An analytical study on motion of a sphere rolling down an inclined plane submerged in a Newtonian fluid

Powder Technology

Volumn 198, Issue 1, 2010, Pages 82-92

  Jalaal, M ^a   Ganji, D D ^b  

^a UNIVERSITY OF TABRIZ   (Iran)

^b BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Acceleration motion; Drag coefficient; Homotopy perturbation method (HPM); Inclined plane; Spherical particle

Indexed keywords

ANALYTICAL SOLUTIONS; EQUATION OF MOTION; HOMOTOPY PERTURBATION METHOD; INCLINED PLANES; MANUFACTURING PROCESS; NEW APPLICATIONS; NEWTONIAN FLUIDS; NEWTONIANS; NONLINEAR PROBLEMS; SPHERICAL PARTICLE; UNSTEADY MOTION;

DRAG; DRAG COEFFICIENT; LINEARIZATION; MACHINERY; PERTURBATION TECHNIQUES; REYNOLDS NUMBER; SPHERES;

EQUATIONS OF MOTION;

GLYCEROL; OLIVE OIL; WATER;

ACCELERATION; ANALYTIC METHOD; AQUEOUS SOLUTION; ARTICLE; FLOW KINETICS; FLOW RATE; FLUID FLOW; GRAVITY; HOMOTOPY PERTUBATION METHOD; MATHEMATICAL ANALYSIS; MOTION; NEWTONIAN FLUID; NONLINEAR SYSTEM; PARTICLE SIZE; VELOCITY; VISCOSITY;

EID: 72149102421     PISSN: 00325910     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.powtec.2009.10.018     Document Type: Article

References (44)

