Two-dimensional viscous flow through expanding or contracting gaps with permeable walls using Parameterized Perturbation Method (PPM)

Subject Areas : Statistics

Mirollah Hosseini ¹

1 - Asistant Professor, Department of Mechanical Engineering, Islamic Azad University, Ghaemshahr Branch, Ghaemshahr, Mazandaran, Iran

Received: 2020-10-24 Accepted : 2021-03-06 Published : 2022-08-23

Keywords: عدد رینولدز نفوذ, روش اغتشاش پارامتری, آهنگ اتساع دیواره بدون بعد,

Abstract :

In this study, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved using a series based analytical techniques Parameterized Perturbation Method (PPM). The concept of this method is briefly introduced, and its application for this problem is studied. Then, the results are compared with numerical results and the validity of these methods is shown. After this verification, we analyze the effects of some physical applicable parameters to show the efficiency of PPM for this type of problems. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate ( ) and permeation Reynolds number ( ) on the velocity, normal pressure distribution and wall shear stress. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels.

References:

 

[1] H.N. Chang, J.S. Ha, J.K. Park, I.H. Kim, H.D. Shin, Velocity field of pulsatile flow in a porous tube, J. Biomech. 22: 1257-1262, (1989)

 

[2] E.C. Dauenhauer, J. Majdalani, Unsteady flows in semi-infinite expanding channels with wall injection, in: AIAA paper, 99-3523, (1999)

 

[3] J. Majdalani, C. Zhou, Moderate-to-large injection and suction driven channel flows with expanding or contracting walls, ZAMM Z. Angew. Math. Mech., 83: 181-196, (2003)

 

[4] Y.Z. Boutros, M.B. Abd-el-Malek, N.A. Badran, H.S. Hassan, Lie-group method for unsteady flows in a semi-infinite expanding or contracting pipe with injection or suction through a porous wall, J. Comput. Appl. Math. 197 (2): 465-494, (2006)

 

[5] J.H. He, Homotopy perturbation method for bifurcation on nonlinear problems, Int. J. Nonlinear Sci.

Numer.Simul. 6: 207–208, (2005)

 

[6] J.H. He, A review on some new recently developed nonlinear analytical techniques, Int. J. Non-linear

Sci. Numer. Simul., 1, 51–70, (2000)

 

[7] D.H. Shou, J.H. He, Application of parameter-expanding method to strongly nonlinear oscillators.

Int. J. Nonlinear. Sci. Numer. Simul 8 (1): 121, (2007)

 

[8] D. D. Ganji, H.Bararnia, S. Soleimani and E. Ghasemi, “Analytical solution of Magneto-Hydrodinamic flow over a Nonlinear Stretching Sheet”, Mode. Phys. Lett B. 23: 1-16, (2009)

[9] M. Jalaal , D.D. Ganji, On Unsteady Rolling Motion of Spheres in Inclined Tubes Filled with Incompressible Newtonian Fluids, Advanced Powder Technology,  (2010)

 

[10] M. Jalaal , D.D. Ganji, G.Ahmadi, Analytical Investigation on Acceleration Motion of a Vertically

Falling Spherical Particle in Incompressible Newtonian Media, Advanced Powder Technology,

(2009)

 

[11] M. Jalaal , D.D. Ganji, An Analytical Study on Motion of a Sphere Rolling Down an Inclined Plane Submerged in a Newtonian Fluid, Powder Technology, 198: 82–92, (2010)

 

[12] J. Majdalani, C. Zhou, C.A. Dawson, Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability, J. Biomech 35: 1399-1403, (2002)

 

[13] A.S. Berman, Laminar flow in channels with porous walls, J. Appl. Phys. 24: 1232_1235, (1953)

 

[14] He J.H., Recent developments in asymptotic methods for nonlinear ordinary equations, Nonlinear

Sci. Numer. Simul, 4: 81–83, (1999)