Influence of velocity slip and temperature jump conditions on the peristaltic flow of a Jeffrey fluid in contact with a Newtonian fluid. (English) Zbl 1386.76012
Summary: In this paper, we investigate the peristaltic transport of a two layered fluid model consisting of a Jeffrey fluid in the core region and a Newtonian fluid in the peripheral region. The channel is bounded by permeable heat conducting walls. The analysis is carried out in the wave reference frame under the assumptions of long wave length and low Reynolds number. The analytical expressions for stream function, temperature field, pressure-rise and the frictional force per wavelength in both the regions are obtained. The effects of the physical parameters associated with the flow and heat transfer are presented graphically and analyzed. It is noticed that the pressure rise decrease with increasing slip parameter \(\beta\) in the pumping region \((\Delta P > 0)\). The temperature field decreases with increasing Jeffrey number and the velocity slip parameter; whereas the temperature field increases with increasing thermal slip parameter. Furthermore, the size of the trapped bolus increases with increasing Jeffrey number and decreases with increasing slip parameter. We believe that this model can help in understanding the behavior of two immiscible physiological fluids in living objects.
Keywords:
peristalsis; two-layer flow; trapping phenomenon; Jeffrey fluid; Newtonian fluid; heat transferReferences:
| [1] | J. G. Brasseur, S. Corrsin, Nan Q. Lu, The influence of a peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids, J. Fluid Mech. 174(1987) 495 -519.; Brasseur, J. G.; Corrsin, S.; Lu, Nan Q., The influence of a peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids, J. Fluid Mech, 174, 495-519 (1987) |
| [2] | J. G. Brasseur, A fluid mechanical perspective on esophageal bolus transport, Dysphagia 2 (1987) 32-39.; Brasseur, J. G., A fluid mechanical perspective on esophageal bolus transport, Dysphagia, 2, 32-39 (1987) |
| [3] | G. Bugliarello, J. Sevilla, Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes, Biorheology 7(2) (1970) 85-107.; Bugliarello, G.; Sevilla, J., Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes, Biorheology, 7, 2, 85-107 (1970) |
| [4] | G. R. Cokelet, The rheology of human blood: In Biomechanics, its foundation and objectives, (Prentice-Hall, Englewood Cliffs, New Jersey, 1972), pp. 63-103.; Cokelet, G. R., The rheology of human blood: In Biomechanics, its foundation and objectives, pp. 63-103 (1972) |
| [5] | U. Farooq, T. Hayat, A. Alsaedi, Shijun Liao, Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel, Appl. Math. Comput. 242 (2014) 528 -540.; Farooq, U.; Hayat, T.; Alsaedi, A.; Liao, Shijun, Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel, Appl. Math. Comput, 242, 528-540 (2014) · Zbl 1334.80004 |
| [6] | D. J. Griffiths, Dynamics of the upper urinary tract: I. Peristaltic flow through a distensible tube of limited length, Phys. Med. Biol. 32(7) (1987) 813 -822.; Griffiths, D. J., Dynamics of the upper urinary tract: I. Peristaltic flow through a distensible tube of limited length, Phys. Med. Biol, 32, 7, 813-822 (1987) |
| [7] | Tasawar Hayat, Nasir Ali, Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube, Commun. Nonlinear Sci. Numer. Simul 13 (2008) 1343 - 1352.; Tasawar, Hayat; Nasir, Ali, Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube, Commun. Nonlinear Sci. Numer. Simul, 13, 1343-1352 (2008) · Zbl 1221.76016 |
