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Mathematical Modelling of Peristaltic Pumping of Nano-Fluids

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Modelling and Simulation of Diffusive Processes

Part of the book series: Simulation Foundations, Methods and Applications ((SFMA))

Abstract

A theoretical study is presented to examine the peristaltic pumping with double-diffusive (thermal and concentration diffusion) convection in nano-fluids through a deformable channel. The model is motivated by the need to explore nano-fluid dynamic effects on peristaltic transport in biological vessels, as typified by transport of oxygen and carbon dioxide, food molecules, ions, wastes, hormones, and heat in blood flow. Approximate solutions are obtained under the restrictions of large wavelength and low Reynolds number, for nanoparticle fraction field, concentration field, temperature field, axial velocity, volume flow rate, pressure gradient, stream function, and wave amplitude. The influence of the dominant hydrodynamic parameters (Brownian motion, thermophoresis, Dufour and Soret) and Grashof numbers (thermal, concentration, and nanoparticle) on peristaltic flow patterns are discussed with the help of computational results obtained with the Mathematica software. The classical Newtonian viscous model, presented by Shapiro and others, constitutes a special case of the present model. Applications of the study include novel pharmaco-dynamic pumps, and engineered gastro-intestinal mechanisms.

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References

  1. Mazumdar J (1999) An introduction to mathematical physiology and biology, 2nd edn. Cambridge University Press, UK

    Book  MATH  Google Scholar 

  2. Shyy W, Lian Y, Tang J, Viieru D, Liu H (2008) Aerodynamics of Low Reynolds Number Flyers. Cambridge aerospace series (No. 22). Cambridge University Press, UK

    Google Scholar 

  3. Hou TY, Stredie VG, Wu TY (2007) Mathematical modeling and simulation of aquatic and aerial animal locomotion. J Comput Phys 225:1603–1631

    Article  MATH  MathSciNet  Google Scholar 

  4. Bar-Cohen Y (2006) Biomimetics-using nature to inspire human innovation. Bioinspir Biomim 1:P1–P12

    Article  Google Scholar 

  5. Schwarz R (2008) Biological modelling and simulation-a survey of practical models, algorithms and numerical methods. MIT, Cambridge

    Google Scholar 

  6. Anderl R, Eigner M, Sendler U, Stark R (2012) Smart engineering … show all 4 hide. Springer, Berlin

    Google Scholar 

  7. Skalak R, Ozkaya N, Skalak TC (1989) Biofluid mechanics. Ann Rev Fluid Mech 21:167–200

    Article  MathSciNet  Google Scholar 

  8. Fung YC (1997) Biomechanics: circulation. Springer, New York

    Book  Google Scholar 

  9. Bathe KJ, Zhang H, Ji S (1999) Finite element analysis of fluid flows fully coupled with structural interactions. Computer Structures, 72:1–16

    Article  MATH  Google Scholar 

  10. Pedley TJ, Hung TK, Skalak R (1981) Fluid mechanics of cardiovascular flow. In: Reul H, Ghista DN, Rau G (eds) Perspectives in biomechanics. Harvard Academic Publishers, Aachen, 1, pp 113–226

    Google Scholar 

  11. Hung TK, Tsai TMC (2004) Nonlinear pulsatile flows in rigid and distensible arteries. J Mech Med Biol 4:419–434

    Article  Google Scholar 

  12. Pavlov VV (2006) Dolphin skin as a natural anisotropic compliant wall. Bioinspir Biomim 1:31–40

    Article  Google Scholar 

  13. Whittlesey RW, Liska S, Dabiri JO (2010) Fish schooling as a basis for vertical axis wind turbine farm design. Bioinspir Biomim 5:035005

    Article  Google Scholar 

  14. Von Ellenreider KD, Parker K, Soria J (2008) Fluid mechanics of flapping wings. Exp Therm Fluid Sci 32:1578–1589

    Article  Google Scholar 

  15. Bég OA, Parsa AB, Rashidi MM, Sadri SM (2013) Semi-computational simulation of magneto-hemodynamic flow in a semi-porous channel using optimal homotopy and differential transform methods-a model for surgical blood flow control. Comput Biol Med 43(9):1142–1153

