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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 423421, 12 pages
Approximate Analytic Solutions of Transient Nonlinear Heat Conduction with Temperature-Dependent Thermal Diffusivity
1Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar
2Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, P.O. Box 5087, Dhahran 31261, Saudi Arabia
3Department of Mathematics, Hafr Al-Batin Community College, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Received 7 April 2014; Accepted 17 June 2014; Published 13 July 2014
Academic Editor: Mariano Torrisi
Copyright © 2014 M. T. Mustafa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations: An Introduction, Cambridge University Press, New York, NY, USA, 1994.
- J. Blobner, R. A. Białecki, and G. Kuhn, “Boundary-element solution of coupled heat conduction-radiation problems in the presence of shadow zones,” Numerical Heat Transfer B: Fundamentals, vol. 39, no. 5, pp. 451–478, 2001.
- B. Chen, Y. Gu, Z. Guan, and H. Zhang, “Nonlinear transient heat conduction analysis with precise time integration method,” Numerical Heat Transfer B, vol. 40, no. 4, pp. 325–341, 2001.
- F. Asllanaj, A. Milandri, G. Jeandel, and J. R. Roche, “A finite difference solution of non-linear systems of radiative-conductive heat transfer equations,” International Journal for Numerical Methods in Engineering, vol. 54, no. 11, pp. 1649–1668, 2002.
- A. Fic, R. A. Białecki, and A. J. Kassab, “Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite-element method,” Numerical Heat Transfer B: Fundamentals, vol. 48, no. 2, pp. 103–124, 2005.
- W. F. Ames, Nonlinear Partial Differential Equations in Engineering, vol. 1, Academic Press, New York, NY, USA, 1965.
- G. W. Bluman and S. Anco, Symmetry and Integration Methods for Differential Equations, Springer, New York, NY, USA, 2002.
- N. H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, vol. 4, John Wiley & Sons, Chichester, UK, 1999.
- P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, NY, USA, 1986.
- L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, NY, USA, 1982.
- J. H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999.
- J. He, “Bookkeeping parameter in perturbation methods,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 2, no. 3, pp. 257–264, 2001.
- J.-H. He, “Addendum: new interpretation of homotopy perturbation method,” International Journal of Modern Physics B, vol. 20, no. 18, pp. 2561–2568, 2006.
- H. Azad, M. T. Mustafa, and A. F. M. Arif, “Analytic solutions of initial-boundary-value problems of transient conduction using symmetries,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4132–4140, 2010.
- L. Dresner, Similarity Solutions of Nonlinear Partial Differential Equations, vol. 88 of Research Notes in Mathematics Series, Longman, 1983.
- A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1064–1068, 2009.
- S. Mukhopadhyay, K. Bhattacharyya, and G. C. Layek, “Steady boundary layer flow and heat transfer over a porous moving plate in presence of thermal radiation,” International Journal of Heat and Mass Transfer, vol. 54, no. 13-14, pp. 2751–2757, 2011.