THERMAL SCIENCE

International Scientific Journal

A VARIATIONAL ITERATION METHOD INTEGRAL TRANSFORM TECHNIQUE FOR HANDLING HEAT TRANSFER PROBLEMS

ABSTRACT
In this paper, we consider the heat transfer equations at the low excess temperature. The variational iteration method integral transform technique is used to find the approximate solutions for the problems. The used method is accurate and efficient.
KEYWORDS
PAPER SUBMITTED: 2017-03-05
PAPER REVISED: 2017-05-01
PAPER ACCEPTED: 2017-06-15
PUBLISHED ONLINE: 2017-12-02
DOI REFERENCE: https://doi.org/10.2298/TSCI17S1055Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S55 - S61]
REFERENCES
  1. Cannon, J. R., The One-Dimensional Heat Equation, Cambridge University Press, Cambridge, UK, 1984
  2. Khan, S. I., et al., Variation of Parameters Method for Heat Diffusion and Heat Convection Equations, International Journal of Applied and Computational Mathematics, 3 (2017), 1, pp. 185-193
  3. Bluman, G. W., et al., The General Similarity Solution of the Heat Equation, Journal of Mathematics and Mechanics, 18 (1969), 11, pp. 1025-1042
  4. Jarny, Y., et al., A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction, International Journal of Heat and Mass Transfer, 34 (1991), 11, pp. 2911-2919
  5. Dawson, C. N., et al., A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation, Mathematics of Computation, 57 (1991), 195, pp. 63-71
  6. Marinca, V., et al., Application of Optimal Homotopy Asymptotic Method for Solving Nonlinear Equations Arising in Heat Transfer, International Communications in Heat and Mass Transfer, 35 (2008), 6, pp. 710-715
  7. Ganji, D. D., The Application of He's Homotopy Perturbation Method to Nonlinear Equations Arising in Heat Transfer, Physics letters A, 355 (2006), 4, pp. 337-341
  8. Ganji, D. D., et al., Application of Homotopy-Perturbation and Variational Iteration Methods to Nonlinear Heat Transfer and Porous Media Equations, Journal of Computational and Applied mathematics, 207 (2007), 1, pp. 24-34
  9. Momani, S., Analytical Approximate Solution for Fractional Heat-Like and Wave-Like Equations with Variable Coefficients Using the Decomposition Method, Applied Mathematics and Computation, 165 (2005), 2, pp. 459-472
  10. Pamuk, S., An Application for Linear and Nonlinear Heat Equations by Adomian's Decomposition Method, Applied Mathematics and Computation,163 (2005), 1, pp. 89-96
  11. Yang, X. J., A New Integral Transform Operator for Solving the Heat-Diffusion Problem, Applied Mathematics Letters, 64 (2017), Feb., pp. 193-197
  12. Yang, X. J., A New Integral Transform with an Application in Heat Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S677-S681
  13. Yang, X. J., A New Integral Transform Method for Solving Steady Heat Transfer Problem, Thermal Science, 20 (2016), Suppl. 3, pp. S639-S642
  14. Gao, F., et al., Exact Traveling Wave Solutions for a New Non-Linear Heat Transfer Equation, Thermal Science, 21 (2017), 4, pp. 1833-1838
  15. He, J.-H., Asymptotic Methods for Solitary Solutions and Compactons, Abstract and Applied Analysis, 2012 (2012), ID 916793
  16. He, J.-H., Variational Iteration Method for Delay Differential Equations, Communications in Nonlinear Science and Numerical Simulation, 2 (1997), 4, pp. 235-236
  17. Yang, X. J., et al., A New Technology for Solving Diffusion and Heat Equations, Thermal Science, 21 (2017), 1A, pp. 133-140

© 2017 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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