A series solution of the long porous slider

Tribology Transactions

Volumn 54, Issue 2, 2011, Pages 187-191

  Khan, Yasir ^a   Faraz, Naeem ^b   Yildirim, Ahmet ^c   Wu, Qingbiao ^a  

^a ZHEJIANG UNIVERSITY   (China)

^b DONGHUA UNIVERSITY   (China)

^c EGE UNIVERSITY   (Turkey)

Author keywords

Homotopy Perturbation Method; Porous Slider; Reynolds Number; Series Solution

Indexed keywords

HOMOTOPY PERTURBATION METHOD; MOMENTUM EQUATION; NONLINEAR ORDINARY DIFFERENTIAL EQUATION; NUMERICAL RESULTS; POROUS SLIDER; REYNOLDS; SERIES SOLUTIONS; SIMILARITY SOLUTION; VELOCITY FIELD;

NONLINEAR EQUATIONS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; REYNOLDS NUMBER;

PERTURBATION TECHNIQUES;

EID: 78650559809     PISSN: 10402004     EISSN: 1547397X     Source Type: Journal    
DOI: 10.1080/10402004.2010.533818     Document Type: Article

References (47)

1. Wang, C. Y. (1974), "Fluid Dynamics of the Circular Porous Slider," Journal of Applied Mechanics, 41, pp 343-347.
2. Shalak, F. M., and Wang, C. Y. (1975), "Fluid Dynamics of a Long Porous Slider," Journal of Applied Mechanics, 42, pp 893-894.
3. Shalak, F. M., and Wang, C. Y. (1978), "On the Nonunique Solutions of Laminar Flow through a Porous Tube or Channel," SIAM Journal on Applied Mathematics, 34, pp 535-544.
4. Wang, C. Y. (1978), "The Elliptic Porous Slider at Low Crossflow Reynolds Numbers," Journal of Lubrication Technology, 100, pp 444-446.
5. Watson, L. T., Li, T. Y., and Wang, C. Y. (1978), "Fluid Dynamics of the Elliptic Porous Slider," Journal of Applied Mechanics, 45, pp 435-436.
6. Bhatt, B. S. (1981), "The Elliptic Porous Slider at Low Cross-Flow Reynolds Number Using a Non-Newtonian Second-Order Fluid," Wear, 71, pp 249-253.
7. Ariel, P. D. (1993), "Flow of Viscoelastic Fluids through a Porous Channel-I," International Journal for Numerical Methods in Fluids, 17, pp 605-633.
8. Berman, A. S. (1953), "Laminar Flow in a Channel with Porous Walls," Journal of Applied Physics, 24, pp 1232-1235.
9. Proudman, L. (1960), "An Example of Study Laminar Flow at large Reynolds Number," Journal of Applied Mechanics, 9, pp 593-602.
10. Terrill, R. M. (1964), "Laminar Flow in a Uniformly Porous Channel," Aeronautical Quarterly, 15, pp 299-310.
11. Elkouh, A. F. (1968), "Laminar Flow between Rotating Porous Disks," Journal of the Engineering Mechanics Division, 94, pp 919-929.
12. Rasmussen, H. (1970), "Steady Viscous Flow between Two Porous Disks," Zeitschrift für Angewandte Mathematik und Physik, 21, pp 187-195.
13. Brady, J. F. (1984), "Flow Development in a Porous Channel and Tube," Physics of Fluids, 27, pp 1061-1067.
14. Cox, S. M. (1991), "Two Dimensional Flow of a Viscous Fluid in a Channel with Porous Walls," Journal of Fluid Mechanics, 227, pp 1-33.
15. Sellars, J. R. (1955), "Laminar Flow in Channels with Porous Walls at High Suction Reynolds Numbers," Journal of Applied Physics, 26, pp 489-490.
16. White, F. M., Barfield, B. F., and Goglia, M. J. (1958), "Laminar Flow in a Uniform Porous Channel," Journal of Applied Mechanics, 25, pp 613-617.
17. Yuan, S. W. (1956), "Further Investigation of Laminar Flow in Channels with Porous Walls," Journal of Applied Physics, 27, pp 267-269.
18. Zaturska, M. B., Drazin, P. G., and Banks, W. H. H. (1988), "On the Flow of a Viscous Fluid Driven along a Channel by Suction at Porous Walls," Fluid Dynamics Research, 4, pp 151-178.
19. Murti, P. R. K. (1974), "Analysis of Porous Slider Bearings," Wear, 28, pp 131-134.
20. Srinivasan, U. (1977), "The Analysis of a Double-Layered Porous Slider Bearing," Wear, 42, pp 205-215.
21. Verma, P. D. S., Agrawal, V. K., and Bhatt, S. B. (1978), "The Optimal Profile for a Porous Slider Bearing," Wear, 48, pp 9-14.
22. Kumar, V. (1980), "Friction of a Plane Porous Slider of Optimal Profile," Wear, 62, pp 417-418.
23. Sanni, S. A., and Ayomidele, I. O. (1991), "Hydrodynamic Lubrication of a Porous Slider: Limitations of the Simplifying Assumption of a Small Porous Facing Thickness," Wear, 147, pp 1-7.
24. Ishizawa, S., and Hori, E. (1966), "The Flow of a Viscous Fluid through a Porous Wall into a Narrow Gap (a Consideration of the Slip of Fluid on a Porous Wall Surface)," Bulletin of the JSME, 9(36), pp 719-730.
