1887
Volume 2013, Issue 1
  • E-ISSN: 2223-506X

Abstract

In this paper, the differential equation of a vertically falling non-spherical particle in incompressible Newtonian media is solved by homotopy analysis method (HAM). The results are analyzed using graphs and comparison tables.

Loading

Article metrics loading...

/content/journals/10.5339/connect.2013.23
2013-10-01
2019-11-17
Loading full text...

Full text loading...

/deliver/fulltext/connect/2013/1/connect.2013.23.html?itemId=/content/journals/10.5339/connect.2013.23&mimeType=html&fmt=ahah

References

  1. Yaghoobi H, Torabi M. Analytical solution for settling of non-spherical particles in incompressible Newtonian media. Powder Technol. 2012; 221::453463
    [Google Scholar]
  2. Jalaal M, Ganji DD. An analytical study on motion of a sphere rolling down an inclined plane submerged in a Newtonian fluid. Powder Technol. 2010; 198:1:8292
    [Google Scholar]
  3. Chhabra RP, Agarwal L, Sinha NK. Drag on non-spherical particles: an evaluation of available methods. Powder Technol. 1999; 101:3:288295
    [Google Scholar]
  4. Chhabra RP. Wall effects on terminal velocity of non-spherical particles in non-Newtonian polymer solutions. Powder Technol. 1996; 88:1:3944
    [Google Scholar]
  5. Jalaal M, Ganji DD, Ahmadi G. An analytical study on settling of non-spherical particles. Asia-Pac J Chem Eng. 2012; 7:1:6372
    [Google Scholar]
  6. Jalaal M, Ganji DD, Ahmadi G. Analytical investigation on acceleration motion of a vertically falling spherical particle in incompressible Newtonian media. Advan Powder Technol. 2010; 21:3:298304
    [Google Scholar]
  7. Jalaal M, Ganji DD. On unsteady rolling motion of spheres in inclined tubes filled with incompressible Newtonian fluids. Advan Powder Technol. 2011; 22:1:5867
    [Google Scholar]
  8. Jalaal M, Nejad MG, Jalili P, Esmaeilpour M, Bararnia H, Ghasemi E, Soleimani S, Ganji DD, Moghimi SM. Homotopy perturbation method for motion of a spherical solid particle in plane couette fluid flow. Comp Math Appl. 2011; 61:8:22672270
    [Google Scholar]
  9. Chhabra RP, Ferreira JM. An analytical study of the motion of a sphere rolling down a smooth inclined plane in an incompressible Newtonian fluid. Powder Technol. 1999; 104:2:130138
    [Google Scholar]
  10. Yaghoobi H, Torabi M. Novel solution for acceleration motion of a vertically falling non-spherical particle by VIM-Padé approximant. Powder Technol. 2012; 215–216::206209
    [Google Scholar]
  11. Clift R, Grace J, Weber ME. Bubbles, Drops and Particles. New York: Academic Press 1978;
    [Google Scholar]
  12. Chien S-F. Settling Velocity of Irregularly Shaped Particles. SPE Drill Complet. 1994; 9:4:281289
    [Google Scholar]
  13. Abbasbandy S. Homotopy analysis method for generalized Benjamin-Bona-lMahony equation. Z angew Math Phys. 2008; 59:1:5162
    [Google Scholar]
  14. Abbasbandy S, Zakaria FS. Soliton solutions for the fifth-order KdV equation with the homotopy analysis method. Nonlinear Dyn. 2007; 51:1–2:8387
    [Google Scholar]
  15. Abbasbandy S. Homotopy analysis method for the Kawahara equation. Nonlinear Anal Real World Appl. 2010; 11:1:307312
    [Google Scholar]
  16. Abbasbandy S, Shivanian E, Vajravelu K. Mathematical properties of - curve in the frame work of the homotopy analysis method. Comm Nonlinear Sci Numer Simulat. 2011; 16:11:42684275
    [Google Scholar]
  17. Abbasbandy S. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys Lett A. 2006; 360:1:109113
    [Google Scholar]
  18. Abbasbandy S. The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation. Phys Lett A. 2007; 361:6:478483
    [Google Scholar]
  19. Liao SJ. Beyond Perturbation: Introduction to the Homotopy Analysis Method. CRC Series: Modern mechanics and mathematics. Boca Raton, Chapman and Hall: CRC Press 2003;
    [Google Scholar]
  20. Liao S. On the homotopy analysis method for nonlinear problems. Appl Math Comput. 2004; 147:2:499513
    [Google Scholar]
  21. Liao S. Comparison between the homotopy analysis method and homotopy perturbation method. Appl Math Comput. 2005; 169:2:11861194
    [Google Scholar]
  22. Gurtin ME, MacCamy RC. On the diffusion of biological populations. Math Biosci. 1977; 33:1–2:3549
