Microsystem Technologies

, Volume 25, Issue 1, pp 151–173 | Cite as

Biomechanically driven flow of a magnetohydrodynamic bio-fluid in a micro-vessel with slip and convective boundary conditions

  • K. RameshEmail author
  • N. S. Akbar
  • M. Usman
Technical Paper


The main objective of the present study is to model the peristaltic transport of an incompressible couple stress fluid in an inclined asymmetric channel under the impact of porous medium, inclined magnetic field, heat and mass transfer. The effects of viscous dissipation, thermal radiation, Joule heating, chemical reaction, slip and convective boundary conditions are also taken into account. The entropy generation analysis is also studied. The non-dimensional and non-linear partial differential equations that govern the fluid flow model are simplified under the long wavelength and low Reynolds number assumptions. The entropy generation number due to heat transfer, fluid friction and magnetic field is formulated. The exact solutions for the stream function, pressure gradient, temperature, concentration, heat transfer coefficient and Nusselt number are derived. The trapping phenomenon is also presented for different wave shapes through streamline patterns. The comparison has been made with the results obtained in the symmetric and asymmetric channel, and Newtonian and couple stress fluid model. The results indicate that the entropy generation number achieves higher values in the region close to the walls of the channel, while it gains low values near the center of the channel. Temperature is a decreasing function of radiation parameter, Prandtl number and thermal Biot number. The size of the trapped bolus is greater in the Newtonian fluid model than the couple stress fluid model.



