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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 675287, 17 pages
Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid
1Department of Mechanical Engineering, Celal Bayar University, Muradiye, 45140 Manisa, Turkey
2Applied Mathematics and Computation Center, Celal Bayar University, Muradiye, 45140 Manisa, Turkey
Received 27 September 2012; Accepted 27 October 2012
Academic Editor: Fazal M. Mahomed
Copyright © 2012 M. B. Akgül 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.
- H. Blasius, “Grenzschichten in Flussigkeiten mit kleiner Reibung,” Zeitschrift für Mathematik und Physik, vol. 56, no. 1, pp. 1–37, 1908.
- A. R. A. Khaled and K. Vafai, “Heat transfer and hydromagnetic control of flow exit conditions inside oscillatory squeezed thin films,” Numerical Heat Transfer A, vol. 43, no. 3, pp. 239–258, 2003.
- E. M. A. Elbashbeshy and M. A. A. Bazid, “Heat transfer over an unsteady stretching surface,” Heat and Mass Transfer, vol. 41, no. 1, pp. 1–4, 2004.
- M. Mahmood, S. Asghar, and M. A. Hossain, “Squeezed flow and heat transfer over a porous surface for viscous fluid,” Heat and Mass Transfer, vol. 44, no. 2, pp. 165–173, 2007.
- R. C. Bataller, “Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface,” Journal of Material Processing Technology, vol. 203, no. 1–3, pp. 176–183, 2008.
- S. Mukhopadhyay, “Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium,” Heat and Mass Transfer, vol. 52, no. 13-14, pp. 3261–3265, 2009.
- 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.
- A. Aziz, “Hydrodynamic and thermal slip flow boundary layers over a flat plate with constant heat flux boundary condition,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 3, pp. 573–580, 2010.
- A. Ishak, “Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 837–842, 2010.
- S. Yao, T. Fang, and Y. Zhong, “Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 752–760, 2011.
- M. M. Rahman, “Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition,” Meccanica, vol. 46, no. 5, pp. 1127–1143, 2011.
- A. Ishak, R. Nazar, and I. Pop, “Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature,” Nonlinear Analysis. Real World Applications, vol. 10, no. 5, pp. 2909–2913, 2009.
- G. C. Layek, S. Mukhopadhyay, and S. A. Samad, “Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing,” International Communications in Heat and Mass Transfer, vol. 34, pp. 347–356, 2007.
- R. Tsai, K. H. Huang, and J. S. Huang, “Flow and heat transfer over an unsteady stretching surface with non-uniform heat source,” International Communications in Heat and Mass Transfer, vol. 35, no. 10, pp. 1340–1343, 2008.
- S. Sivasankaran, M. Bhuvaneswari, P. Kandaswamy, and E. K. Ramasami, “Lie group analysis of natural convection heat and mass transfer in an inclined surface,” Lithuanian Association of Nonlinear Analysis, vol. 11, no. 2, pp. 201–212, 2006.
- S. Sivasankaran, M. Bhuvaneswari, P. Kandaswamy, and E. K. Ramasami, “Lie group analysis of natural convection heat and mass transfer in an inclined porous surface with heat generation,” International Journal of Applied Mathematics and Mechanics, vol. 2, no. 1, pp. 34–40, 2006.
- M. Pakdemirli, “Similarity analysis of boundary layer equations of class of non-Newtonian fluids,” International Journal of Nonlinear Mechanics, vol. 29, no. 2, pp. 187–196, 1994.
- M. Pakdemirli, M. Yürüsoy, and A. Küçükbursa, “Symmetry groups of boundary layer equations of class of non-Newtonian fluids,” International Journal of Nonlinear Mechanics,, vol. 31, no. 3, pp. 267–276, 1996.
- M. Yürüsoy and M. Pakdemirli, “Symmetry reductions of unsteady three-dimensional boundary layers of some non-Newtonian fluids,” International Journal of Engineering Science, vol. 35, no. 8, pp. 731–740, 1997.
- G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer, New York, NY, USA, 1989.
- H. Stephani, Differential Equations: Their Solution Using Symmetries, Cambridge University Press, New York, NY, USA, 1989.
- Wolfram Mathematica, MathLie 3.0, Dr. Gerd Baumann, 1992.
- L. F. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with MATLAB, chapter 3, Cambridge University Press, 2003.
- J. Kierzenka and L. F. Shampine, “A BVP solver based on residual control and the MATLAB PSE,” ACM Transactions on Mathematical Software, vol. 27, no. 3, pp. 299–316, 2001.