    Article  Google Scholar 

  16. Gan RZ, Cheng T, Dai C, Yang F, Wood MW (2009) Finite element modeling of sound transmission with perforations of tympanic membrane. J Acoust Soc Am 126:243–253

    Article  Google Scholar 

  17. Tripathi D, Pandey SK, Siddiqui A, Bég OA (2012) Non-steady peristaltic propulsion with exponential variable viscosity: a study of transport through the digestive system. Comput Meth Biomech Biomed Eng. doi:10.1080/10255842.2012.703660

    Google Scholar 

  18. Tripathi D, Bég OA (2012) Magnetohydrodynamic peristaltic flow of a couple stress fluid through coaxial channels containing a porous medium. J Mech Med Biol 12:1250088

    Article  Google Scholar 

  19. Tripathi D, Bég OA, Curiel-Sosa JL (2012) Homotopy semi-numerical simulation of peristaltic flow of generalised oldroyd-b fluids with slip effects. Comput Meth Biomech Biomed Eng. doi:10.1080/10255842.2012.688109

    Google Scholar 

  20. Bég TA, Rashidi MM, Bég OA, Rahimzadeh N (2012) Differential transform semi-numerical analysis of biofluid-particle suspension flow and heat transfer in non-darcian porous media. Comput Meth Biomech Biomed Eng doi:10.1080/10255842.2011.643470

    Google Scholar 

  21. Ronco C (2007) Fluid mechanics and cross filtration in hollow-fiber hemodialyzers, hemodiafiltration. In: Canaud B, Aljama P (eds) Contributions to nephrology. Basel, Switzerland, 158, p 34–49

    Google Scholar 

  22. Andrews JC (2004) Intralabyrinthine fluid dynamics: Meniere disease. Curr Opin Otolaryngol Head Neck Surg 12:408–412

    Article  Google Scholar 

  23. Rashidi MM, Keimanesh M, Bég OA, Hung TK (2010) Magnetohydrodynamic biorheological transport phenomena in a porous medium: a simulation of magnetic blood flow control and filtration. Int J Numer Meth Biomed Eng 27:805–821

    Article  Google Scholar 

  24. Fin L, Grebe R (2003) Three-dimensional modeling of the cerebrospinal fluid dynamics and brain interactions in the aqueduct of sylvius. Comput Meth Biomech Biomed Eng 6:163–170

    Article  Google Scholar 

  25. Guasto JS, Rusconi R, Stocker R (2012) Fluid mechanics of planktonic microorganisms. Ann Rev Fluid Mech 44:373–400

    Article  MathSciNet  Google Scholar 

  26. Bég OA, Rashidi MM, Bég TA, Asadi M (2012) Homotopy analysis of transient magneto-bio-fluid dynamics of micropolar squeeze film in a porous medium: a model for magneto-bio-rheological lubrication. J Mech Med Biol 12:1250051.1–1250051.21

    Google Scholar 

  27. Zueco J, Bég OA (2010) Network numerical analysis of hydromagnetic squeeze film flow dynamics between two parallel rotating disks with induced magnetic field effects. Tribol Int 43:532–543

    Article  Google Scholar 

  28. Becker S, Kniesburges S, Müller S, Delgado A, Link G, Kaltenbacher M, Döllinger M (2009) Flow-structure-acoustic interaction in a human voice model. J Acoust Soc Am 125:1351–1361

    Article  Google Scholar 

  29. Bhargava R, Sharma S, Bég OA, Zueco J (2010) Finite element study of nonlinear two-dimensional deoxygenated biomagnetic micropolar flow. Commun Nonlinear Sci Numer Simul 15:1210–1233

    Article  MATH  MathSciNet  Google Scholar 

  30. Bég OA, Bhargava R, Rawat S, Takhar HS, Halim MK (2008) Computational modeling of biomagnetic micropolar blood flow and heat transfer in a two-dimensional non-darcian porous medium. Meccanica 43:391–410

    Article  MATH  MathSciNet  Google Scholar 

  31. Dasi LP, Simon HA, Sucosky P, Yoganathan AP (2009) Fluid mechanics of artificial heart valves. Clin Exp Pharmacol Physiol 36:225–237

