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Published September 1, 1988 | public
Journal Article

Similarity Solutions of a Heat Equation with Nonlinearly Varying Heat Capacity

Abstract

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.

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.

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024