A Numerical Study of Oscillating Peristaltic Flow of Generalized Maxwell Viscoelastic Fluids Through a Porous Medium

Transport in Porous Media

Volumn 95, Issue 2, 2012, Pages 337-348

  Tripathi, Dharmendra ^a   Bég, O Anwar ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY ROPAR   (India)

^b SHEFFIELD HALLAM UNIVERSITY   (United Kingdom)

Author keywords

Fractional Maxwell model; Homotopy perturbation method (HPM); Oscillating flow; Peristalsis; Porous medium; Pumping; Trapping

Indexed keywords

HOMOTOPY PERTURBATION METHOD (HPM); MAXWELL MODELS; PERISTALSIS; POROUS MEDIUM; TRAPPING;

FLOW RATE; MAXWELL EQUATIONS; OPTICAL PUMPING; POROUS MATERIALS; PUMPS; RELAXATION TIME; REYNOLDS NUMBER;

OSCILLATING FLOW;

FLOW MODELING; NUMERICAL MODEL; OSCILLATING FLOW; PERTURBATION; POROUS MEDIUM; REYNOLDS NUMBER; VISCOELASTIC FLUID;

EID: 84867103825     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-012-0046-5     Document Type: Article

References (36)

1. Bég O. A., Takhar H. S., Soundalgekar V. M.: Thermoconvective flow in a saturated, isotropic, homogeneous porous medium using Brinkman's model: numerical study. Int. J. Numer. Methods Heat Fluid Flow 8, 559-589 (1998).
2. Bég O. A., Zueco J., Ghosh S. K.: Unsteady hydromagnetic natural convection of a short-memory viscoelastic fluid in a non-Darcian regime: network simulation. Chem. Eng. Commun. 198, 172-190 (2011).
3. He J. H.: Homotopy perturbation technique. Comput. Meth. Appl. Mech. Eng. 178, 257-262 (1999).
4. Khan M.: The Rayleigh-Stokes problem for an edge in a viscoelastic fluid with a fractional derivative model. Nonlinear Anal. Real World Appl. 10, 3190-3195 (2009a).
5. Khan M.: Exact solutions for the accelerated flows of a generalized second-grade fluid between two sidewalls perpendicular to the plate. J. Porous Media 12, 919-926 (2009b).
6. Khan M., Ali S. H., Fetecau H., Qi C.: Decay of potential vortex for a viscoelastic fluid with fractional Maxwell model. Appl. Math. Model. 33, 2526-2533 (2009a).
7. Khan M., Ali S. H., Qi H.: On accelerated flows of a viscoelastic fluid with the fractional Burgers' model. Nonlinear Anal. Real World Appl. 10, 2286-2296 (2009b).
8. Khan M., AliS H., Qi H.: Exact solutions of starting flows for a fractional Burgers' fluid between coaxial cylinders. Nonlinear Anal. Real World Appl. 10, 1775-1783 (2009c).
9. Khan M., Anjum A., Fetecau H., Qi C.: Exact solutions for some oscillating motions of a fractional Burgers' fluid. Math. Comput. Modell. 51, 682-692 (2010).
10. Liu Y., Zheng L., Zhang X.: Unsteady MHD Couette flow of a generalized Oldroyd-B fluid with fractional derivative. Comput. Math. Appl. 61, 443-450 (2011).
11. Mainardi F., Spada G.: Creep, relaxation and viscosity properties for basic fractional models in rheology. Eur. Physi. J. Special Top. 193, 133-160 (2011).
12. Nadeem S.: General periodic flows of fractional Oldroyd-B fluid for an edge. Phys. Lett. A 368, 181-187 (2007).
13. Qi H., Jin H.: Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders. Acta Mech. Sin. 22, 301-305 (2006).
14. Qi H., Xu M.: Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative. Appl. Math. Model. 33, 4184-4191 (2009).
15. Rashidi M. M., Keimanesh M., Bég O. A., Hung T. K.: Magneto-hydrodynamic biorheological transport phenomena in a porous medium: a simulation of magnetic blood flow control and filtration. Int. J. Numer. Methods Biomed. Eng. 27, 805-821 (2011).