1. Delleur J.W. New results and research needs on sediment movement in urban drainage. J. Water Resour. Plan. Manage., ASCE 127 3 (2001) 186-193
2. Hvitved-Jacobsen T., Vollertsen J., and Tanaka N. Wastewater quality changes during transport in sewers: an integrated aerobic and anaerobic model concept for carbon and sulfur microbial transformations. Water Sci. Technol. 38 10 (1998) 257-264
3. Cao Z.X. Equilibrium near-bed concentration of suspended sediment. J. Hydraul. Eng., ASCE 125 12 (1999) 1270-1278
4. Bridge J.S., and Bennett S.J. A model for the entrainment and transport of sediment grains of mixed sizes, shapes, and densities. Water Resour. Res. 28 2 (1992) 337-363
5. Duran J. The physics of fine powders: plugging and surface instabilities. C.R. Phys. 3 2 (2002) 17-227
6. Yates J.G. Fundamentals of fluidized-bed processes (1983), Butterworths, London
7. Cheng N.S. Simplified settling velocity formula for sediment particle. J. Hydraul. Eng. 123 (1997) 149-152
8. Boillat J.L., and Graf N.H. Vitesse de sedimentation de particules spheriques en milieu turbulent. J. Hydraul. Res. 30 (1982) 395-413
9. Joseph D.D., Liu Y.L., Poletto M., and Feng J. Aggregation and dispersion of spheres falling in viscoelastic liquids. J. Non-Newtonian Fluid mech 54 (1994) 45-86
10. Clift R., Grace J.R., and Weber M.E. Bubbles, drops and particles (1978), Academic Press, New York
11. Khan A.R., and Richardson J.F. The resistance to motion of a solid sphere in a fluid. Chem. Eng. Commun. 62 (1987) 135-150
12. Chhabra R.P. Bubbles, drops and particles in non-Newtonian fluids (1993), CRC Press, Boca Raton, FL
13. Hartman M., and Yates J.G. Free-fall of solid particles through fluids. Collect. Czechoslov. Chem. Commun. 58 5 (1993) 961-982
14. Ferreira J.M., and Chhabra R.P. Accelerating motion of a vertically falling sphere in incompressible Newtonian media: an analytical solution. J. Powder Technol. 97 (1998) 6-15
15. Jan C.D., and Chen J.C. Movements of a sphere rolling down an inclined plane. J. Hydraulic Res. 35 5 (1997) 689-706
16. Chhabra R.P., and Ferreira J.M. An analytical study of the motion of a sphere rolling down a smooth inclined plane in an incompressible Newtonian fluid. Powder Technol. 104 (1999) 130-138
17. Rumpf H. Particle technology (1990), Chapman and Hall, London
18. Ferreira J.M., Duarte Naia M., and Chhabra R.P. An analytical study of the transient motion of a dense rigid sphere in an incompressible Newtonian fluid. Chem. Eng. Commun. 168 1 (1998)
19. Oseen C. Hydrodynamik, Chapter 10 (1927), Akademische Verlagsgesellschaft, Leipzig
20. He J.H. Homotopy perturbation technique. J. Comput. Math. Appl. Mech. Eng 17 8 (1999) 257-262
21. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. J. Comput. Math. Appl. Mech. Eng 167 (1998) 57-68
22. He J.H. A review on some new recently developed nonlinear analytical techniques. Internat J. Nonlinear Sci. Numer. Simul. 1 (2000) 51-70
23. He J.H. Modified Lindstedt-Poincare methods for some non-linear oscillations. Part III: double series expansion. Internat J. Nonlinear Sci. Numer. Simul. 2 (2001) 317-320
24. He J.H. Homotopy perturbation method for bifurcation on nonlinear problems. Internat J. Nonlinear Sci. Numer. Simul. 6 (2005) 207-208
25. He J.H. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod Phys. B 20 (2006) 1141-1199
26. Ganji D.D., and Rajabi A. Assessment of homotopy-perturbation and perturbation methods in heat radiation equations. Internat. Comm. Heat Mass Transfer 33 (2006) 391-400
27. Ganji D.D., and Sadighi A. Application of He's Homotopy-perturbation Method to Nonlinear Coupled Systems of Reaction-diffusion Equations. Internat J. Nonlinear Sci. Numer. Simul. 7 4 (2006) 411-418
28. Ariel P.D., Hayat T., and Asghar S. Homotopy perturbation method and axisymmetric Flow over a stretching sheet. Internat J. Nonlinear Sci. Numer. Simul. 7 4 (2006) 399-406
29. Hosein Nia S.H., Ranjbar A.N., Ganji D.D., Soltani H., and Ghasemi J. Maintaining the stability of nonlinear differential equations by the enhancement of HPM. Physics Letters A 372 16 (2008) 2855-2861
30. Ganji Z.Z., and Ganji D.D. Approximate solutions of thermal boundary-layer problems in a semi-infinite flat plate by using He's homotopy perturbation method. Internat J. Nonlinear Sci. Numer. Simul. 9 4 (2008) 415-422
31. Beléndez A., Beléndez T., Márquez A., and Neipp C. Application of He's homotopy perturbation method to conservative truly nonlinear oscillators. Chaos, Solitons Fractals 37 3 (2008) 770-780
32. Morsch F., Tolou N., and Herder J.L. Comparison of methods for large deflection analysis of a cantilever beam under free end point load cases, Proceedings of the 33th ASME DETC Biennial (2009), Mechanisms and Robotics Conference, San Diego, Calif, USA August-September
33. Siddiqui A.M., Zeb A., Ghori Q.K., and Benharbit A.M. Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates. Chaos, Solitons Fractals 36 1 (2008) 182-192
34. Rafei M., Daniali H., Ganji D.D., and Pashaei H. Solution of the prey and predator problem by homotopy perturbation method. Appl. Math. Comput. 188 2 (2007) 1419-1425
35. L.N. Zhang, J.H. He, Homotopy perturbation method for the solution of the electrostatic potential differential equation. Mathematical Problems in Engineering, Art. No. 83878(2006).
36. Ganji D.D., and Sadighi A. Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations. J. Comput. Math. Appl. Mech. Eng 207 1 (2007) 24-34
37. Esmaeilpour M., and Ganji D.D. Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate. Physics Letters A 372 1 (2007) 33-38
38. Rajabi A., Ganji D.D., and Taherian H. Application of homotopy perturbation method in nonlinear heat conduction and convection equations. Physics Letters A. 360 (2007) 570-573
39. Ganji D.D., and Rafei M. Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method. Physics Letters A 356 (2006) 131-137
40. Ganji D.D., Afrouzi G.A., and Talarposhti R.A. Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations. Physics Letters A 368 (2007) 450-457
41. Ganji D.D. The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer. Physics Letters A 355 (2006) 337-341
42. Ramiar A., Ganji D.D., and Esmaili Q. Homotopy perturbation method and variational iteration method for orthogonal 2-D and axisymmetric impinging jet problems. Internat J. Nonlinear Sci. Numer. Simul. 9 2 (2008) 115-130
43. Yildirim A. Exact solutions of nonlinear differential-difference equations by He's homotopy perturbation method. Internat J. Nonlinear Sci. Numer. Simul. 9 2 (2008) 111-114
44. Mahmood M., Hossain M.A., and Asghar S. Application of homotopy perturbation method to deformable channel with wall suction and injection in a porous medium. Internat J. Nonlinear Sci. Numer. Simul. 9 2 (2008) 195-206