    Article  Google Scholar 

  32. Norouzi M, Davoodi M, Bég OA, Joneidi AA (2013) Analysis of the effect of normal stress differences on heat transfer in creeping viscoelastic dean flow. Int J Thermal Sci. doi:org/10.1016/j.ijthermalsci. 2013.02.002

    Google Scholar 

  33. Hörschler I, Meinke M, Schroder W (2003) Numerical simulation of the velocity field in a model of the nasal cavity. Comput Fluids 32:39–45

    Article  MATH  Google Scholar 

  34. Choi SUS (1995) Enhancing thermal conductivity of fluid with nanoparticles. In: Siginer DA, Wang HP (eds) Developments and application of non-newtonian flows, vol 66. ASME, New York, pp. 99–105

    Google Scholar 

  35. Keblinski P, Eastman JA, Cahill DG (2005) Nanofluids for thermal transport. Materials Today June:36–44

    Article  Google Scholar 

  36. Hilt JZ, Peppas NA (2005) Microfabricated drug delivery devices. Int J Pharm 306:15–23

    Article  Google Scholar 

  37. Patel GM, Patel GC, Patel RB, Patel JK, Patel M (2006) Nanorobot: a versatile tool in nanomedicine. J Drug Targeting 14:63–67

    Article  Google Scholar 

  38. Emerich DF, Thanos CG (2006) The pinpoint promise of nanoparticle-based drug delivery and molecular diagnosis. Biomol Eng 23:171–184

    Article  Google Scholar 

  39. Su D, Ma R, Zhu L (2011) Numerical study of nanofluid infusion in deformable tissues for hyperthermia cancer treatments. J Med Biol Eng 49:1233–1240

    Article  Google Scholar 

  40. Burygin GL (2009) On the enhanced antibacterial activity of antibiotics mixed with gold nanoparticles. Nanoscale Res Lett 4:794–801

    Article  Google Scholar 

  41. Coco R, Plapied L, Pourcelle V, Jérôme Ch, Brayden DJ, Schneider YJ, Préat V (2013) Drug delivery to inflamed colon by nanoparticles: comparison of different strategies. Int J Pharm 440:3–12

    Article  Google Scholar 

  42. Paolino D, Fresta M, Sinha P, Ferrari M (2006) Drug delivery systems. . In: Webster JG (ed) Encyclopedia of medical devices and instrumentation 2nd edn. Wiley, New York

    Google Scholar 

  43. Bég OA (2013) Peristaltic pumps- FSI modelling. Technical report, Gort Engovation, BIO-FSI/02-13., February, pp 142

    Google Scholar 

  44. Bayliss WM, Starling EH (1899) The movements and innervation of the small Intestine. J Physiol (London) 24:99–143

    Google Scholar 

  45. Fung YC (1971) Peristaltic pumping: a bioengineering model. In Proceedings of Workshop Hydrodynamics. Upper UrinaryTract, Natl Acad Sci, Washington DC

    Google Scholar 

  46. Latham TW (1966) Fluid motion in peristaltic pump. MS thesis. MIT, USA

    Google Scholar 

  47. Shapiro AH, Jafferin MY, Weinberg SL (1969) Peristaltic pumping with long wavelengths at low Reynolds number. J Fluid Mech 37:699–825

    Article  Google Scholar 

  48. Fung YC, Yih CS (1968) Peristaltic transport. ASME J Appl Mech 35:669–675

    Article  MATH  Google Scholar 

  49. Burns JC, Parkes T (1967) Peristaltic motion. J Fluid Mech 29:731–743

    Article  Google Scholar 

  50. Barton C, Raynor S (1968) Peristaltic flow in tubes. Bull Math Biophys 30:663–680

    Article  MATH  Google Scholar 

  51. Chaw TS (1970) Peristaltic transport in a circular cylindrical pipe. ASME J Appl Mech 37:901–905

    Article  Google Scholar 

  52. Jafferin MY (1973) Inertia and streamline curvature effects on peristaltic pumping. Int J Eng Sci 11:681–699

    Article  Google Scholar 

  53. Bohme G, Friedrich R (1983) Peristaltic flow of viscoelastic liquids. J Fluid Mech 128:109–122

    Article  Google Scholar 

  54. Tsiklauri D, Beresnev I (2001) Non-Newtonian effects in the peristaltic flow of a Maxwell fluid. Phys Rev E 64:036303-1–036303-5

