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FRACTAL HEAT CONDUCTION PROBLEM SOLVED BY LOCAL FRACTIONAL VARIATION ITERATION METHOD

ABSTRACT
This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.
KEYWORDS
PAPER SUBMITTED: 2012-11-24
PAPER REVISED: 2012-10-27
PAPER ACCEPTED: 2012-11-27
DOI REFERENCE: https://doi.org/10.2298/TSCI121124216Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2013, VOLUME 17, ISSUE 2, PAGES [625 - 628]
REFERENCES
  1. Hooft. G, A Confrontation with Infinity, Int. J. Mod. Phys. A., 15 (2000), pp.4395
  2. M. Majumder, N. Chopra, R. Andrews, et al. Nanoscale Hydrodynamics - Enhanced Flow in Carbon Nanotubes, Nature, 438 (2005), pp.44
  3. Y. Xuan, Wilfried Roetzel, Conceptions for Heat Transfer Correlation of Nanofluids, Int. J. Heat Mass Transfer, 43 (2000), pp.3701-3707
  4. Daniel Rayneau-Kirkhope, Y. Mao, Robert Farr, Ultralight Fractal Structures from Hollow Tubes, Phys. Rev. Letts, 109 (2012), 204301
  5. X. J. Yang, Heat Transfer in Discontinuous Media, Adv. Mech. Eng. Appl., 1 (3) (2012) pp. 47-53
  6. X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, USA, 2012.
  7. M. S. Hu, X. J. Yang, J. Fan, Approximation Solution to Local Fractional Volterra Integral Equations Arising in Fractal Heat Transfer, J. Nano Res., accepted, 2012.
  8. T. M. Shih, A literature survey on numerical heat transfer, Num. Heat Transfer, 5(4) (1982), pp. 369-420
  9. Meilanov, R., Shabanova, M., Akhmedov, E., A research note on a Solution of Stefan Problem with Fractional Time and Space Derivatives, Int. Rev. Chem. Eng., 3 (6) (2011), pp. 810-813
  10. Siddique, I., Vieru, D., Stokes Flows of a Newtonian Fluid with Fractional Derivatives and Slip at the Wall, Int. Rev. Chem. Eng., 3(6) (2011), pp. 822- 826.
  11. Y. Z. Povstenko, Thermoelasticity that uses fractional heat conduction equation, J. Math. Sci., 51 (2) (2009), pp. 293-246
  12. J. Hristov, Approximate solutions to fractional sub-diffusion equations: The heat-balance integral method, Eur. Phys. J. Spec. Topics, 193 (4) (2011), pp. 229-243
  13. J. Hristov, Heat-balance integral to fractional (half-time) heat diffusion sub-model, Thermal Sci., 14 (2) (2010), pp. 291-316
  14. J. Hristov, An exercise with the He's variation iteration method to a fractional bernoulli equation arising in transient conduction with non-linear heat flux at the boundary, Int. Rev. Chem. Eng., 4 (5) (2012), pp.489-497
  15. J. H. He, A new fractal derivation, Thermal Sci., 15 (2011), pp. 145-147
  16. Q. L. Wang, J.H. He, Z.B. Li, Fractional model for heat conduction in polar hairs, Thermal Sci.,16 (2) (2012), 339-342.
  17. Molliq, R. Y., Noorani, M. S. M., Hashim, I., Variational Iteration Method for Fractional Heat- and Wave-Like Equations, Nonlinear Analysis: R.W.A., 10 (3) (2009), pp. 1854-1869
  18. Sakar, M. G., Erdogan, F., Yyldirim, A., Variational Iteration Method for the Time-Fractional Fornberg-Whitham Equation, Comput. Math. Appl., 63 (9) (2012), pp. 1382-1388
  19. J. H. He, Q. L. Wang, J. Sun, Can polar bear hairs absorb environmental energy? Thermal Sci., 15 (3) (2011), 911-913
  20. J. Fan, J. F. Liu, J.H. He, Hierarchy of wool fibers and fractal dimensions, Int. J. Nonlin. Sci. Num., 9 (3) (2008), 293-296
  21. X. J. Yang, F. R Zhang, Local fractional variational iteration method and its algorithms, Adv. Comput. Math. Appl., 1(3) (2012), pp.139-145
  22. X. J. Yang, Local Fractional Integral Transforms, Progress in Nonlinear Science, 4 (2011), pp. 1-225
  23. X. J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic publisher Limited, Hong Kong, China, 2011
  24. J. H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B, 20 (10) (2006), 1141-1199
  25. G. C. Wu, Applications of the variational iteration method to fractional diffusion equations: local versus nonlocal Ones, Int. Rev. Chem. Eng., 4 (5) (2012), 505-510
  26. J. H. He, G. C. Wu, F. Austin, The Variational iteration method which should be followed, Nonlinear Sci. Letts. A, 1 (1) (2010), pp.1-30
  27. J. H. He, Asymptotic methods for solitary solutions and compactons, Abstract and Applied Analysis, 2012, 916793

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