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Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
2018 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 492, p. 2316-2335Article in journal (Refereed) Published
Abstract [en]

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grunwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 492, p. 2316-2335
Keywords [en]
Cattaneo type heat conduction law, Fractional distributed-order constitutive equation, Integral transforms, Finite differences
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-223493DOI: 10.1016/j.physa.2017.11.150ISI: 000423495100192Scopus ID: 2-s2.0-85036553223OAI: oai:DiVA.org:kth-223493DiVA, id: diva2:1185079
Note

QC 20180223

Available from: 2018-02-23 Created: 2018-02-23 Last updated: 2018-02-23Bibliographically approved

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Zeli, Velibor
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Solid Mechanics (Dept.)Linné Flow Center, FLOW
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