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BioNanoScience

, Volume 9, Issue 3, pp 723–739 | Cite as

Joint Effect of Magnetic Field and Heat Transfer on Particulate Fluid Suspension in a Catheterized Wavy Tube

  • I. M. Eldesoky
  • Sara I. AbdelsalamEmail author
  • W. A. El-Askary
  • A. M. El-Refaey
  • M. M. Ahmed
Article
  • 63 Downloads

Abstract

The effect of wall slip conditions, porous media, and heat transfer on peristaltic inflow of MHD Newtonian fluid with suspended particles in a catheterized tube has been studied with long-wavelength and low-Reynolds number approximations. The analytical solution has been derived for velocity and temperature. The amplitude ratio, particle concentration, catheter size, and the dimensionless flow rate were used to discuss the pressure gradient. The solutions for velocity and temperature derived in the analysis have been computed numerically and investigated. The tube surface is maintained at a fixed temperature. The variations of physical variables with the pertinent parameters were discussed graphically. The mathematical model presented corresponds to the flow in the annular space between two concentric tubes. It has been deduced that the thermal energy is reduced with particles’ concentration and with slip condition through the catheterized tube. The flow accelerates with the magnetic field and slip condition at the wall, whereas it decreases at the catheter. The catheter size has a different effect on both pressure drop and friction force.

Keywords

Peristalsis Catheter Heat transfer Particle suspension MHD 

Notes

Compliance with Ethical Standards

Conflict of Interest

None.

Research Involving Humans and Animals Statement

None.

Informed Consent

None.

Funding Statement

None.