  1. Abd elmaboud Y, Mekheimer KS (2011) Non-linear peristaltic transport of a second-order fluid through a porous medium. Appl Math Model 35(6):2695–2710MathSciNetzbMATHGoogle Scholar
  2. Abd-Alla AM, Abo-Dahab SM (2015) Magnetic field and rotation effects on peristaltic transport of a Jeffrey fluid in an asymmetric channel. J Magn Magn Mater 374:680–689Google Scholar
  3. Adesanya SO, Kareem SO, Falade JA, Arekete SA (2015) Entropy generation analysis for a reactive couple stress fluid flow through a channel saturated with porous material. Energy 93:1239–1245Google Scholar
  4. Akbar NS (2015) Influence of magnetic field on peristaltic flow of a Casson fluid in an asymmetric channel: application in crude oil refinement. J Magn Magn Mater 378:463–468Google Scholar
  5. Akbar NS (2015) Entropy generation and energy conversion rate for the peristaltic flow in a tube with magnetic field. Energy 82:23–30Google Scholar
  6. Akbar NS, Nadeem S (2011) Simulation of heat transfer on the peristaltic flow of a Jeffrey-six constant fluid in a diverging tube. Int Commun Heat Mass Transf 38(2):154–159Google Scholar
  7. Akbar NS, Nadeem S (2012) Thermal and velocity slip effects on the peristaltic flow of a six constant Jeffrey’s fluid model. Int J Heat Mass Transf 55(15):3964–3970zbMATHGoogle Scholar
  8. Akbarzadeh M, Rashidi S, Bovand M, Ellahi R (2016) A sensitivity analysis on thermal and pumping power for the flow of nanofluid inside a wavy channel. J Mol Liquids 220:1–13Google Scholar
  9. Akram S, Nadeem S (2013) Influence of induced magnetic field and heat transfer on the peristaltic motion of a Jeffrey fluid in an asymmetric channel: closed form solutions. J Magn Magn Mater 328:11–20Google Scholar
  10. Ali N, Hayat T (2008) Peristaltic flow of a micropolar fluid in an asymmetric channel. Comput Math Appl 55(4):589–608MathSciNetzbMATHGoogle Scholar
  11. Anggiansah A, Taylor G, Bright N, Wang J, Owen WA, Rokkas T, Jones AR, Owen WJ (1994) Primary peristalsis is the major acid clearance mechanism in reflux patients. Gut 35(11):1536–1542Google Scholar
  12. Basak T, Anandalakshmi R, Kumar P, Roy S (2012) Entropy generation vs. energy flow due to natural convection in a trapezoidal cavity with isothermal and non-isothermal hot bottom wall. Energy 37(1):514–532Google Scholar
  13. Bejan A (1980) Second law analysis in heat transfer. Energy 5:720–732Google Scholar
  14. Bejan A (2001) Thermodynamic optimization of geometry in engineering flow systems. Exergy 4:269–277Google Scholar
  15. Bhatti MM, Abbas MA (2016) Simultaneous effects of slip and MHD on peristaltic blood flow of Jeffrey fluid model through a porous medium. Alex Eng J 55(2):1017–1023Google Scholar
  16. Bhatti MM, Ellahi R, Zeeshan A (2016) Study of variable magnetic field on the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct having compliant walls. J Mol Liquids 222:101–108Google Scholar
  17. Bhatti MM, Zeeshan A, Ellahi R (2016) Heat transfer analysis on peristaltically induced motion of particle–fluid suspension with variable viscosity: clot blood model. Comput Methods Progr Biomed 137:115–124Google Scholar
  18. Bhatti MM, Zeeshan A, Ellahi R, Ijaz 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. J Mol Liquids 230:237–246Google Scholar
  19. Bhatti MM, Zeeshan A, Ellahi R (2017) Simultaneous effects of coagulation and variable magnetic field on peristaltically induced motion of Jeffrey nanofluid containing gyrotactic microorganism. Microvasc Res 110:32–42Google Scholar
  20. Ellahi R, Shivanian E, Abbasbandy S, Rahman SU, Hayat T (2012) Analysis of steady flows in viscous fluid with heat/mass transfer and slip effects. Int J Heat Mass Transf 55(23):6384–6390Google Scholar
  21. Ellahi R, Hassan M, Zeeshan A (2015) Shape effects of nanosize particles in Cu-\(\text{ H }_2\)O nanofluid on entropy generation. Int J Heat Mass Transf 81:449–456Google Scholar
  22. Ellahi R, Zeeshan A, Hassan M (2016) Particle shape effects on Marangoni convection boundary layer flow of a nanofluid. Int J Numer Methods Heat Fluid Flow 26(7):2160–2174Google Scholar
  23. Elshehawey EF, Eldabe NT, Elghazy EM, Ebaid A (2006) Peristaltic transport in an asymmetric channel through a porous medium. Appl Math Comput 182(1):140–150MathSciNetzbMATHGoogle Scholar
  24. Eytan O, Elad D (1999) Analysis of intra-uterine fluid motion induced by uterine contractions. Bull Math Biol 61(2):221–238zbMATHGoogle Scholar
  25. Fung FC, Yih CS (1968) Peristaltic transport. J Appl Mech 85:669–675zbMATHGoogle Scholar
  26. Hayat T, Tanveer A, Alsaadi F, Alotaibi ND (2015) Homogeneous-heterogeneous reaction effects in peristalsis through curved geometry. AIP Adv 5(6):067172Google Scholar
  27. Hayat T, Zahir H, Tanveer A, Alsaedi A (2016) Numerical study for MHD peristaltic flow in a rotating frame. Comput Biol Med 79:215–221Google Scholar
  28. Hayat T, Tanveer A, Alsaedi A (2016) Mixed convective peristaltic flow of Carreau–Yasuda fluid with thermal deposition and chemical reaction. Int J Heat Mass Transf 96:474–481Google Scholar
  29. Hayat T, Bibi S, Rafiq M, Alsaedi A, Abbasi FM (2016) Effect of an inclined magnetic field on peristaltic flow of Williamson fluid in an inclined channel with convective conditions. J Magn Magn Mater 401:733–745Google Scholar
  30. Hayat T, Shafique M, Tanveer A, Alsaedi A (2016) Magnetohydrodynamic effects on peristaltic flow of hyperbolic tangent nanofluid with slip conditions and Joule heating in an inclined channel. Int J Heat Mass Transf 102:54–63Google Scholar
  31. Hayat T, Farooq S, Ahmad B, Alsaedi A (2017) Effectiveness of entropy generation and energy transfer on peristaltic flow of Jeffrey material with Darcy resistance. Int J Heat Mass Transf 106:244–252Google Scholar