25. Beavers, G. S., and Joseph, D. D. (1967), "Boundary Conditions at a Naturally Permeable Wall," Journal of Fluid Mechanics, 30(1), pp 191-207.
26. Lin, J.-R. (2001), "Optimal Design of One-Dimensional Porous Slider Bearings Using the Brinkman Model," Tribology International, 34, pp 57-64.
27. Lin, J.-R. (2001), "Performance Characteristics of Finite Porous Slider Bearings: Brinkman Model," Tribology International, 34, pp 181-189.
28. He, J. H. (2006), "Homotopy Perturbation Method for Solving Boundary Value Problems," Physics Letters A, 350, pp 87-88.
29. He, J. H. (1999), "Homotopy Perturbation Technique," Computational Methods in Applied Mechanics and Engineering, 178, pp 257-262.
30. He, J. H. (2008), "Recent Development of the Homotopy Perturbation Method," Topological Methods in Nonlinear Analysis, 31, pp 205-209.
31. He, J. H. (2006), "Some Asymptotic Methods for Strongly Nonlinear Equations," International Journal of Modern Physics B, 20, pp 1141-1199.
32. He, J. H. (2006), "New Interpretation of Homotopy Perturbation Method," International Journal of Modern Physics B, 20, pp 2561-2568.
33. He, J. H. (2008), "An Elementary Introduction to Recently Developed Asymptotic Methods and Nanomechanics in Textile Engineering," International Journal of Modern Physics B, 22, pp 3487-3578.
34. Yildirim, A., and Öziş, T. (2007), "Solutions of Singular IVPs of Lane-Emden Type by Homotopy Perturbation Method," Physics Letters A, 369, pp 70-76.
35. Yildirim, A. (2008), "Solution of BVPs for Fourth-Order Integro-Differential Equations by Using Homotopy Perturbation Method," Computers & Mathematics with Applications, 56, pp 3175-3180.
36. Yildirim, A. (2008), "The Homotopy Perturbation Method for Approximate Solution of the Modified KdV Equation," Zeitschrift für Naturforschung A, A Journal of Physical Sciences, 63a, pp 621-626.
37. Shakeri, F., and Dehghan, M. (2007), "Inverse Problem of Diffusion Equation by He's Homotopy Perturbation Method," Physica Scripta, 75, pp 551-556.
38. Dehghan, M., and Shakeri, F. (2007), "Solution of a Partial Differential Equation Subject to Temperature Overspecification by He's Homotopy Perturbation Method," Physica Scripta, 75, pp 778-787.
39. Ganji, D. D., and Sadighi, A. (2006), "Application of He's Homotopy-Perturbation Method to Nonlinear Coupled Systems of Reaction-Diffusion Equations," International Journal of Nonlinear Sciences and Numerical Simulation, 7(4), pp 411-418.
40. Achouri, T., and Omrani, K. (2009), "Application of the Homotopy Perturbation Method to the Modified Regularized Long Wave Equation," Numerical Methods for Partial Differential Equations, 26, pp 399-411.
41. Wazwaz, A. M. (2000), "A New Algorithm for Calculating Adomian Polynomials for Nonlinear Operators," Applied Mathematics and Computation, 111, pp 53-69.
42. Khan, Y. (2009), "An Effective Modification of the Laplace Decomposition Method for Nonlinear Equations," International Journal of Nonlinear Sciences and Numerical Simulation, 10(11-12), pp 1373-1376.
43. Khan, Y., and Wu, Q. (2010), "Homotopy Perturbation Transform Method for Nonlinear Equations Using He's Polynomials," Computers and Mathematics with Applications, DOI: 10.10161/J.camwa.2010.08.022.
44. Hesameddini, E., and Latifizadeh, H. (2009), "An Optimal Choice of Initial Solutions in the Homotopy Perturbation Method," International Journal of Nonlinear Sciences and Numerical Simulation, 10, pp 1389-1398.
45. Hesameddini, E., and Latifizadeh, H. (2009), "A New Vision of the He's Homotopy Perturbation Method," International Journal of Nonlinear Sciences and Numerical Simulation, 10, pp 1415-1424.
46. Mousa, M. M., and Kaltayev, A. (2009), "Application of the Homotopy Perturbation Method to a Magneto-Elastico-Viscous Fluid along a Semi-Infinite Plate," International Journal of Nonlinear Sciences and Numerical Simulation, 10, pp 1113-1120.
47. Mehmood, A., and Ali, A. (2009), "An Application of He's Homotopy Perturbation Method in Fluid Mechanics," International Journal of Nonlinear Sciences and Numerical Simulation, 10, pp 239-246.