    Article  Google Scholar 

  55. Tripathi D (2011) Peristaltic flow of couple-stress conducting fluids through a porous channel: applications to blood flow in the micro-circulatory system. J Biol Syst 19:461–477

    Article  MATH  Google Scholar 

  56. Tripathi D (2011) Peristaltic transport of fractional maxwell fluids in uniform tubes: application of an endoscope. Comput Math Appl 62:1116–1126

    Article  MATH  MathSciNet  Google Scholar 

  57. Tripathi D (2011) Numerical and analytical simulation of peristaltic flows of generalized Oldroyd-B Fluids. Int J Numer Meth Fluids 67:1932–1943

    Article  MATH  Google Scholar 

  58. Hayat T, Mahomed FM, Asghar S (2005) Peristaltic flow of a magnetohydrodynamic Johnson-Segalman fluid. Nonlinear Dyn 40:375–385

    Article  MATH  MathSciNet  Google Scholar 

  59. Tripathi D, Pandey SK, Bég. OA (2013) Mathematical modelling of heat transfer effects on swallowing dynamics of viscoelastic food bolus through the human oesophagus. Int J Therm Sci 70:41–53

    Article  Google Scholar 

  60. Bég OA, Keimanesh M, Rashidi MM, Davoodi M (2013) Multi-Step dtm simulation of magneto-peristaltic flow of a conducting Williamson viscoelastic fluid. Int J Appl Math Mech 9:1–24

    Google Scholar 

  61. Bhargava R, Sharma S, Takhar HS, Bég TA, Bég OA, Hung TK (2006) Peristaltic pumping of micropolar fluid in porous channel—model for stenosed arteries. J Biomech 39:S649–S669

    Article  Google Scholar 

  62. Tiwari RK, Das MK (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf 50:2002–2018

    Article  MATH  Google Scholar 

  63. Rashidi MM, Bég OA, Mehr NF, Hosseini A, Gorla RSR (2012) Homotopy simulation of axisymmetric laminar mixed convection nanofluid boundary layer flow over a vertical cylinder. Theor Appl Mech 39:365–390

    Article  MATH  MathSciNet  Google Scholar 

  64. Bég OA, Gorla RSR, Prasad VR, Vasu B, Prashad RD (2011) Computational study of mixed thermal convection nanofluid flow in a porous medium. 12th UK National Heat Transfer Conference, Chemical Engineering Department, University of Leeds, West Yorkshire, Session 8, ID 0004

    Google Scholar 

  65. Rana P, Bhargava R, Bég OA (2013) Finite element modeling of conjugate mixed convection flow of al2o3-water nanofluid from an inclined slender hollow cylinder. Phys Scripta 87:15

    Article  Google Scholar 

  66. Buongiorno J (2006) Convective transport in nanofluids. ASME J Heat Transf 128:240–250

    Article  Google Scholar 

  67. Xuan Y, Li Q (2003) Investigation on convective heat transfer and flow features of nanofluids. ASME J Heat Transf 125:151–155

    Article  Google Scholar 

  68. Pak BC, Cho Y (2003) Hydrodynamics and heat transfer study of dispersed fluids with submicron metallic oxide particles. Exp Heat Transf 11:151–170

    Article  Google Scholar 

  69. Eastman JA, Phillpot SR, Choi SUS, Keblinski P (2004) Thermal transport in nanofluids. Ann Rev Mater Res 34:219–146

    Article  Google Scholar 

  70. Wang XQ, Majumdar AS (2007) Heat transfer characteristics of nanofluids: a review. Int J Therm Sci 46:1–19

    Article  MATH  Google Scholar 

  71. Trisaksri V, Wongwises SP (2007) Critical review of heat transfer characteristics of nanofluids. Renew Sust Energ Rev 11:512–523

