THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Yuzhu Zhang

,

Ai-Min Yang

,

Xiao-Jun Yang

1-D HEAT CONDUCTION IN A FRACTAL MEDIUM: A SOLUTION BY THE LOCAL FRACTIONAL FOURIER SERIES METHOD

ABSTRACT
In this communication 1-D heat conduction in a fractal medium is solved by the local fractional Fourier series method. The solution developed allows relating the basic properties of the fractal medium to the local heat transfer mechanism.
KEYWORDS
fractal medium, heat-conduction, local fractional Fourier series method
PAPER SUBMITTED: 2013-03-03
PAPER REVISED: 2013-03-08
PAPER ACCEPTED: 2013-04-10
PUBLISHED ONLINE: 2013-04-21
DOI REFERENCE: https://doi.org/10.2298/TSCI130303041Z
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THERMAL SCIENCE YEAR 2013, VOLUME 17, ISSUE Issue 3, PAGES [953 - 956]
REFERENCES
  1. D. Lesnic and L. Elliott, The decomposition approach to inverse heat conduction, Journal of Mathematical Analysis and Applications 232 (1999), 1, pp. 82-98.
  2. Y. Z. Povstenkoa, Theory of thermoelasticity based on the space-time-fractional heat conduction equation, Physica Scripta, T136 (2009) 014017 (6pp)
  3. M. S. Hu, D. Baleanu, X. J. Yang, One-phase problems for discontinuous heat transfer in fractal media, Mathematical Problems in Engineering, 2013, 358473.
  4. X. J. Yang, D. Baleanu, 2012. "Fractal heat conduction problem solved by local fractional variation iteration method". Thermal Science., in PRESS Doi: 10.2298/TSCI1211242 16Y.
  5. M. S. Hu, Agarwal, R. P., X. J. Yang, 2012. "Local fractional Fourier series with application to wave equation in fractal vibrating string". Abstract and Applied Analysis. 2012, Article ID 567401.
  6. X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012
  7. X. J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher, Hong Kong, China, 2011.
  8. J.H. He, Variational iteration method - a kind of non-linear analytical technique: Some examples, Int. J. Non-L. Mech. 34 (1999), 4, pp. 699-708.
  9. G. C. Wu, Applications of the variational iteration method to fractional diffusion equations: local versus nonlocal ones, International Review of Chemical Engineering, 4 (2012), 5, pp.505-510.
  10. J. Hristov, An exercise with the He's variation iteration method to a fractional Bernoulli equation arising in a transient conduction with a non-linear boundary heat flux, International Review of Chemical Engineering, 4 (2012), 5, pp.489-497.
  11. J. H. He, Homotopy perturbation method for bifurcation on nonlinear problems, Int. J. Nonlinea. Sci. Numer. Simul., 6 (2005), 2, pp. 207-208
  12. J. H. He, Asymptotic methods for solitary solutions and compactons. Abstract and Applied Analysis,2012, Article ID 916793.
  13. J. Hristov, Approximate solutions to fractional sub-diffusion equations: The heat-balance integral method, Eur. Phys. J. Special Topics, 193 (2011), 4, pp. 229-243.
  14. J. Hristov, Heat-balance integral to fractional (half-time) heat diffusion sub-model, Thermal Science, 14 (2010), 2, pp. 291-316.
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1-D heat conduction in a fractal medium: A solution by the local fractional Fourier series method

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence