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Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-08-10
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
We use an approximation method to study the solution to a nonlinear heat conduction equation in a semi-infinite domain.
By expanding an energy density function (defined as the internal energy per unit volume) as a Taylor polynomial in a spatial domain, we reduce the partial differential equation to a set of first-order ordinary differential equations in time.
We describe a systematic approach to derive approximate solutions using Taylor polynomials of a different degree.
For a special case, we derive an analytical solution and compare it with the result of a self-similar analysis.
A comparison with the numerically integrated results demonstrates good accuracy of our approximate solutions.
We also show that our approximation method can be applied to cases where boundary energy density and the corresponding effective conductivity are more general than those that are suitable for the self-similar method.
Propagation of nonlinear heat waves is studied for different boundary energy density and the conductivity functions.
American Psychological Association (APA)
Yu, Jun& Yang, Yi& Campo, Antonio. 2010. Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-24.
https://search.emarefa.net/detail/BIM-470945
Modern Language Association (MLA)
Yu, Jun…[et al.]. Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain. Mathematical Problems in Engineering No. 2010 (2010), pp.1-24.
https://search.emarefa.net/detail/BIM-470945
American Medical Association (AMA)
Yu, Jun& Yang, Yi& Campo, Antonio. Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain. Mathematical Problems in Engineering. 2010. Vol. 2010, no. 2010, pp.1-24.
https://search.emarefa.net/detail/BIM-470945
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-470945