THERMAL SCIENCE

International Scientific Journal

Xiao-Jun YangORCID

,

Feng GaoORCID

A NEW TECHNOLOGY FOR SOLVING DIFFUSION AND HEAT EQUATIONS

ABSTRACT
In this paper, a new technology combing the variational iterative method and an integral transform similar to Sumudu transform is proposed for the first time for solutions of diffusion and heat equations. The method is accurate and efficient in development of approximate solutions for the partial differential equations.
KEYWORDS
heat transfer, diffusion equation, heat equation, integral transform, approximate solution
PAPER SUBMITTED: 2016-04-11
PAPER REVISED: 2016-05-21
PAPER ACCEPTED: 2016-06-10
PUBLISHED ONLINE: 2016-10-01
DOI REFERENCE: https://doi.org/10.2298/TSCI160411246Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE No. 1, PAGES [133 - 140]
REFERENCES
[1] Carslaw, H. S., Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, Oxford, 1959, 10.1016/0022-5096(59)90029-8
[2] Ozisik, M. N., Heat Conduction, Wiley, New York, 1993
[3] Incropera, F. P., Dewitt, D. P., Introduction to Heat Transfer, New York: Wiley, 1990, 10.1039/bk9781782623588-00099
[4] Povstenko, Y. Z. Fractional Heat Conduction Equation and Associated Thermal Stress, Journal of Thermal Stresses, 28(2004), 1, pp.83-102, 10.1080/014957390523741
[5] Khalil, H., Khan, R. A., A New Method Based on Legendre Polynomials for Solutions of the Fractional Two-dimensional Heat Conduction Equation, Computers & Mathematics with Applications, 67(2014), 10, pp.1938-1953, 10.1016/j.camwa.2014.03.008
[6] Tarasov, V. E., Heat Transfer in Fractal Materials, International Journal of Heat and Mass Transfer, 93(2016), 1, pp.427-430, 10.1016/j.ijheatmasstransfer.2015.09.086
[7] Yang, X. J., Srivastava, H. M., Cattani, C., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differential Equations Arising in Mathematical Physics, Romanian Reports in Physics, 67(2015), 3, pp.752-761
[8] Zhang, Y., Srivastava, H. M., Baleanu, M. C., Local Fractional Variational Iteration Algorithm II for Non-homogeneous Model Associated with the Non-differentiable Heat Flow, Advances in Mechanical Engineering, 7(2015), 10, pp.1-7, 10.1177/1687814015608567
[9] Yang, X.-J., Srivastava, H. M., He, J. H., Baleanu, D., Cantor-type Cylindrical-coordinate Method for Differential Equations with Local Fractional Derivatives, Physics Letters A, 377(2013), 28, pp.1696-1700, 10.1016/j.physleta.2013.04.012
[10] Hristov, J., An Approximate Analytical (Integral-Balance) Solution to A Nonlinear Heat Diffusion Equation, Thermal Science, 19 (2015), 2, pp. 723-733, 10.2298/tsci140326074h
[11] Galaktionov, V. A., On New Exact Blow-up Solutions for Nonlinear Heat Conduction Equations with Source and Applications, Differential and Integral Equations, 3(1990), 5, pp.863-874, 10.57262/die/1378730129
[12] Geng, F., Lin, Y., Application of the Variational Iteration Method to Inverse Heat Source Problems, Computers & Mathematics with Applications, 58(2009), 11, pp.2098-2102, 10.1016/j.camwa.2009.03.002
[13] He, J., Variational Iteration Method for Delay Differential Equations, Communications in Nonlinear Science and Numerical Simulation, 2(1997), 4, pp.235-236, 10.1016/s1007-5704(97)90008-3
[14] Ganji, D. D., Afrouzi, G. A., Talarposhti, R. A., 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, 10.1016/j.physleta.2006.12.086
[15] Hesameddini, E., Latifizadeh, H., Reconstruction of Variational Iteration Algorithms Using the Laplace Transform, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2009), 11-12, pp.1377-1382, 10.1515/ijnsns.2009.10.11-12.1377
[16] Goswami, P., Alqahtani, R. T., Solutions of Fractional Differential Equations by Sumudu Transform and Variational Iteration Method, Journal of Nonlinear Science and Applications, 9 (2016), 3, pp.1944-1951, 10.22436/jnsa.009.04.48
[17] Yang, X.-J., A New Integral Transform Method for Solving Steady Heat-transfer Problem, Thermal Science, 20(2016), Suppl. 2, in press, 10.2298/tsci16s3639y
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A new technology for solving diffusion and heat equations

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