CaltechAUTHORS
  A Caltech Library Service

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. http://resolver.caltech.edu/CaltechAUTHORS:20170613-090149803

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20170613-090149803

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1093/imamat/40.3.217DOIArticle
https://academic.oup.com/imamat/article-abstract/40/3/217/624608/Similarity-Solutions-of-a-Heat-Equation-with?redirectedFrom=fulltextPublisherArticle
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.
Funders:
Funding AgencyGrant Number
Science and Engineering Research Council (SERC)UNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ7
Record Number:CaltechAUTHORS:20170613-090149803
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170613-090149803
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
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Jun 2017 16:07
Last Modified:22 Aug 2017 21:02

Repository Staff Only: item control page