References

  1. 1.
    Rao, A. R., & Usha, S. (1995). Peristaltic transport of two immiscible viscous fluid in a circular tube. Journal of Fluid Mechanics, 298, 271–285.CrossRefzbMATHGoogle Scholar
  2. 2.
    Takabatake, S., Ayukawa, K., & Mori, A. (1988). Peristaltic pumping in circular tubes: a numerical study of fluid transport and its efficiency. Journal of Fluid Mechanics, 193, 267–283.CrossRefGoogle Scholar
  3. 3.
    Abd Elmaboud, Y., Mekheimer, K. S., & Abdelsalam, S. I. (2014). A study of nonlinear variable viscosity in finite-length tube with peristalsis. Applied Bionics and Biomechanics, 11(4), 197–206.CrossRefGoogle Scholar
  4. 4.
    Abd Elmaboud, Y., Abdelsalam, S. I., & Mekheimer, K. H. S. (2018). Couple stress fluid flow in a rotating channel with peristalsis. Journal of Hydrodynamics, Series B, 30(2), 307–316.CrossRefGoogle Scholar
  5. 5.
    Abdelsalam, S. I., & Bhatti, M. M. (2018). The study of non-Newtonian nanofluid with Hall and ion slip effects on peristaltically induced motion in a non-uniform channel. RSC Advances, 8, 7904–7915.CrossRefGoogle Scholar
  6. 6.
    Elkoumy, S. R., Barakat, E. I., & Abdelsalam, S. I. (2013). Hall and transverse magnetic field effects on peristaltic flow of a Maxwell fluid through a porous medium. Global Journal of Pure and Applied Mathematics, 9(2), 187–203.Google Scholar
  7. 7.
    Mekheimer, K. S., Elkomy, S. R., & Abdelsalam, S. I. (2013). Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel. Chinese Physics B, 22(12), 124702–121–10.CrossRefGoogle Scholar
  8. 8.
    Elkoumy, S. R., Barakat, E. I., & Abdelsalam, S. I. (2012). Hall and porous boundaries effects on peristaltic transport through porous medium of a Maxwell model. Transport in Porous Media, 94(3), 643–658.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Ellahi, R., Bhatti, M. M., & Khalique, C. M. (2017). Three-dimensional flow analysis of Carreau fluid model induced by peristaltic wave in the presence of magnetic field. Journal of Molecular Liquids, 241, 1059–1068.CrossRefGoogle Scholar
  10. 10.
    Ellahi, R., Raza, M., & Akbar, N. S. (2017). Study of peristaltic flow of nanofluid with entropy generation in a porous medium. Journal Porous Media, 20(5), 461–478.CrossRefGoogle Scholar
  11. 11.
    Abdelsalam, S. I., & Vafai, K. (2017). Particulate suspension effect on peristaltically induced unsteady pulsatile flow in a narrow artery: blood flow model. Mathematical Biosciences, 283, 91–105.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Eldesoky, I. M., Abdelsalam, S. I., Abumandour, R. M., Kamel, M. H., & Vafai, K. (2017). Peristaltic transport of a compressible liquid with suspended particles in a planar channel. Journal of Applied Mathematics and Mechanics, 38(1), 137–154.CrossRefzbMATHGoogle Scholar
  13. 13.
    Latham, T.W.. (1966) Fluid motions in peristaltic pump. MS Thesis, MIT, Cambridge, MassachussettsGoogle Scholar
  14. 14.
    Shapiro, A.H., Jaffrin, M.Y., Weinberg, S.L.. (1969) Peristaltic pumping with long wavelength at low Reynolds number. .Google Scholar
  15. 15.
    Abd Elnaby, M. A., & Haroun, M. H. (2008). Influence of compliant wall properties on peristaltic motion in two-dimensional channel. Communications in Nonlinear Science and Numerical Simulation, 13, 738–752.CrossRefGoogle Scholar
  16. 16.
    Muthu, P., Rathish Kumar, B. V., & Chandra, P. (2003). Peristaltic motion of micropolar fluid in circular cylindrical tubes with elastic wall properties. ANZIAM Journal, 45, 232–245.CrossRefGoogle Scholar
  17. 17.
    El Shehawey, E. F., Mekheimer, K. S., Kaldas, S. F., & Afifi, N. A. S. (1999). Peristaltic transport through a porous medium. Journal of Biomathematics, 14, 16–38.Google Scholar
  18. 18.
    Srinivas, S., Gayathri, R., & Kothandapani, M. (2009). The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport. Computer Physics Communications, 180, 2115–2122.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Hayat, T., Javad, M., & Ali, N. (2008). MHD peristaltic channel flow of a Jeffrey fluid with complaint walls and porous medium. Transport in Porous Media, 74, 243–259.CrossRefGoogle Scholar
  20. 20.
    Derek, C., Tretheway, D. C., & Meinhart, C. D. (2002). Slip flow on peristaltic transport. Physics of Fluids, 14, 23–43.Google Scholar
  21. 21.
    Hron, J., Le Roux, C., Málek, J., & Rajagopal, K. R. (2008). Flows of incompressible fluids subject to Navier’s slip on the boundary. Computers & Mathematcs with Applications, 56(8), 2128–2143.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Kwang-Hua, W. C., & Fang, J. (2000). Peristaltic transport in a slip flow. European Physical Journal, 16, 511–513.Google Scholar
  23. 23.
    El-Shehawy, E. F., El-Dabe, N. T., & Eldesoky, I. M. (2006). Slip effects on the peristaltic flow of a non-Newtonian Maxwellian fluid. Acta Mechanica, 186(1–4), 141–159.CrossRefzbMATHGoogle Scholar
  24. 24.
    Eldesoky, I. M. (2012). Slip effects on the unsteady MHD pulsatile blood flow through porous medium in an artery under the effect of body acceleration. International Journal of Mathematics and Mathematical Sciences, 2012, 26.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Kamel, M. H., Eldesoky, I. M., Maher, B. M., & Abumandour, R. M. (2015). Slip effects on peristaltic transport of a particle-fluid suspension in a planar channel. Applied Bionics and Biomechanics, 2015, 14.CrossRefGoogle Scholar
  26. 26.
    Eldesoky, I. M., Kamel, M. H., & Abumandour, R. M. (2010). Numerical study of slip effect of unsteady MHD pulsatile flow through porous medium in an artery using generalized differential quadrature method (comparative study). World Journal of Engineering and Technology, 2(02), 131–142.CrossRefGoogle Scholar
  27. 27.
    Eldesoky, I. M. Unsteady MHD pulsatile blood flow through porous medium in stenotic channel with slip at permeable walls subjected to time dependent velocity (injection/suction). Walailak Journal of Science and Technology (WJST), 2014, 11(11), 901–922.Google Scholar
  28. 28.
    Eldesoky, I. M. (2013). Effect of relaxation time on MHD pulsatile flow of blood through porous medium in an artery under the effect of periodic body acceleration. Journal of Biological Systems, 21(2), 1350011(1–1350011(135001117.Google Scholar
  29. 29.
    Eldesoky, I. M., Abumandour, R. M., & Abdelwahab, E. T. (2019). Analysis for various effects of relaxation time and wall properties on compressible Maxwellian peristaltic slip flow. Zeitschrift für Naturforschung A, 74(4).  https://doi.org/10.1515/zna-2018-0479.
  30. 30.
    Sud, V. K., Sekhon, G. S., & Mishra, R. K. (1977). Effect of a moving magnetic field on blood flow. Mathematical Biosciences, 39, 373–385.Google Scholar
  31. 31.
    Ebaid, A. (2008). MHD and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel. Physics Letters A, 372, 4479–4493.zbMATHGoogle Scholar
  32. 32.
    Radhakrishnamacharya, G., Srinivasulu, C. H., & Mecanique, C. R. (2007). Interaction of peristalsis with heat transfer for the motion of a viscous incompressible Newtonian fluid in a channel with wall effects. CR Mechanique, 335, 348–369.Google Scholar
  33. 33.
    Nadeem, S. N., & Akbar, S. (2009). MHD peristaltic flow of an incompressible Newtonian fluid in a uniform channel with variable viscosity in the presence of heat transfer analysis. Communications in Nonlinear Science and Numerical Simulation, 14, 3836–3844.Google Scholar
  34. 34.
    Kothandapani, M., & Srinivas, S. (2008). On the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium. Physics Letters A, 372(25), 4586–4591.CrossRefzbMATHGoogle Scholar
  35. 35.
    Radhakrishnamacharya, G., & Srinisvasulu, C. H. (2007). Influence of wall properties on peristaltic transport with heat transfer. CR Mechanique, 335, 369–373.CrossRefzbMATHGoogle Scholar
  36. 36.
    Taneja, R., & Jain, N. C. (2004). MHD flow with slip effects and temperature dependent heat source in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall. Defence Science Journal, 20(4), 327–340.Google Scholar
  37. 37.
    Abdelsalam, S.I., Bhatti, M.M.. (2018) The impact of impinging TiO2 nanoparticles in Prandtl nanofluid along with endoscopic and variable magnetic field effects on peristaltic blood flow. Multidiscipline Modeling in Materials and Structures 14(3), pp. 530–548.Google Scholar
  38. 38.
    Abdelsalam, S. I., & Vafai, K. (2017). Combined effects of magnetic field and rheological properties on the peristaltic flow of a compressible fluid in a microfluidic channel. European Journal of Mechanics - B/Fluids, 65, 398–411.MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Hayat, T., Sajjad, R., Muhammad, T., Alsaedi, A., & Ellahi, R. (2017). On MHD nonlinear stretching flow of Powell-Eyring nanomaterial. Research in Physics, 7, 535–543.Google Scholar
