- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
International Journal of Differential Equations
Volume 2013 (2013), Article ID 865464, 8 pages
An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid
1Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
2Department of Mathematics, Faculty of Science, Ain Shams University, Egypt
Received 4 April 2013; Accepted 22 April 2013
Academic Editor: Jürgen Geiser
Copyright © 2013 Abdelhalim Ebaid 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.
- S. U. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” in The Proceedings of the ASME International Mechanical Engineering Congress and Exposition, ASME, FED 231/MD 66, pp. 99–105, San Francisco, Calif, USA, 1995.
- H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, “Alterlation of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (Dispersion of g-Al2O3, SiO2, and TiO2 ultra-fine particles),” Netsu Bussei, vol. 7, no. 4, pp. 227–233, 1993.
- J. Buongiorno and W. Hu, “Nanofluid coolants for advanced nuclear power plants,” in Proceedings of ICAPP ’05, Paper no. 5705, Seoul, Republic of Korea, May 2005.
- S. U. S. Choi, Z. G. Zhang, W. Yu, F. E. Lockwood, and E. A. Grulke, “Anomalous thermal conductivity enhancement in nanotube suspensions,” Applied Physics Letters, vol. 79, no. 14, pp. 2252–2254, 2001.
- S. Kakaç and A. Pramuanjaroenkij, “Review of convective heat transfer enhancement with nanofluids,” International Journal of Heat and Mass Transfer, vol. 52, no. 13-14, pp. 3187–3196, 2009.
- S. K. Das, S. U. S. Choi, W. Yu, and T. Pradeep, Nanofluids: Science and Technology, Wiley-Interscience, Hoboken, NJ, USA, 2007.
- J. Buongiorno, “Convective transport in nanofluids,” Journal of Heat Transfer, vol. 128, no. 3, pp. 240–250, 2006.
- D. A. Nield and A. V. Kuznetsov, “The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid,” International Journal of Heat and Mass Transfer, vol. 52, no. 25-26, pp. 5792–5795, 2009.
- K. Khanafer, K. Vafai, and M. Lightstone, “Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids,” International Journal of Heat and Mass Transfer, vol. 46, no. 19, pp. 3639–3653, 2003.
- W. Daungthongsuk and S. Wongwises, “A critical review of convective heat transfer of nanofluids,” Renewable and Sustainable Energy Reviews, vol. 11, no. 5, pp. 797–817, 2007.
- R. K. Tiwari and M. K. Das, “Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids,” International Journal of Heat and Mass Transfer, vol. 50, no. 9-10, pp. 2002–2018, 2007.
- L. Wang and X. Wei, “Heat conduction in nanofluids,” Chaos, Solitons and Fractals, vol. 39, no. 5, pp. 2211–2215, 2009.
- H. F. Oztop and E. Abu-Nada, “Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids,” International Journal of Heat and Fluid Flow, vol. 29, no. 5, pp. 1326–1336, 2008.
- A. V. Kuznetsov and D. A. Nield, “Natural convective boundary-layer flow of a nanofluid past a vertical plate,” International Journal of Thermal Sciences, vol. 49, no. 2, pp. 243–247, 2010.
- A. V. Kuznetsov and D. A. Nield, “Effect of local thermal non-equilibrium on the onset of convection in a porous medium layer saturated by a nanofluid,” Transport in Porous Media, vol. 83, no. 2, pp. 425–436, 2010.
- E. H. Aly and A. Ebaid, “New exact solutions for boundary-layer flow of a nanofluid past a stretching sheet,” Journal of Computational and Theoretical Nanoscience. In press.
- P. Cheng and W. J. Minkowycz, “Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike,” Journal of Geophysical Research, vol. 82, no. 14, pp. 2040–2044, 1977.
- W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet,” International Journal of Heat and Mass Transfer, vol. 53, no. 11-12, pp. 2477–2483, 2010.
- J. P. Boyd, “Padé-approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain,” Computers in Physics, vol. 11, no. 3, pp. 299–303, 1997.
- A. M. Wazwaz, “The modified decomposition method and Padé approximants for solving the Thomas-Fermi equation,” Applied Mathematics and Computation, vol. 105, no. 1, pp. 11–19, 1999.
- A. M. Wazwaz, “The modified decomposition method and Padé approximants for a boundary layer equation in unbounded domain,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 737–744, 2006.
- A. M. Wazwaz, “Padé approximants and Adomian decomposition method for solving the Flierl-Petviashivili equation and its variants,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1812–1818, 2006.
- A. M. Wazwaz, “The variational iteration method for solving two forms of Blasius equation on a half-infinite domain,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 485–491, 2007.