  32. Hina S, Hayat T, Asghar S, Hendi AA (2012) Influence of compliant walls on peristaltic motion with heat/mass transfer and chemical reaction. Int J Heat Mass Transf 55(13):3386–3394Google Scholar
  33. Javed M, Hayat T, Mustafa M, Ahmad B (2016) Velocity and thermal slip effects on peristaltic motion of Walters-B fluid. Int J Heat Mass Transf 96:210–217Google Scholar
  34. Khaled ARA, Vafai K (2003) The role of porous media in modeling flow and heat transfer in biological tissues. Int J Heat Mass Transf 46(26):4989–5003zbMATHGoogle Scholar
  35. Latham TW (1966) Fluid motion in a peristaltic pump. MIT, CambridgeGoogle Scholar
  36. Maiti S, Misra JC (2011) Peristaltic flow of a fluid in a porous channel: a study having relevance to flow of bile within ducts in a pathological state. Int J Eng Sci 49(9):950–966MathSciNetzbMATHGoogle Scholar
  37. Maiti S, Misra JC (2012) Peristaltic transport of a couple stress fluid: some applications to hemodynamics. J Mech Med Biol 12(3):1250048Google Scholar
  38. Misra JC, Mallick B, Sinha A (2018) Heat and mass transfer in asymmetric channels during peristaltic transport of an MHD fluid having temperature-dependent properties. Alex Eng J 57(1):391–406Google Scholar
  39. Mustafa M, Abbasbandy S, Hina S, Hayat T (2014) Numerical investigation on mixed convective peristaltic flow of fourth grade fluid with Dufour and Soret effects. J Taiwan Inst Chem Eng 45(2):308–316Google Scholar
  40. Nadeem S, Akram S (2010) Peristaltic flow of a Williamson fluid in an asymmetric channel. Commun Nonlinear Sci Numer Simul 15(7):1705–1716MathSciNetzbMATHGoogle Scholar
  41. Nadeem S, Akram S (2010) Influence of inclined magnetic field on peristaltic flow of a Williamson fluid model in an inclined symmetric or asymmetric channel. Math Comput Model 52(1):107–119MathSciNetzbMATHGoogle Scholar
  42. Narayan R, Goswamy R (1994) Subendometrial-myometrial contractility in conception and non-conception embryo transfer cycles. Ultrasound Obstet Gynecol 4:499–504Google Scholar
  43. Raissi P, Shambooli M, Sepasgozar SME, Ayani M (2016) Numerical investigation of two-dimensional and axisymmetric unsteady flow between parallel plates. Propul Power Res 5(4):318–325Google Scholar
  44. Ramesh K (2016) Effects of slip and convective conditions on the peristaltic flow of couple stress fluid in an asymmetric channel through porous medium. Comput Methods Progr Biomed 135:1–14Google Scholar
  45. Ramesh K (2016) 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 Liquids 219:256–271Google Scholar
  46. Reddy MVS, Rao AR, Sreenadh S (2007) Peristaltic motion of a power-law fluid in an asymmetric channel. Int J Non Linear Mech 42(10):1153–1161Google Scholar
  47. Shapiro AH (1967) Pumping and retrograde diffusion in peristaltic waves. In: Proceedings of the workshop ureteral reftm children, National Academy of Science, Washington, DCGoogle Scholar
  48. Shapiro AH, Jafrin MY, Weinberg SL (1969) Peristaltic pumping with long wavelengths at low Reynolds number. J Fluid Mech 37:799–825Google Scholar
  49. Shirvan KM, Mamourian M, Mirzakhanlari S, Ellahi R (2017) Numerical investigation of heat exchanger effectiveness in a double pipe heat exchanger filled with nanofluid: a sensitivity analysis by response surface methodology. Powder Technol 313:99–111Google Scholar
  50. Shit GC, Ranjit NK (2016) Role of slip velocity on peristaltic transport of couple stress fluid through an asymmetric non-uniform channel: application to digestive system. J Mol Liquids 221:305–315Google Scholar
  51. Shit GC, Ranjit NK, Sinha A (2016) Electro-magnetohydrodynamic flow of biofluid induced by peristaltic wave: a non-Newtonian model. J Bionic Eng 13(3):436–448Google Scholar
  52. Srinivas S, Pushparaj V (2008) Non-linear peristaltic transport in an inclined asymmetric channel. Commun Nonlinear Sci Numer Simul 13(9):1782–1795Google Scholar
  53. Srinivasacharya D, Hima Bindu K (2016) Entropy generation in a porous annulus due to micropolar fluid flow with slip and convective boundary conditions. Energy 111:165–177Google Scholar
  54. Stokes VK (1966) Couple stresses in fluids. Phys Fluids 9(9):1709–1715Google Scholar
  55. Tripathi D (2013) Study of transient peristaltic heat flow through a finite porous channel. Math Comput Model 57(5):1270–1283MathSciNetGoogle Scholar
  56. Tripathi D, Beg OA (2014) A study on peristaltic flow of nanofluids: application in drug delivery systems. Int J Heat Mass Transf 70:61–70Google Scholar
  57. Tripathi D, Beg OA (2015) Peristaltic transport of Maxwell viscoelastic fluids with a slip condition: homotopy analysis of gastric transport. J Mech Med Biol 15(3):1550021Google Scholar
  58. Tripathi D, Beg OA, Gupta PK, Radhakrishnamacharya G, Mazumdar J (2015) DTM simulation of peristaltic viscoelastic biofluid flow in asymmetric porous media: a digestive transport model. J Bionic Eng 12(4):643–655Google Scholar
  59. Turan I, Kitapcioglu G, Goker ET, Sahin G, Bor S (2016) In vitro fertilization-induced pregnancies predispose to gastroesophageal reflux disease. United Eur Gastroenterol J 4(2):221–228Google Scholar
  60. Wang Y, Ali N, Hayat T, Oberlack M (2011) Peristaltic motion of a magnetohydrodynamic micropolar fluid in a tube. Appl Math Model 35(8):3737–3750MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsLovely Professional UniversityJalandharIndia
  2. 2.Department of MathematicsDBS&H CEME National University of Sciences and TechnologyIslamabadPakistan
  3. 3.Department of MathematicsUniversity of DaytonDaytonUSA

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