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Similarity Solutions of a Heat Equation with Nonlinearly Varying Heat Capacity

Stuart, Andrew (1988) Similarity Solutions of a Heat Equation with Nonlinearly Varying Heat Capacity. IMA Journal of Applied Mathematics, 40 (3). pp. 217-234. ISSN 0272-4960. doi:10.1093/imamat/40.3.217.

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A reaction-diffusion equation, coupled through variable heat capacity and source term to a temporally evolving ordinary differential equation, is examined. The model is a prototype for the study of combustion processes where the heat capacity of a composite solid medium changes significantly as the reactant within the medium is consumed. Similarity solutions are sought by analysing the invariance of the equations to various stretching groups. The resulting two-point boundary-value problem is singular at the origin and posed on the semi-infinite domain. By employing series expansion techniques we derive a regular problem posed on a finite domain. This problem is amenable to standard numerical solution by means of Newton-Kantorovich iteration. Results of the computations are presented and interpreted in terms of the governing partial differential equation.

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Additional Information:© 1988 Oxford University Press. Received 28 October 1987; Published: 01 September 1988. Part of this work was conducted at the Mathematical Institute, Oxford University, where I was funded by the Science and Engineering Research Council. I wish to thank Dr T. Boddington, of Leeds University, for valuable discussions about the form of the reaction rate.
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Science and Engineering Research Council (SERC)UNSPECIFIED
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Andrew StuartJ7
Issue or Number:3
Record Number:CaltechAUTHORS:20170613-090149803
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Official Citation:ANDREW STUART; Similarity Solutions of a Heat Equation with Nonlinearly Varying Heat Capacity. IMA J Appl Math 1988; 40 (3): 217-234. doi: 10.1093/imamat/40.3.217
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78153
Deposited By: Tony Diaz
Deposited On:13 Jun 2017 16:07
Last Modified:15 Nov 2021 17:37

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