| [8] | T. Hayat, S. Hina, Effects of heat and mass transfer on peristaltic flow of Williamson fluid in a non-uniform channel with slip conditions, Int. J. Numer. Meth. Fluids (2010) .; Hayat, T.; Hina, S., Effects of heat and mass transfer on peristaltic flow of Williamson fluid in a non-uniform channel with slip conditions, Int. J. Numer. Meth. Fluids (2010) · Zbl 1379.76006 · doi:10.1002/fld.2433 |
| [9] | A. Kavitha, R. H. Reddy, A.N.S. Srinivas, S. Sreenadh, R. Saravana, Peristaltic pumping of a Jeffrey fluid between porous walls with suction and injection, International Journal of Mechanical and Materials Engineering (IJMME) 7(2) (2012) 152-157.; Kavitha, A.; Reddy, R. H.; Srinivas, A. N.S.; Sreenadh, S.; Saravana, R., Peristaltic pumping of a Jeffrey fluid between porous walls with suction and injection, International Journal of Mechanical and Materials Engineering (IJMME), 7, 2, 152-157 (2012) |
| [10] | A. Kavitha, R. Hemadri Reddy, R. Saravana, S. Sreenadh, Peristaltic transport of a Jeffrey fluid in contact with a Newtonian fluid in an inclined channel, Ain Shams Engineering Journal (2015) .; A.; Hemadri Reddy, R.; Saravana, R.; Sreenadh, S., Peristaltic transport of a Jeffrey fluid in contact with a Newtonian fluid in an inclined channel, Ain Shams Engineering Journal (2015) · Zbl 1317.76106 · doi:10.1016/j.asej.2015.10.014 |
| [11] | M. Kothandapani, S. Srinivas, Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel, Int. J. Nonlinear Mech. 43 (2008) 915 - 924.; Kothandapani, M.; Srinivas, S., Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel, Int. J. Nonlinear Mech, 43, 915-924 (2008) · Zbl 1217.76105 |
| [12] | Masako Sugihara-Sekia, Bingmei M. Fu, Blood flow and permeability in microvessels, Fluid Dyn. Res. 37 (2005) 82-132.; Masako, Sugihara-Sekia; Fu, Bingmei M., Blood flow and permeability in microvessels, Fluid Dyn. Res, 37, 82-132 (2005) · Zbl 1153.76457 |
| [13] | Kh. S. Mekheimer, Peristaltic flows of blood under effect of a magnetic field in a non-uniform channels, Appl. Math. Comput. 153 (2004) 763-777.; Mekheimer, Kh. S., Peristaltic flows of blood under effect of a magnetic field in a non-uniform channels, Appl. Math. Comput, 153, 763-777 (2004) · Zbl 1041.92006 |
| [14] | J.C. Misra, S.K. Pandey, A Mathematical Model for Oesophageal Swallowing of a Food Bolus, Math. Comput. Modell. 33 (2001) 997-1009.; Misra, J. C.; Pandey, S. K., A Mathematical Model for Oesophageal Swallowing of a Food Bolus, Math. Comput. Modell, 33, 997-1009 (2001) · Zbl 0965.92020 |
| [15] | J. C. Misra, S. K. Pandey, Peristaltic transport of blood in small vessels: study of a mathematical model, Comput. Math. Appl. 43 (2002) 1183 - 1193.; Misra, J. C.; Pandey, S. K., Peristaltic transport of blood in small vessels: study of a mathematical model, Comput. Math. Appl, 43, 1183-1193 (2002) · Zbl 1045.92015 |
| [16] | S. Nadeem, SafiaAkram, Slip effects on the peristaltic flow of a Jeffrey fluid in an asymmetric channel under the effect of induced magnetic field, Int. J. Numer. Meth. Fluids 63 (2010) 374 -394.; Nadeem, S.; Safia, Akram, Slip effects on the peristaltic flow of a Jeffrey fluid in an asymmetric channel under the effect of induced magnetic field, Int. J. Numer. Meth. Fluids, 63, 374-394 (2010) · Zbl 1352.76124 |