- S. A. Kechil and I. Hashim, “Non-perturbative solution of free-convective boundary-layer equation by Adomian decomposition method,” Physics Letters A, vol. 363, no. 1-2, pp. 110–114, 2007.
- S. A. Kechil and I. Hashim, “Series solution of flow over nonlinearly stretching sheet with chemical reaction and magnetic field,” Physics Letters A, vol. 372, no. 13, pp. 2258–2263, 2008.
- E. Alizadeh, K. Sedighi, M. Farhadi, and H. R. Ebrahimi-Kebria, “Analytical approximate solution of the cooling problem by Adomian decomposition method,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 462–472, 2009.
- T. Hayat, Q. Hussain, and T. Javed, “The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet,” Nonlinear Analysis: Real World Applications, vol. 10, no. 2, pp. 966–973, 2009.
- S. Abbasbandy and T. Hayat, “Solution of the MHD Falkner-Skan flow by Hankel-Padé method,” Physics Letters A, vol. 373, no. 7, pp. 731–734, 2009.
- M. M. Rashidi and E. Erfani, “A novel analytical solution of the thermal boundary-layer over a flat plate with a convective surface boundary condition using DTM-Padé,” in Proceedings of the International Conference on Signal Processing Systems (ICSPS '09), pp. 905–909, Singapore, May 2009.
- M. M. Rashidi and S. A. M. Pour, “A novel analytical solution of steady flow over a rotating disk in porous medium with heat transfer by DTM-Padé,” African Journal of Mathematics and Computer Science Research, vol. 3, no. 6, pp. 93–100, 2010.
- M. M. Rashidi and S. A. M. Pour, “Explicit solution of axisymmetric stagnation flow towards a shrinking sheet by DTM-Padé,” Applied Mathematical Sciences, vol. 4, no. 53–56, pp. 2617–2632, 2010.
- M. M. Rashidi and M. Keimanesh, “Using differential transform method and Padé approximant for solving mhd flow in a laminar liquid film from a horizontal stretching surface,” Mathematical Problems in Engineering, vol. 2010, Article ID 491319, 14 pages, 2010.
- J. K. Zhou, Differential Transformation and Its Applications for Electrical circuIts, Huazhong University Press, Wuhan, China, 1986.
- S. H. Ho and C. K. Chen, “Analysis of general elastically end restrained non-uniform beams using differential transform,” Applied Mathematical Modelling, vol. 22, no. 4-5, pp. 219–234, 1998.
- C. K. Chen and S. H. Ho, “Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform,” International Journal of Mechanical Sciences, vol. 41, no. 11, pp. 1339–1356, 1999.
- C. K. Chen and S. H. Ho, “Solving partial differential equations by two-dimensional differential transform method,” Applied Mathematics and Computation, vol. 106, no. 2-3, pp. 171–179, 1999.
- M. J. Jang, C. L. Chen, and Y. C. Liy, “On solving the initial-value problems using the differential transformation method,” Applied Mathematics and Computation, vol. 115, no. 2-3, pp. 145–160, 2000.
- M. J. Jang, C. L. Chen, and Y. C. Liu, “Two-dimensional differential transform for partial differential equations,” Applied Mathematics and Computation, vol. 121, no. 2-3, pp. 261–270, 2001.
- M. Köksal and S. Herdem, “Analysis of nonlinear circuits by using differential Taylor transform,” Computers and Electrical Engineering, vol. 28, no. 6, pp. 513–525, 2002.
- F. Ayaz, “Solutions of the system of differential equations by differential transform method,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 547–567, 2004.
- A. Arikoglu and I. Ozkol, “Solution of boundary value problems for integro-differential equations by using differential transform method,” Applied Mathematics and Computation, vol. 168, no. 2, pp. 1145–1158, 2005.
- S. H. Chang and I. L. Chang, “A new algorithm for calculating one-dimensional differential transform of nonlinear functions,” Applied Mathematics and Computation, vol. 195, no. 2, pp. 799–808, 2008.
- A. S. V. R. Kanth and K. Aruna, “Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations,” Chaos, Solitons and Fractals, vol. 41, no. 5, pp. 2277–2281, 2009.
- A. S. V. R. Kanth and K. Aruna, “Differential transform method for solving the linear and nonlinear Klein-Gordon equation,” Computer Physics Communications, vol. 180, no. 5, pp. 708–711, 2009.
- A. Ebaid, “Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 7, pp. 1921–1927, 2010.
- L. J. Crane, “Flow past a stretching plate,” Zeitschrift für Angewandte Mathematik und Physik, vol. 21, no. 4, pp. 645–647, 1970.
- A. Ebaid and M. D. Aljoufi, “New theoretical and numerical results for the boundary-layer flow of a nanofluid past a stretching sheet,” Advanced Studies in Theoretical Physics. In press.