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CALCULATION OF CRITICAL PARAMETERS FOR SPONTANEOUS COMBUSTION FOR SOME COMPLEX GEOMETRIES USING AN INDIRECT NUMERICAL METHOD

Part of: Partial differential equations, boundary value problems Numerical problems in dynamical systems Partial differential equations

Published online by Cambridge University Press:  26 February 2018

QUANBING LUO Open the ORCID record for QUANBING LUO [Opens in a new window] ,
DONG LIANG ,
TING REN  and
JIAN ZHANG
QUANBING LUO*
Affiliation:
School of Environmental Science and Engineering, Guangdong University of Technology, Guangzhou 510006, China email [email protected]
DONG LIANG
Affiliation:
School of Engineering, Sun Yat-sen University, Guangzhou 510006, China email [email protected] Guangdong Provincial Key Laboratory of Fire Science and Technology, Guangzhou 510006, China
TING REN
Affiliation:
School of Civil, Mining and Environmental Engineering, University of Wollongong, Wollongong 2522, Australia email [email protected], [email protected]
JIAN ZHANG
Affiliation:
School of Civil, Mining and Environmental Engineering, University of Wollongong, Wollongong 2522, Australia email [email protected], [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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In the theory of spontaneous combustion, identifying the critical value of the Frank-Kamenetskii parameter corresponds to solving a bifurcation point problem. There are two different numerical methods used to solve this problem—the direct and indirect numerical methods. The latter finds the bifurcation point by solving a partial differential equation (PDE) problem. This is a better method to find the bifurcation point for complex geometries. This paper improves the indirect numerical method by combining the grid-domain extension method with the matrix equation computation method. We calculate the critical parameters of the Frank-Kamenetskii equation for some complex geometries using the indirect numerical method. Our results show that both the curve of the outer boundary and the height of the geometries have an effect on the values of the critical Frank-Kamenetskii parameter, however, they have little effect on the critical dimensionless temperature.

Keywords

critical parametersFrank-Kamenetskiiindirect numerical methodbifurcation pointspontaneous combustion

MSC classification

Primary: 65P30: Bifurcation problems
Secondary: 65N06: Finite difference methods 35B32: Bifurcation
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 3 , January 2018 , pp. 402 - 412
Copyright
© 2018 Australian Mathematical Society 

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