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Magnetohydrodynamic peristalsis of variable viscosity Jeffrey liquid with heat and mass transfer

  • Farooq, S. (Department of Mathematics, Quaid-I-Azam University) ;
  • Awais, M. (Department of Mathematics, COMSATS Institute of Information Technology) ;
  • Naseem, Moniza (Department of Mathematics, COMSATS Institute of Information Technology) ;
  • Hayat, T. (Department of Mathematics, Quaid-I-Azam University) ;
  • Ahmad, B. (Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2017.06.12
  • Accepted : 2017.07.09
  • Published : 2017.10.25

Abstract

The mathematical aspects of Dufour and Soret phenomena on the peristalsis of magnetohydrodynamic (MHD) Jeffrey liquid in a symmetric channel are presented. Fluid viscosity is taken variably. Lubrication approach has been followed. Results for the velocity, temperature, and concentration are constructed and explored for the emerging parameters entering into the present problem. The plotted quantities lead to comparative study between the constant and variable viscosities fluids. Graphical results indicate that for non-Newtonian materials, pressure gradient is maximum, whereas pressure gradient is slowed down for variable viscosity. Also both velocity and temperature in the case of variable viscosity are at maximum when compared with results for constant viscosity.

References

  1. T.W. Latham, Fluid Motion in Peristaltic Pump, M.S. Thesis, MIT Cambridge, MA, 1966.
  2. A.H. Shapiro, M.Y. Jafferin, S.L. Weinberg, Peristaltic pumping with long wavelength at low Reynolds number, J. Fluid Mech. 37 (1969) 799-825. https://doi.org/10.1017/S0022112069000899
  3. D. Tripathi, S.K. Pandey, S. Das, Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel, App. Math. Comp. 215 (2010) 3645-3654. https://doi.org/10.1016/j.amc.2009.11.002
  4. A. Ebaid, Remarks on the homotopy perturbation method for the peristaltic flow of Jeffrey fluid with nanoparticles in an asymmetric channel, Comp. Math. Appl. 68 (2014) 77-85. https://doi.org/10.1016/j.camwa.2014.05.008
  5. K. Ramesh, M. Devakar, Effect of heat transfer on the peristaltic transport of a MHD second grade fluid through a porous medium in an inclined asymmetric channel, Chin. J. Phys. 55 (2017) 825-844. https://doi.org/10.1016/j.cjph.2016.10.028
  6. Kh.S. Mekheimer, S.Z.A. Husseny, Y. Abd Elmaboud, Effect of heat transfer on peristaltic flow in a vertical asymmetric channel: perturbation solution, Numer. Methods Partial Differ. Equ. 26 (2010) 747-770.
  7. T. Hayat, N. Ali, Effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel, Appl. Math. Model. 32 (2008) 761-774. https://doi.org/10.1016/j.apm.2007.02.010
  8. Y. Abd Elmaboud, Influence of induced magnetic field on peristaltic flow in an annulus, Commun. Nonlinear Sci. Numer. Simulat. 17 (2012) 685-698. https://doi.org/10.1016/j.cnsns.2011.05.039
  9. M.M. Bhatti, A. Zeeshan, R. Ellahi, Heat transfer analysis on peristaltically induced motion of particle-fluid suspension with variable viscosity: clot blood model, Comp. Methods Prog. Biomed. 137 (2016) 115-124. https://doi.org/10.1016/j.cmpb.2016.09.010
  10. A. Alsaedi,N. Ali, D. Tripathi, T.Hayat, Peristaltic flowof couple stress fluid through uniform porous medium, Appl. Math. Mech. Engl. Ed. 35 (2014) 469-480. https://doi.org/10.1007/s10483-014-1805-8
  11. T. Hayat, M. Rafiq, B. Ahmad, Influences of rotation and thermophoresis on MHD peristaltic transport of Jeffrey fluid with convective conditions and wall properties, J. Mag. Mag. Mater. 410 (2016) 89-99. https://doi.org/10.1016/j.jmmm.2016.03.001
  12. M. Awais, S. Farooq, H. Yasmin, T. Hayat, A. Alsaedi, Convective heat transfer analysis for MHD peristaltic flow of Jeffrey fluid in an asymmetric channel, Int. J. Biomath. 7 (2014) 1450023.
  13. T. Hayat, F.M. Abbasi, B. Ahmad, A. Alsaedi, MHD mixed convection peristaltic flow with variable viscosity and thermal conductivity, Sains Malays. 43 (2014) 1583-1590.
  14. S.I. Abdelsalam, K. Vafai, Particulate suspension effect on peristaltically induced unsteady pulsatile flow in a narrow artery: blood flow model, Math. Biosci. 283 (2017) 91-105. https://doi.org/10.1016/j.mbs.2016.11.012
  15. T. Hayat, N. Saleem, S. Asghar, M.S. Althothuali, A. Althomaidan, Influence of induced magnetic field and heat transfer on peristaltic transport of a Carreau fluid, Commun. Nonlinear Sci. Numer. Simul. 16 (2011) 3559-3577. https://doi.org/10.1016/j.cnsns.2010.12.038
  16. R. Ellahi, F. Hussain, Simultaneous effects of MHD and partial slip on peristaltic flow of Jeffery fluid in a rectangular duct, J. Mag. Mag. Mater. 393 (2015) 284-292. https://doi.org/10.1016/j.jmmm.2015.05.071
