- 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
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 219486, 7 pages
New Analytical and Numerical Solutions for Mixed Convection Boundary-Layer Nanofluid Flow along an Inclined Plate Embedded in a Porous Medium
1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt
3Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Received 17 July 2013; Accepted 23 August 2013
Academic Editor: Mohamed Fathy El-Amin
Copyright © 2013 Emad H. Aly and Abdelhalim Ebaid. 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 Proceedings of the ASME International Mechanical Engineering Congress and Exposition, pp. 99–105, ASME, San Francisco, Calif, USA, 1995.
- 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.
- 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-Al2O3SiO2, and TiO2 ultra-fine particles),” Netsu Bussei, vol. 7, pp. 227–233, 1993.
- S. Lee, S. U.-S. Choi, S. Li, and J. A. Eastman, “Measuring thermal conductivity of fluids containing oxide nanoparticles,” Journal of Heat Transfer, vol. 121, no. 2, pp. 280–288, 1999.
- 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.
- 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.
- N. Bachok, A. Ishak, and I. Pop, “Boundary-layer flow of nanofluids over a moving surface in a flowing fluid,” International Journal of Thermal Sciences, vol. 49, no. 9, pp. 1663–1668, 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, vol. 10, no. 4, pp. 2591–2594, 2013.
- J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999.
- J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000.
- J.-H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73–79, 2003.
- J.-H. He, “Comparison of homotopy perturbation method and homotopy analysis method,” Applied Mathematics and Computation, vol. 156, no. 2, pp. 527–539, 2004.
- J.-H. He, “Asymptotology by homotopy perturbation method,” Applied Mathematics and Computation, vol. 156, no. 3, pp. 591–596, 2004.
- J.-H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters A, vol. 350, no. 1-2, pp. 87–88, 2006.
- J.-H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 695–700, 2005.
- P. D. Ariel, “The three-dimensional flow past a stretching sheet and the homotopy perturbation method,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 920–925, 2007.
- S. Pamuk and N. Pamuk, “He's homotopy perturbation method for continuous population models for single and interacting species,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 612–621, 2010.
- H. Aminikhah, “The combined Laplace transform and new homotopy perturbation methods for stiff systems of ODEs,” Applied Mathematical Modelling, vol. 36, no. 8, pp. 3638–3644, 2012.
- A. H. Nayfeh, Perturbation Methods, John Wiley & Sons, New York, NY, USA, 1973.
- E. H. Aly, M. Benlahsen, and M. Guedda, “Similarity solutions of a MHD boundary-layer flow past a continuous moving surface,” International Journal of Engineering Science, vol. 45, no. 2-8, pp. 486–503, 2007.
- M. Guedda, E. H. Aly, and A. Ouahsine, “Analytical and ChPDM analysis of MHD mixed convection over a vertical flat plate embedded in a porous medium filled with water at C,” Applied Mathematical Modelling, vol. 35, no. 10, pp. 5182–5197, 2011.
- E. H. Aly and A. Ebaid, “On the exact analytical and numerical solutions of nano boundary-layer fluid flows,” Abstract and Applied Analysis, vol. 2012, Article ID 415431, 22 pages, 2012.
- R. A. van Gorder, E. Sweet, and K. Vajravelu, “Nano boundary layers over stretching surfaces,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 6, pp. 1494–1500, 2010.
- P. Rana, R. Bhargava, and O. A. Bég, “Numerical solution for mixed convection boundary layer flow of a nanofluid along an inclined plate embedded in a porous medium,” Computers & Mathematics with Applications, vol. 64, no. 9, pp. 2816–2832, 2012.
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 4th edition, 1972.
- E. M. E. Elbarbary and S. M. El-Sayed, “Higher order pseudospectral differentiation matrices,” Applied Numerical Mathematics, vol. 55, no. 4, pp. 425–438, 2005.