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Criticality in Reactors under Domain or External Temperature Perturbations

Van de Velde, Eric F. and Ward, Michael J. (1991) Criticality in Reactors under Domain or External Temperature Perturbations. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 434 (1891). pp. 341-367. ISSN 1364-5021. https://resolver.caltech.edu/CaltechAUTHORS:20150121-124136794

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Abstract

The conditions for the onset of thermal runaway in reactors with small non uniformities is investigated. The reaction is modelled by an Arrhenius heat generation term with a finite activation energy and the dimensionless temperature, u_o, is taken to satisfy a nonlinear equation of the form Δu_0+λ_0F(u_0) = 0, xєD; ∂_vu_0+bu_0 = 0, xє∂D. We investigate three classes of perturbations of this problem. First, we treat a small temperature variation maintained on the boundary of the domain. Secondly, we consider a small distortion of the boundary of a circular cylindrical domain, and thirdly, we analyse the effect of a small hole in the domain. In each case we derive asymptotic expansions for the critical Frank-Kamenetskii parameter, λ_c(є), where є is a measure of the size of the perturbation. A numerical scheme is then used to determine numerical values for the coefficients in the asymptotic expansion of λ_c. Finally, some of the asymptotic results are compared with corresponding numerical results obtained from a full numerical solution of the perturbed problem.


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http://www.jstor.org/stable/51834?seq=1#page_scan_tab_contentsJSTORArticle
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Additional Information:© 1991 The Royal Society. Received 22 October 1990; accepted 22 January 1991. The authors thank Professor Joel N. Franklin and Dr David L. Harrar II for helpful discussions on the material in §3.3. We also thank Professor Joseph B. Keller for his helpful comments on the manuscripts. M.J.W. is very grateful to the members of the Math Science, Department at the I.B.M. Thomas Watson Research Laboratory for donating computer time for this project. This work was supported by the NSF under Cooperative Agreement no. CCR-8809615 and by AFSOR and ONR.
Funders:
Funding AgencyGrant Number
NSFCCR-8809615
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
Issue or Number:1891
Record Number:CaltechAUTHORS:20150121-124136794
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150121-124136794
Official Citation:Criticality in Reactors under Domain or External Temperature Perturbations (pp. 341-367) Eric F. Van De Velde and Michael J. Ward Stable URL: http://www.jstor.org/stable/51834
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:53948
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 Jan 2015 21:21
Last Modified:03 Oct 2019 07:53

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