The disappearance of criticality for small activation energy with arbitrary biot number
✍ Scribed by K.F. Fenaughty; A.A. Lacey; G.C. Wake
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 223 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0010-2180
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✦ Synopsis
For exothermic reactions obeying the Arrhenlus equation the critical conditions for thermal ignition are known to exist for activation energy E large enough satisfying e E RTa/E < err. This transition value e~ of e has values less than 0.25 in all geometries, (Boddington et al. [1]) and exactly 0.25 for the uniform temperature reactor (the Semenov case). The precise values of air and the corresponding values of the maximum dimensionless temperature 0 and the Frank-Kameuetskii parameter 6 (the transition values) were calculated for a slab by Boddington et al. [2] and Kordylewski [3] for infinite Biot number (Frank-Kameuetskii conditions). Kordylewski [3] gave a precise criterion for the appearance of these transition conditions and calculated the transition values for the other class A geometries of an infinite circular cylinder and a sphere, also for infmite Biot number. This criterion is modified here to the case of finite Biot number to obtain the transition values for a range of Biot numbers. The transition values are shown to match on to the values of the Semenov case for small values of the Biot number a as err = 0.25 -O(~2), 6tr = 4(/" + 1)a/e 2 + O(,~2), 0tr0r a = 4 + O(~), wherej = 0, 1,2 for slab, cylinder, and sphere, respectively.