    [Google Scholar]
  23. Gurney WSC, Nisbet RM. The regulation of inhomogeneous populations. J Theor Biol. 1975; 52:2:441457
    [Google Scholar]
  24. Lu Y-G. Hölder estimates of solutions of biological population equations. Appl Math Lett. 2000; 13:6:123126
    [Google Scholar]
  25. Tan Y, Abbasbandy S. Homotopy analysis method for quadratic Riccati differential equation. Comm Nonlinear Sci Numer Simulat. 2008; 13:3:539546
    [Google Scholar]
  26. Hayat T, Khan M, Asghar S. Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid. Acta Mechanica. 2004; 168:3–4:213232
    [Google Scholar]
  27. Hayat T, Khan M. Homotopy solutions for a generalized second-grade fluid past a porous plate. Nonlinear Dyn. 2005; 42:4:395405
    [Google Scholar]
  28. Mohyud-Din ST, Yildirim A. Numerical solution of the three-dimensional Helmholtz equation. Chin Phys Lett. 2010; 27:6:060201
    [Google Scholar]
  29. Yildirim A, Mohyud-Din ST. Analytical approach to space- and time-fractional Burgers equations. Chin Phys Lett. 2010; 27:9:090501
    [Google Scholar]
  30. Hassan QM, Jamshed M, Shakeel M, Mohyud-Din ST. Homotopy analysis method using modified Riemann-Liouville derivative for solving space and time-fractional KdV equations. Int J Modern Math Sci. 2013; 5:1:1426
    [Google Scholar]
  31. Guo J. Motion of spheres falling through fluids. Journal of Hydraul Res. 2011; 49:1:3241
    [Google Scholar]
  32. Mohazzabi P. Falling and rising in a fluid with both linear and quadratic drag. Can J Phys. 2010; 88:9:623626
    [Google Scholar]
  33. Podlubny I. Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications. San Diego: Academic Press 1999:198
    [Google Scholar]
  34. Caputo M. Linear models of dissipation whose Q is almost frequency independent-II. Geophys J Int. 1967; 13:5:529539
    [Google Scholar]
  35. Yang X-J. Advanced Local Fractional Calculus and Its Applications. New York, NY: World Science Publisher 2012;
    [Google Scholar]
  36. Yang X-J, Baleanu D. Fractal heat conduction problem solved by local fractional variation iteration method. Therm Sci. 2013; 7:2:625628
    [Google Scholar]
  37. Yang X-J, Srivastava HM, He J-H, Baleanu D. Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives. Phys Lett A. 2013; 377:28–30:16961700
    [Google Scholar]
  38. Ellahi R. Effects of the slip boundary condition on non-Newtonian flows in a channel. Comm Nonlinear Sci Numer Simulat. 2009; 14:4:13771384
    [Google Scholar]
  39. Ellahi R, Riaz A. Analytical solutions for MHD flow in a third-grade fluid with variable viscosity. Math Comp Model. 2010; 52:9–10:17831793
    [Google Scholar]
  40. Ellahi R, Raza M, Vafai K. Series solutions of non-Newtonian nanofluids with Reynolds' model and Vogel's model by means of the homotopy analysis method. Math Comp Model. 2012; 55:7–8:18761891
    [Google Scholar]
  41. Ellahi R. A study on the convergence of series solution of non-Newtonian third grade fluid with variable viscosity: by means of homotopy analysis method. Advan Math Phys. 2012; 2012::111
    [Google Scholar]
  42. Ellahi R, Shivanian E, Abbasbandy S, Rahman SU, Hayat T. Analysis of steady flows in viscous fluid with heat/mass transfer and slip effects. Int J Heat Mass Trans. 2012; 55:23–24:63846390
    [Google Scholar]
  43. Ellahi R. The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions. Appl Math Model. 2013; 37:3:14511467
    [Google Scholar]
  44. Ellahi R, Zeeshan A. Series solutions of nonlinear partial differential equations with slip boundary conditions for non-Newtonian MHD fluid in porous space. J Appl Math Inform Sci. 2013; 7:1:253261
    [Google Scholar]
  45. Ellahi R, Aziz S, Zeeshan A. Non-Newtonian nanofluid flow through a porous medium between two coaxial cylinders with heat transfer and variable viscosity. J Porous Media. 2013; 16:3:205216
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.5339/connect.2013.23
Loading
/content/journals/10.5339/connect.2013.23
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): 02.30.Ik , 02.30.Jr , 05.45.Yv , h-curve , homotopy analysis method , non-spherical and nonlinear problems
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error