Abstract
This article presents a numerical study on oscillating peristaltic flow of generalized Maxwell fluids through a porous medium. A sinusoidal model is employed for the oscillating flow regime. A modified Darcy-Brinkman model is utilized to simulate the flow of a generalized Maxwell fluid in a homogenous, isotropic porous medium. The governing equations are simplified by assuming long wavelength and low Reynolds number approximations. The numerical and approximate analytical solutions of the problem are obtained by a semi-numerical technique, namely the homotopy perturbation method. The influence of the dominating physical parameters such as fractional Maxwell parameter, relaxation time, amplitude ratio, and permeability parameter on the flow characteristics are depicted graphically. The size of the trapped bolus is slightly enhanced by increasing the magnitude of permeability parameter whereas it is decreased with increasing amplitude ratio. Furthermore, it is shown that in the entire pumping region and the free pumping region, both volumetric flow rate and pressure decrease with increasing relaxation time, whereas in the co-pumping region, the volumetric flow rate is elevated with rising magnitude of relaxation time.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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)
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)
He J.H.: Homotopy perturbation technique. Comput. Meth. Appl. Mech. Eng. 178, 257–262 (1999)
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)
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)
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)
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)
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)
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)
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)
Mainardi F., Spada G.: Creep, relaxation and viscosity properties for basic fractional models in rheology. Eur. Physi. J. Special Top. 193, 133–160 (2011)
Nadeem S.: General periodic flows of fractional Oldroyd-B fluid for an edge. Phys. Lett. A 368, 181–187 (2007)
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)
Qi H., Xu M.: Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative. Appl. Math. Model. 33, 4184–4191 (2009)
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)
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)
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)
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)
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)
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)
Tripathi, D.: Numerical study on creeping flow of Burgers’ fluids through a peristaltic tube. ASME J. Fluids Eng. 133, 121104-1-9 (2011a)
Tripathi D.: A mathematical model for the peristaltic flow of chyme movement in small intestine. Math. Biosci. 233, 90–97 (2011b)
Tripathi D.: Peristaltic transport of fractional Maxwell fluids in uniform tubes: application of an endoscope. Comput. Math. Appl. 62, 1116–1126 (2011c)
Tripathi D.: Numerical and analytical simulation of peristaltic flows of generalized Oldroyd-B fluids. Int. J. Numer. Methods Fluids 67, 1932–1943 (2011d)
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)
Tripathi D.: Peristaltic transport of a viscoelastic fluid in a channel. Acta Astron. 68, 1379–1385 (2011f)
Tripathi D.: Numerical study on peristaltic transport of fractional bio-fluids. J. Mech. Med. Biol. 11, 1045–1058 (2011g)
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)
Tripathi D.: Peristaltic hemodynamic flow of couple-stress fluids through a porous medium with slip effect. Transp. Porous Media 92, 559–572 (2012)
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)
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)
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)
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)
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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tripathi, D., Bég, O.A. A Numerical Study of Oscillating Peristaltic Flow of Generalized Maxwell Viscoelastic Fluids Through a Porous Medium. Transp Porous Med 95, 337–348 (2012). https://doi.org/10.1007/s11242-012-0046-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-012-0046-5