| [17] | Noreen Sher Akbar, S. Nadeem, and Mohamed Ali, Jeffrey fluid model for blood flow through a tapered artery with a stenosis, J. Mech. Med. Biol. 11 (2011) 529-545.; Akbar, Noreen Sher; Nadeem, S.; Mohamed, Ali, Jeffrey fluid model for blood flow through a tapered artery with a stenosis, J. Mech. Med. Biol, 11, 529-545 (2011) · Zbl 1293.76185 |
| [18] | Noreen Sher Akbar, T. Hayat, S. Nadeem, Awatif A. Hendi, Effects of slip and heat transfer on the peristaltic flow of a third order fluid in an inclined asymmetric channel, Int. J. Heat Mass Transfer 54 (2011) 1654-1664.; Akbar, Noreen Sher; Hayat, T.; Nadeem, S.; Hendi, Awatif A., Effects of slip and heat transfer on the peristaltic flow of a third order fluid in an inclined asymmetric channel, Int. J. Heat Mass Transfer, 54, 1654-1664 (2011) · Zbl 1211.80001 |
| [19] | Noreen Sher Akbar and S. Nadeem, Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis, Commun. Theor. Phys. 57(1) (2012) 133-140.; Akbar, Noreen Sher; Nadeem, S., Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis, Commun. Theor. Phys, 57, 1, 133-140 (2012) · Zbl 1247.76005 |
| [20] | Noreen Sher Akbar, S. Nadeem, Changhoon Lee, Characteristics of Jeffrey fluid model for peristaltic flow of chyme in small intestine with magnetic field, Results in Physics 3 (2013) 152-160.; Akbar, Noreen Sher; Nadeem, S.; Lee, Changhoon, Characteristics of Jeffrey fluid model for peristaltic flow of chyme in small intestine with magnetic field, Results in Physics, 3, 152-160 (2013) |
| [21] | S. K. Pandey, D. Tripathi, Unsteady model of transportation of Jeffrey fluid by peristalsis, Int. J. Biomath 3(4) (2010) 473-491.; Pandey, S. K.; Tripathi, D., Unsteady model of transportation of Jeffrey fluid by peristalsis, Int. J. Biomath, 3, 4, 473-491 (2010) · Zbl 1403.92052 |
| [22] | R. Ponalagusamy, R. Tamil Selvi, Influence of magnetic field and heat transfer on two-phase fluid model for oscillatory blood flow in an arterial stenosis, Meccanica 50 (2015) 927-943.; Ponalagusamy, R.; Tamil Selvi, R., Influence of magnetic field and heat transfer on two-phase fluid model for oscillatory blood flow in an arterial stenosis, Meccanica, 50, 927-943 (2015) · Zbl 1317.76105 |
| [23] | A. Ramachandra Rao, S. Usha, Peristaltic transport of two immiscible viscous fluids in a circular tube, J. Fluid Mech. 298 (1995) 271-285.; Ramachandra Rao, A.; Usha, S., Peristaltic transport of two immiscible viscous fluids in a circular tube, J. Fluid Mech, 298, 271-285 (1995) · Zbl 0848.76100 |
| [24] | G. Ravikumur, G. Radhakrishnamacharya, Effect of homogeneous and heterogeneous chemical reactions on peristaltic transport of a Jeffrey fluid through a porous medium with slip condition, J. Appl. Fluid Mech. 8(3) (2015) 521- 528.; Ravikumur, G.; Radhakrishnamacharya, G., Effect of homogeneous and heterogeneous chemical reactions on peristaltic transport of a Jeffrey fluid through a porous medium with slip condition, J. Appl. Fluid Mech, 8, 3, 521-528 (2015) |
| [25] | P. G. Saffman, On the Boundary Conditions at the Surface of a Porous Medium, Stud. Appl. Math. 1 (1971) 93-101.; Saffman, P. G., On the Boundary Conditions at the Surface of a Porous Medium, Stud. Appl. Math, 1, 93-101 (1971) · Zbl 0271.76080 |
| [26] | A.H. Shapiro, M.Y. Jaffrin, S.L. Weinberg, Peristaltic pumping with long wavelengths at low Reynolds number, J. Fluid Mech. 37 (1969) 799-825.; Shapiro, A. H.; Jaffrin, M. Y.; Weinberg, S. L., Peristaltic pumping with long wavelengths at low Reynolds number, J. Fluid Mech, 37, 799-825 (1969) |
