of ignition by a power source are established. For a slab the energy input is spread uniformly over one boundary surface. In the case of cylindrical or spherical symmetry it originates from a cylindrical core or from a small, central sphere, respectively. The size of source and reactant body is important in the last two cases. With the exception of the initial temperature distribution, the equations investigated are similar in form to those of Weber et al. [5,9] and, as a prelude to the present study, with very simple adaptation, it has been possible to reproduce the results of the earlier work. We then go on to report the result of calculations for the initiation of ignition under different geometries with various initial and boundary conditions.

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