Analytical investigation for fluid behavior over a flat plate with oscillating motion and wall transpiration

Abstract

In this paper, fluid behavior over a flat plate with oscillating motion, starting from rest and wall transpiration is presented. The classical solution of this problem is given by Panton [22] and is found to be an especial case of the solution here presented. The analytical solution is obtained without the use of any special transformations, such as Laplace or Fourier transforms. Three highly accurate and simple semi analytical methods, Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM) and Adomians Decomposition Method (ADM) are used to solve this problem. The results show the effects of suction and injection of the wall on fluid behavior and reveal that VIM, HPM and ADM are very effective and accurate in comparison with the exact solution. A non-dimensional number is used to take in to account the injection or suction of fluid at the wall. This parameter is shown to be of great influence on the proposed velocity solution

Keywords

• Semi Analytical Methods (ADM,HPM,VIM),Oscillating wall; Navier-Stokes equation

Analytical investigation for fluid behavior over a flat plate with oscillating motion and wall transpiration

Öz

References

1. Adomian, G., 1992. A review of the decomposition method and some recent results for nonlinear equations, mathematical & computer modeling. 13, 17-43.
2. Adomian, G., 1994. Solution of physical problems by decomposition, computers & mathematics with applications. 27, 145-154.
3. Ahmadi, A.R., Zahmatkesh, A., Hatami, M., Ganji, D. D., 2014. A comprehensive analysis of the flow and heat transfer for a nanofluid over an unsteady stretching flat plate, Powder Technology. 258, 125–133.
4. Almeida Cruz, D.O., Ferreira Lins, E., 2010. The unsteady flow generated by an oscillating wall with transpiration, international journal of non-linear mechanics. 45, 453-457.
5. Das, S., Jana, M., Guria, M., Janna, R.N., 2008. Unsteady Viscous Incompressible Flow Due to an Oscillating plate in a Rotating Fluid, Journal of Physical Sciences. 12, 51-64.
6. Domairry, G., Hatami, M., 2014. Squeezing Cu–water nanofluid flow analysis between parallel plates by DTM
7. Padé Method, Journal of Molecular Liquids. 193, 37-44. Erdogan, M.E., Imrak, C.E., 2009. On the comparison of the solutions obtained by using two different transform methods for the second problem of stokes for newtonian fluids, International Journal of Non-Linear Mechanics. 44, 27
8. Ganji, D.D., Afrouzi,G.A., Talarposhti,R.A., 2007. Application of variational iteration method and homotopy perturbation method for nonlinear heat diffusion and heat transfer equations, phys. lett A. 368, 450-457.

9. Ganji, D.D., HashemiKachapi, S.H., 2011, Analysis of Nonlinear Equations in Fluids,progress in nonlinear science,volume 3, Asian Academic Publisher Limited, Hong Kong, China,pp. 1-294.
10. Ganji, D.D., Jannatabadi, M., Mohseni, E., 2007. Application of He’s Variational iteration method to nonlinear jaulent-Miodek equations and comparing it with ADM, journal of Computional and applied mathematics. 207, 35
11. HashemiKachapi, S.H., Barari, A., Tolou, N., Ganji, D.D., 2009. Solution of Strongly nonlinear oscillation systems using Variational approach, Journal of Applied Functional Analysis. 4, 528-535.
12. Hashemi, S.H., MohammadiDaniali, H.R., Ganji, D.D., 2007. Numerical simulation of the generalized Huxley equation by He’s homotopy perturbation method, Applied Mathematics and Computation. 192, 157-161.
13. Hatami, M., Ganji, D. D., 2014. Heat transfer and nanofluid flow in suction and blowing process between parallel disks in presence of variable magnetic field, Journal of Molecular Liquids. 190, 159–168.
14. Hatami, M., Ganji, D. D., 2013. Heat transfer and flow analysis for SA-TiO2 non-Newtonian nanofluid passing through the porous media between two coaxial cylinders, Journal of Molecular Liquids. 188, 155–161.
15. Hatami, M., Ganji, D. D., 2013. Thermal and flow analysis of microchannel heat sink (MCHS) cooled by Cu– water nanofluid using porous media approach and least square method, Energy Conversion and Management. 78, 347–358.