| [27] | L. M. Srivastava, V. P. Srivastava, Peristaltic transport of a two-layered model of physiological fluid, J. Biomech. 15 (1982) 257-265.; Srivastava, L. M.; Srivastava, V. P., Peristaltic transport of a two-layered model of physiological fluid, J. Biomech, 15, 257-265 (1982) · Zbl 0551.33004 |
| [28] | L. M. Srivastava, V. P. Srivastava, Peristaltic transport of blood, Casson model-II, J. Biomech. 17(1984) 821-829.; Srivastava, L. M.; Srivastava, V. P., Peristaltic transport of blood, Casson model-II, J. Biomech, 17, 821-829 (1984) · Zbl 1246.33007 |
| [29] | 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.; Srivastava, L. M.; Srivastava, V. P., Peristaltic transport of a power-law fluid: applications to the ductus efferentes of the reproductive tract, Rheol. Acta, 27, 428-433 (988) |
| [30] | Dharmendra Tripathi, A mathematical model for the peristaltic flow of chyme movement in small intestine, Math. Biosci. 233 (2011) 90-97.; Dharmendra, Tripathi, A mathematical model for the peristaltic flow of chyme movement in small intestine, Math. Biosci, 233, 90-97 (2011) · Zbl 1226.92015 |
| [31] | J. C. Umavathi, I. C. Liu, M. Shekar Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall, Appl. Math. Mech. -Engl Ed 33(7) (2012) 931-950.; Umavathi, J. C.; Liu, I. C.; Shekar, M., Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall, Appl. Math. Mech, -Engl Ed 33, 7, 931-950 (2012) · Zbl 1266.76019 |
| [32] | S. Usha, A. Ramachandra Rao, Peristaltic transport of two layered Power- law fluids, Trans. ASME, J. Biomech. Engng.119(1997) 483-488.; Usha, S.; Ramachandra Rao, A., Peristaltic transport of two layered Power- law fluids, Trans. ASME, J. Biomech. Engng, 119, 483-488 (1997) |
| [33] | K. Vajravelu, S. Sreenadh, V. Ramesh Babu, Peristaltic pumping of a Herschel-Bulkley fluid in contact with a Newtonian fluid, Q. Appl. Math. 64(4) (2006) 593 -604.; Vajravelu, K.; Sreenadh, S.; Ramesh Babu, V., Peristaltic pumping of a Herschel-Bulkley fluid in contact with a Newtonian fluid, Q. Appl. Math, 64, 4, 593-604 (2006) · Zbl 1407.76006 |
| [34] | K. Vajravelu, S. Sreenadh, R. Hemadri Reddy, K. Murugeshan, Peristaltic Transport of a Casson fluid in contact with a Newtonian Fluid in a Circular Tube with permeable wall, Int. J. Fluid Mech. Res. 36(3)(2009) 244-254.; Vajravelu, K.; Sreenadh, S.; Hemadri Reddy, R.; Murugeshan, K., Peristaltic Transport of a Casson fluid in contact with a Newtonian Fluid in a Circular Tube with permeable wall, Int. J. Fluid Mech. Res, 36, 3, 244-254 (2009) |
| [35] | K. Vajravelu, S. Sreenadh, R. Saravana, Combined influence of velocity slip, temperature and concentration jump conditions on MHD peristaltic transport of a Carreau fluid in a non-uniform channel, Appl. Math. Comput. 225(2013) 656-676.; Vajravelu, K.; Sreenadh, S.; Saravana, R., Combined influence of velocity slip, temperature and concentration jump conditions on MHD peristaltic transport of a Carreau fluid in a non-uniform channel, Appl. Math. Comput, 225, 656-676 (2013) · Zbl 1334.76174 |
| [36] | K. Vajravelu, S. Sreenadh, P. Lakshminarayana G. Sucharitha, The effect of heat transfer on the nonlinear peristaltic transport of a Jeffrey fluid through a finite vertical porous channel, Int. J .Biomath. 7(2) (2016) 1650023, 1-24.; Vajravelu, K.; Sreenadh, S.; Lakshminarayana, P.; Sucharitha, G., The effect of heat transfer on the nonlinear peristaltic transport of a Jeffrey fluid through a finite vertical porous channel, Int. J .Biomath, 7, 2, 1-24 (2016) · Zbl 1331.76019 · doi:1650023 |
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