  40. 40.
    Bhatti, M. M., Zeeshan, A., Ellahi, R., & Ljaz, N. (2017). Heat and mass transfer of two-phase flow with electric double layer effects induced due to peristaltic propulsion in the presence of transverse magnetic field. Journal of Molecular Liquids, 230, 237–246.CrossRefGoogle Scholar
  41. 41.
    Bhatti, M. M., Zeeshan, A., Ellahi, R., & Shit, G. C. (2018). Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy-Brinkman-Forchheimer porous medium. Advanced Powder Technology, 29(5), 1189–1197.CrossRefGoogle Scholar
  42. 42.
    Abdelsalam, S. I., & Bhatti, M. M. (2019). New insight into AuNP applications in tumor treatment and cosmetics through wavy annuli at the nanoscale. Scientific Reports, 9(1), 1–14 Article 260.CrossRefGoogle Scholar
  43. 43.
    Souayeh, B., Ben-Cheikh, N., & Ben-Beya, B. (2016). Effect of thermal conductivity ratio on flow features and convective heat transfer. Particulate Science and Technology, 35(5), 565–574.  https://doi.org/10.1080/02726351.2016.1180337.CrossRefGoogle Scholar
  44. 44.
    Souayeh, B., Ben-Cheikh, N., & Ben-Beya, B. (2018). Numerical simulation of three-dimensional natural convection in a cubic enclosure induced by an isothermally-heated circular cylinder at different inclinations. International Journal of Thermal Sciences, 110, 325–339.CrossRefGoogle Scholar
  45. 45.
    Hammami, F., Ben-Cheikh, N., Ben-Beya, B., & Souayeh, B. (2017). Combined effects of the velocity and the aspect ratios on the bifurcation phenomena in a two-sided lid-driven cavity flow. International Journal of Numerical Methods for Heat & Fluid Flow, 28(4), 943–962.CrossRefzbMATHGoogle Scholar
  46. 46.
    Hammami, F., Souayeh, B., Ben-Cheikh, N., & Ben-Beya, B. (2017). Computational analysis of fluid flow due to a two-sided lid driven cavity with a circular cylinder. Computers & Fluids, 156, 317–328.MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Vajravelu, K., Radhakrishnamacharya, G., & Radhakrishnamurthy, V. (2007). Peristaltic flow and heat transfer in a vertical porous annulus with long wave approximation. International Journal of Non-Linear Mechanics, 42, 754–759.CrossRefzbMATHGoogle Scholar
  48. 48.
    Mekheimer, K. S., & Abdelmaboud, Y. (2008). The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus application of an endoscope. Physics Letters A, 372, 1657–1665.CrossRefzbMATHGoogle Scholar
  49. 49.
    Mekheimer, K. S., Abdelmaboud, Y., & Abdellateef, A. I. (2008). Peristaltic transport of a particle–fluid suspension through a uniform and non-uniform annulus. Applied Bionics and Biomechanics, 5, 47–57.CrossRefGoogle Scholar
  50. 50.
    Mekheimer, K. S., & Abdelmaboud, Y. (2013). Particulate suspension flow induced by sinusoidal peristaltic waves through eccectric cylinders: Thread annular. International Journal of Biomathematics, 06, 1350026 [25 pages].CrossRefzbMATHGoogle Scholar
  51. 51.
    Drew, D. A. (1979). Stability of stokes layer of a dusty gas. Physics of Fluids, 19, 2081–2084.MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Charm, S. E., & Kurkland, G. S. (1974). Blood flow and microcirculation. New York: Wiley.Google Scholar
  53. 53.
    Tam, C. K. W. (1969). The drag on a cloud of spherical particles in low Reynolds number flow. Journal of Fluid Mechanics, 38, 537–546.CrossRefzbMATHGoogle Scholar
  54. 54.
    Medhavi, A. (2010). Peristaltic pumping of a particulate fluid suspension in a catheterized tube. European Journal of Science and Technology, 5, 77–93.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Basic Engineering Sciences Department, Faculty of EngineeringMenofia UniversityShebin El-KomEgypt
  2. 2.Basic Engineering Sciences Department, Menofia Higher Institute of Engineering and TechnologyMinistry of Higher EducationMenofiaEgypt
  3. 3.Basic Science, Faculty of EngineeringThe British University in EgyptAl-Shorouk CityEgypt
  4. 4.Mechanical Power Engineering Department, Faculty of EngineeringMenofia UniversityShebin El-KomEgypt
  5. 5.Basic Engineering Sciences DepartmentArab Academy for Sciences, Technology & Maritime TransportSmart village GizaEgypt

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