  17. M. Mustafa, S. Abbasbandy, S. Hina, T. Hayat, Numerical investigation on mixed convective peristaltic flow of fourth grade fluid with Dufour and Soret effects, J. Taiwan Inst. Chem. Eng. 45 (2014) 308-316. https://doi.org/10.1016/j.jtice.2013.07.010
  18. G. Sucharitha, P. Lakshminarayana, N. Sandeep, Joule heating and wall flexibility effects on the peristaltic flow of magnetohydrodynamic nanofluid, Int. J. Mech. Sci. 131-132 (2017) 52-62. https://doi.org/10.1016/j.ijmecsci.2017.06.043
  19. A.A. Khan, R. Ellahi, M. Usman, The effects of variable viscosity on the peristaltic flow of nonNewtonian fluid through a porous medium in an inclined channel with slip boundary conditions, J. Porous Media 16 (2013) 59-67. https://doi.org/10.1615/JPorMedia.v16.i1.60
  20. Kh.S. Mekheimer, Y. Abd Elmaboud, A.I. Abdellateef, Peristaltic transport through eccentric cylinders, Mathematical model, Appl. Bio. Biomech. 10 (2013) 19-27. https://doi.org/10.1155/2013/902097
  21. D. Tripathi, A. Sharma, O.A. Beg, Electrothermal transport of nanofluids via peristaltic pumping in a finite microchannel: effects of Joule heating and HelmholtzSmoluchowski velocity, Int. J. Heat Mass Transf. 111 (2017) 138-149. https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.089
  22. T. Hayat, S. Farooq, B. Ahmad, A. Alsaedi, Effectiveness of entropy generation and energy transfer on peristaltic flow of Jeffrey material with Darcy resistance, Int. J. Heat Mass Transf. 106 (2017) 244-252. https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.017
  23. A.M. AbdAlla, S.M. AboDahab, Rotation effect on peristaltic transport of a Jeffrey fluid in an asymmetric channel with gravity field, Alex. Eng. J. 55 (2016) 1725-1735. https://doi.org/10.1016/j.aej.2016.03.018
  24. D. Tripathi, A. Yadav, O.A. Beg, Electrokinetically driven peristaltic transport of viscoelastic physiological fluids through a finite length capillary: mathematical modeling, Math. Biosci. 283 (2017) 155-168. https://doi.org/10.1016/j.mbs.2016.11.017
  25. K. Ramesh, Influence of heat and mass transfer on peristaltic flow of a couple stress fluid through porous medium in the presence of inclined magnetic field in an inclined asymmetric channel, J. Mol. Liq. 219 (2016) 256-271. https://doi.org/10.1016/j.molliq.2016.03.010
  26. S.E. Ghasemi, Thermophoresis and Brownian motion effects on peristaltic nanofluid flow for drug delivery applications, J. Mol. Liq. 238 (2017) 115-121. https://doi.org/10.1016/j.molliq.2017.04.067
  27. J.K. Grabski, J.A. Kolodziej, M. Mierzwiczak, Application of meshless procedure for the peristaltic flow analysis, Eng. Anal. Bound. Elem. 63 (2016) 125-133. https://doi.org/10.1016/j.enganabound.2015.11.005
  28. M.M. Bhatti, A. Zeeshan, R. Ellahi, Simultaneous effects of coagulation and variable magnetic field on peristaltically induced motion of Jeffrey nanofluid containing gyrotactic microorganism, Micro. Res. 110 (2017) 32-42. https://doi.org/10.1016/j.mvr.2016.11.007
  29. M.M. Bhatti, A. Zeeshan, R. Ellahi, N. Ijaz, Heat and mass transfer of twophase flow with electric double layer effects induced due to peristaltic propulsion in the presence of transverse magnetic field, J. Mol. Liq. 230 (2017) 237-246. https://doi.org/10.1016/j.molliq.2017.01.033
  30. M.M. Bhatti, A. Zeeshan, R. Ellahi, Endoscope analysis on peristaltic blood flow of Sisko fluid with Titanium magnetonanoparticles, Comp. Bio. Med. 78 (2016) 29-41. https://doi.org/10.1016/j.compbiomed.2016.09.007
  31. R. Ellahi, M.M. Bhatti, I. Pop, Effects of hall and ion slip on MHD peristaltic flow of Jeffrey fluid in a nonuniform rectangular duct, Int. J. Numer. Methods Heat Fluid Flow 26 (2016) 1802-1820. https://doi.org/10.1108/HFF-02-2015-0045
  32. L.M. Srivastava, V.P. Srivastava, Peristaltic transport of a power law fluid: applications to the ductus efferentes of the reproductive tract, Rheol. Acta 27 (1988) 428-433. https://doi.org/10.1007/BF01332164
  33. H.S. Lew, Y.C. Fung, C.B. Lowenstein, Peristaltic carrying and mixing of chime, J. Biomech. 4 (1971) 297-315. https://doi.org/10.1016/0021-9290(71)90036-4
  34. T. Hayat, S. Farooq, B. Ahmad, A. Alsaedi, Homogeneousheterogeneous reactions and heat source/sink effects in MHD peristaltic flow of micropolar fluid with Newtonian heating in a curved channel, J. Mol. Liq. 223 (2016) 469-488. https://doi.org/10.1016/j.molliq.2016.08.067
  35. T. Hayat, A. Bibi, H. Yasmin, B. Ahmad, Simultaneous effects of Hall current and homogeneous/heterogeneous reactions on peristalsis, J. Taiwan Inst. Chem. Eng. 58 (2016) 28-38. https://doi.org/10.1016/j.jtice.2015.05.037