16. Rashidi M. M., Bég O. A., Rahimzadeh N.: A generalized DTM for combined free and forced convection flow about inclined surfaces in porous media. Chem. Eng. Commun. 199, 257-282 (2012).
17. Tan T., Masuoka W. C., Stokes' first problem for a second grade fluid in a porous half-space with heated boundary. Int. J. Non-Linear Mech. 40, 515-522 (2005a).
18. Tan, W. C., Masuoka T.: Stokes' first problem for an Oldroyd-B fluid in a porous half space. Phys. Fluids 17, Article ID 023101 (2005b).
19. Tan T., Masuoka W. C., Stability analysis of a Maxwell fluid in a porous medium heated from below. Phys. Lett. A 360, 454-460 (2007).
20. Tan W., Pan M., Xu W.: A note on unsteady flows of a viscoelastic fluid with the fractional Maxwell model between two parallel plates. Int. J. Non-Linear Mech. 38, 645-650 (2003).
21. Tripathi, D.: Numerical study on creeping flow of Burgers' fluids through a peristaltic tube. ASME J. Fluids Eng. 133, 121104-1-9 (2011a).
22. Tripathi D.: A mathematical model for the peristaltic flow of chyme movement in small intestine. Math. Biosci. 233, 90-97 (2011b).
23. Tripathi D.: Peristaltic transport of fractional Maxwell fluids in uniform tubes: application of an endoscope. Comput. Math. Appl. 62, 1116-1126 (2011c).
24. Tripathi D.: Numerical and analytical simulation of peristaltic flows of generalized Oldroyd-B fluids. Int. J. Numer. Methods Fluids 67, 1932-1943 (2011d).
25. Tripathi D.: Numerical study on peristaltic flow of generalized Burgers' fluids in uniform tubes in presence of an endoscope. Int. J. Numer. Methods Biomed. Eng. 27, 1812-1828 (2011e).
26. Tripathi D.: Peristaltic transport of a viscoelastic fluid in a channel. Acta Astron. 68, 1379-1385 (2011f).
27. Tripathi D.: Numerical study on peristaltic transport of fractional bio-fluids. J. Mech. Med. Biol. 11, 1045-1058 (2011g).
28. Tripathi D.: Peristaltic flow of couple-stress conducting fluids through a porous channel: applications to blood flow in the micro-circulatory system. J. Biol. Syst. 19, 461-477 (2011h).
29. Tripathi D.: Peristaltic hemodynamic flow of couple-stress fluids through a porous medium with slip effect. Transp. Porous Media 92, 559-572 (2012).
30. Tripathi D., Pandey S. K., Das S.: Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel. Appl. Math. Comput. 215, 3645-3654 (2010).
31. Tripathi D., Pandey S., Das S. K.: Peristaltic transport of a generalized Burgers' fluid: application to the movement of chyme in small intestine. Acta Astron. 69, 30-38 (2011).
32. Vieru D., Fetecau C., Fetecau C.: Flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate. Appl. Math. Comput. 200, 459-464 (2008).
33. Wang S., Xu M.: Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus. Nonlinear Anal. Real World Appl. 10, 1087-1096 (2009).
34. Xue, C., Nie, J.: Exact solutions of Rayleigh-Stokes problem for heated generalized Maxwell fluid in a porous half-space. Math. Prob. Eng. 2008, Article ID 641431 (2008).
35. Zueco J., Bég O. A., Bég T. A.: Numerical solutions for unsteady rotating high-porosity medium channel Couette hydrodynamics. Phys. Scr. 80, 1-8 (2009a).
36. Zueco J., Bég O. A., Bég T. A., Takhar H. S.: Numerical study of chemically-reactive buoyancy driven heat and mass transfer across horizontal cylinder in high-porosity non-Darcian regime. J. Porous Media 12, 519-535 (2009b).