THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Jian-Guo Zhang

THE FOURIER-YANG INTEGRAL TRANSFORM FOR SOLVING THE 1-D HEAT DIFFUSION EQUATION

ABSTRACT
A new Fourier-like integral transform (called the Fourier-Yang integral transform) S[λ(t)]= ε∞∫−∞λ(t)e-jεt dt is considered to find the fundamental solutions of the 1-D heat diffusion equation in the different initial conditions.
KEYWORDS
fundamental solution, heat equation, diffusion equation, Fourier-Yang integral transform, Fourier-like integral transform
PAPER SUBMITTED: 2017-03-10
PAPER REVISED: 2017-05-01
PAPER ACCEPTED: 2017-05-13
PUBLISHED ONLINE: 2017-12-02
DOI REFERENCE: https://doi.org/10.2298/TSCI17S1063Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S63 - S69]
REFERENCES
  1. Bergman, T. L., Introduction to Heat Transfer, John Wiley and Sons, New York, USA, 2011
  2. Ito, K., Diffusion Processes, John Wiley and Sons, New York, USA, 1974
  3. Luikov, A. V., Analytical Heat Diffusion Theory, Elsevier, New York, USA, 2012
  4. Shewmon, P., Diffusion in Solids. Springer, New York, USA, 2016
  5. Yang, X. J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2017), Feb., pp. 193-197
  6. Munier, A., et al., Group Transformations and the Nonlinear Heat Diffusion Equation, SIAM Journal on Applied Mathematics, 40 (1981), 2, pp. 191-207
  7. Yang, X. J., Gao, F., A New Technology for Solving Diffusion and Heat Equations, Thermal Science, 21 (2017), 1A, pp. 133-140
  8. Elliott, D., Diffusion Flow Laws in Metamorphic Rocks, Geological Society of America Bulletin, 84 (1973), 8, pp. 2645-2664
  9. Dykhuizen, R. C., Casey, W. H., An Analysis of Solute Diffusion in Rocks, Geochimica et Cosmochimica Acta, 53 (1989), 11, pp. 2797-2805
  10. Schneider, W. R., Wyss, W., Fractional Diffusion and Wave Equations, Journal of Mathematical Physics, 30 (1989), 1, pp. 134-144
  11. Meerschaert, M. M., et al., Stochastic Solution of Space-Time Fractional Diffusion Equations, Physical Review E, 65 (2002), 4, 041103
  12. Yang, X. J., et al., Anomalous Aiffusion Models with General Fractional Derivatives within the Kernels of the Extended Mittag-Leffler Type Functions, Romanian Reports in Physics, 69 (2017), 3, in press
  13. Yang, X. J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematics Letters, 47 (2015), Sept., pp. 54-60
  14. Yang, X. J., et al., Local Fractional Variational Iteration Method for Diffusion and Wave Equations on Cantor Sets, Romanian Journal of Physics, 59 (2014), 1-2, pp. 36-48
  15. Yang, X. J., et al., A New Numerical Technique for Solving the Local Fractional Diffusion Equation: Two-Dimensional Extended Differential Transform Approach, Applied Mathematics and Computation, 274 (2016), Feb., pp. 143-151
  16. Mikhailov, M. D., Ozisik, M. N., An Alternative General Solution of the Steady-State Heat Diffusion Equation, International Journal of Heat and Mass Transfer, 23 (1980), 5, pp. 609-612
  17. Burgan, J. R., et al., Homology and the Nonlinear Heat Diffusion Equation, SIAM Journal on Applied Mathematics, 44 (1984), 1, pp. 11-18
  18. Ganji, D. D., et al., Application of Variational Iteration Method and Homotopy-Perturbation Method for Nonlinear Heat Diffusion and Heat Transfer Equations, Physics Letters A, 368 (2007), 6, pp. 450-457
  19. Chang, M. J., et al., Improved Alternating-Direction Implicit Method for Solving Transient Three-Dimensional Heat Diffusion Problems, Numerical Heat Transfer, Part B Fundamentals, 19 (1991), 1, pp. 69-84
  20. Kandilarov, J. D., Vulkov, L. G., The Immersed Interface Method for Two-Dimensional Heat-Diffusion Equations with Singular Own Sources, Applied Numerical Mathematics, 57 (2007), 5-7, pp. 486-497
  21. Liang, X, et al., Applications of a Novel Integral Transform to Partial Differential Equations, Journal of Nonlinear Science and Applications, 10 (2017), 2, pp. 528-534
  22. Yang, X. J., New Integral Transforms for Solving a Steady Heat Transform Problem, Thermal Science, 21 (2017), Suppl. 1, pp. S79-S87, (in this issue)
  23. Debnath, L., Bhatta, D., Integral Transforms and Their Applications, CRC press, New York, USA, 2014
  24. Yang, X. J., A New Integral Transform with an Application in Heat-Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S677-S681
  25. Yang, X. J. A New Integral Transform Method for Solving Steady Heat Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S639-S642
PDF VERSION [DOWNLOAD]
The Fourier-Yang integral transform for solving the 1-D heat diffusion equation

© 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