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

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Abstract

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.

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References

  • Abd elmaboud Y, Mekheimer KS (2011) Non-linear peristaltic transport of a second-order fluid through a porous medium. Appl Math Model 35(6):2695–2710

    Article  MathSciNet  MATH  Google Scholar 

  • 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 374:680–689

    Article  Google Scholar 

  • 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 93:1239–1245

    Article  Google Scholar 

  • 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 378:463–468

    Article  Google Scholar 

  • Akbar NS (2015) Entropy generation and energy conversion rate for the peristaltic flow in a tube with magnetic field. Energy 82:23–30

    Article  Google Scholar 

  • 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):154–159

    Article  Google Scholar 

  • 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):3964–3970

    Article  MATH  Google Scholar 

  • 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 220:1–13

    Article  Google Scholar 

  • 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 328:11–20

    Article  Google Scholar 

  • Ali N, Hayat T (2008) Peristaltic flow of a micropolar fluid in an asymmetric channel. Comput Math Appl 55(4):589–608

    Article  MathSciNet  MATH  Google Scholar 

  • 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):1536–1542

    Article  Google Scholar 

  • 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):514–532

    Article  Google Scholar 

  • Bejan A (1980) Second law analysis in heat transfer. Energy 5:720–732

    Article  Google Scholar 

  • Bejan A (2001) Thermodynamic optimization of geometry in engineering flow systems. Exergy 4:269–277

    Article  Google Scholar 

  • 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):1017–1023

    Article  Google Scholar 

  • 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 222:101–108

    Article  Google Scholar 

  • 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 137:115–124

    Article  Google Scholar 

  • 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 230:237–246

    Article  Google Scholar 

  • 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 110:32–42

    Article  Google Scholar 

  • 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):6384–6390

    Article  Google Scholar 

  • 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 81:449–456

    Article  Google Scholar 

  • 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):2160–2174

    Article  Google Scholar 

  • Elshehawey EF, Eldabe NT, Elghazy EM, Ebaid A (2006) Peristaltic transport in an asymmetric channel through a porous medium. Appl Math Comput 182(1):140–150

    MathSciNet  MATH  Google Scholar 

  • Eytan O, Elad D (1999) Analysis of intra-uterine fluid motion induced by uterine contractions. Bull Math Biol 61(2):221–238

    Article  MATH  Google Scholar 

  • Fung FC, Yih CS (1968) Peristaltic transport. J Appl Mech 85:669–675

    Article  MATH  Google Scholar 

  • Hayat T, Tanveer A, Alsaadi F, Alotaibi ND (2015) Homogeneous-heterogeneous reaction effects in peristalsis through curved geometry. AIP Adv 5(6):067172

    Article  Google Scholar 

  • Hayat T, Zahir H, Tanveer A, Alsaedi A (2016) Numerical study for MHD peristaltic flow in a rotating frame. Comput Biol Med 79:215–221

    Article  Google Scholar 

  • 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 96:474–481

    Article  Google Scholar 

  • 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 401:733–745

    Article  Google Scholar 

  • 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 102:54–63

    Article  Google Scholar 

  • 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 106:244–252

    Article  Google Scholar 

  • 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):3386–3394

    Article  Google Scholar 

  • 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 96:210–217

    Article  Google Scholar 

  • 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):4989–5003

    Article  MATH  Google Scholar 

  • Latham TW (1966) Fluid motion in a peristaltic pump. MIT, Cambridge

    Google Scholar 

  • 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):950–966

    Article  MathSciNet  MATH  Google Scholar 

  • Maiti S, Misra JC (2012) Peristaltic transport of a couple stress fluid: some applications to hemodynamics. J Mech Med Biol 12(3):1250048

    Article  Google Scholar 

  • 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):391–406

    Article  Google Scholar 

  • 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):308–316

    Article  Google Scholar 

  • Nadeem S, Akram S (2010) Peristaltic flow of a Williamson fluid in an asymmetric channel. Commun Nonlinear Sci Numer Simul 15(7):1705–1716

    Article  MathSciNet  MATH  Google Scholar 

  • 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):107–119

    Article  MathSciNet  MATH  Google Scholar 

  • Narayan R, Goswamy R (1994) Subendometrial-myometrial contractility in conception and non-conception embryo transfer cycles. Ultrasound Obstet Gynecol 4:499–504

    Article  Google Scholar 

  • 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):318–325

    Article  Google Scholar 

  • 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 135:1–14

    Article  Google Scholar 

  • 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 219:256–271

    Article  Google Scholar 

  • 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):1153–1161

    Article  Google Scholar 

  • Shapiro AH (1967) Pumping and retrograde diffusion in peristaltic waves. In: Proceedings of the workshop ureteral reftm children, National Academy of Science, Washington, DC

  • Shapiro AH, Jafrin MY, Weinberg SL (1969) Peristaltic pumping with long wavelengths at low Reynolds number. J Fluid Mech 37:799–825

    Article  Google Scholar 

  • 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 313:99–111

    Article  Google Scholar 

  • 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 221:305–315

    Article  Google Scholar 

  • 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):436–448

    Article  Google Scholar 

  • Srinivas S, Pushparaj V (2008) Non-linear peristaltic transport in an inclined asymmetric channel. Commun Nonlinear Sci Numer Simul 13(9):1782–1795

    Article  Google Scholar 

  • Srinivasacharya D, Hima Bindu K (2016) Entropy generation in a porous annulus due to micropolar fluid flow with slip and convective boundary conditions. Energy 111:165–177

    Article  Google Scholar 

  • Stokes VK (1966) Couple stresses in fluids. Phys Fluids 9(9):1709–1715

    Article  Google Scholar 

  • Tripathi D (2013) Study of transient peristaltic heat flow through a finite porous channel. Math Comput Model 57(5):1270–1283

    Article  MathSciNet  Google Scholar 

  • Tripathi D, Beg OA (2014) A study on peristaltic flow of nanofluids: application in drug delivery systems. Int J Heat Mass Transf 70:61–70

    Article  Google Scholar 

  • 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):1550021

    Article  Google Scholar 

  • 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):643–655

    Article  Google Scholar 

  • 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):221–228

    Article  Google Scholar 

  • Wang Y, Ali N, Hayat T, Oberlack M (2011) Peristaltic motion of a magnetohydrodynamic micropolar fluid in a tube. Appl Math Model 35(8):3737–3750

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Lovely Professional University, Jalandhar, 144411, India

    K. Ramesh

  2. Department of Mathematics, DBS&H CEME National University of Sciences and Technology, Islamabad, Pakistan

    N. S. Akbar

  3. Department of Mathematics, University of Dayton, Dayton, USA

    M. Usman

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  1. K. Ramesh
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  2. N. S. Akbar
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  3. M. Usman
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Correspondence to K. Ramesh.

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Ramesh, K., Akbar, N.S. & Usman, M. Biomechanically driven flow of a magnetohydrodynamic bio-fluid in a micro-vessel with slip and convective boundary conditions. Microsyst Technol 25, 151–173 (2019). https://doi.org/10.1007/s00542-018-3945-8

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