    Article  Google Scholar 

  72. Wen D, Lin G, Vafaei S, Zhang K (2009) Review of nanofluids for heat transfer applications. Particuology 7:141–150

    Article  Google Scholar 

  73. Saidur R, Leong KY, Mohammad HA (2011) A review on applications and challenges of nanofluids. Renew Sust Energ Rev 15:1646–1668

    Article  Google Scholar 

  74. Kuznetsov AV, Nield DA (2010) Natural convection boundary layer flow of nanofluids past a vertical plate. Int J Therm Sci 49:243–247

    Article  Google Scholar 

  75. Kuznetsov AV, Nield DA (2011) Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 50:712–717

    Article  Google Scholar 

  76. Nield DA, Kuznetsov AV (2011) The onset of double-diffusive convection in a nanofluid layer. Int J Heat Fluid Flow 32:771–776

    Article  Google Scholar 

  77. Nield DA, Kuznetsov AV (2010) The onset of convection in a horizontal nanofluid layer of finite depth. Eur J Mech B/Fluids 29:217–223

    Article  MATH  MathSciNet  Google Scholar 

  78. Nield DA, Kuznetsov AV (2009) Thermal instability in a porous medium layer saturated by a nanofluid. Int J Heat Mass Transf 52:5796–5801

    Article  MATH  Google Scholar 

  79. Nield DA, Kuznetsov AV (2010) The effect of local thermal non-equilibrium on the onset of convection in a nanofluid. ASME J Heat Transf 132:052405-1-7

    Article  Google Scholar 

  80. Kolade B, Goodson KE, Eaton JK (2009) Convective performance of nanofluids in a laminar thermally-developing tube flow. ASME J Heat Transf 131:052402-1-8

    Article  Google Scholar 

  81. Bachok N, Ishak A, Pop I (2010) Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. Int J Therm Sci 49:1663–1668

    Article  Google Scholar 

  82. Rashidi MM, Bég OA, Asadi M, Rastegari MT (2012) DTM- Padé modeling of natural convective boundary layer flow of a nanofluid past a vertical surface. Int J Therm Environ Eng 4:13–24

    Article  Google Scholar 

  83. Bég OA, Bég TA, Rashidi MM, Asadi M (2012) Homotopy semi-numerical modelling of nanofluid convection boundary layers from an isothermal spherical body in a permeable regime. Int J Micro Nano Therm Fluid Transp Phenom 3:237–266

    Google Scholar 

  84. Rashidi MM, Bég OA, Rostami B, Osmond L (2013) DTM- Padé simulation of stagnation-point nanofluid mechanics. Int J Appl Math Mech 9:1–29

    Google Scholar 

  85. Bég OA, Ferdows M, Khan Md S (2013) Numerical study of transient magnetohydrodynamic radiative mixed convection nanofluid flow from a stretching permeable surface. Proceedings of IMECHE–Part E: J Proc Mech Eng

    Google Scholar 

  86. Bég OA, Bég TA, Rashidi MM, Asadi M (2013) DTM- Padé semi-numerical simulation of nanofluid transport in porous media. Int J Appl Math Mech 9:80–107

    Google Scholar 

  87. Bég OA, Prasad VR, Vasu B (2013) Numerical study of mixed bio-convection in porous media saturated with nanofluid containing oxytactic micro-organisms. J Mech Med Biol 13:1350067

    Article  Google Scholar 

  88. Uddin MJ, Yusoff NHM, Bég OA, Ismail AI (2013) Lie group analysis and numerical solutions for non-Newtonian nanofluid flow in a porous medium with internal heat generation. Physica Scripta 87:14

    Article  Google Scholar 

  89. Akbar NS, Nadeem S (2011) Endoscopic effects on peristaltic flow of a nanofluid. Commun Theor Phys 56:761

    Article  MATH  Google Scholar 

  90. Akbar NS, Nadeem S, Hayat T, Hendi AA (2012) Peristaltic flow of a nanofluid with slip effects. Meccanica 47:1283–1294

    Article  MathSciNet  Google Scholar 

  91. Akbar NS, Nadeem S, Hayat T, Hendi AA (2012) Peristaltic flow of a nanofluid in a non-uniform tube. Heat Mass Transf 48:451–459

    Article  Google Scholar 

  92. Mustafa M, Hina S, Hayat T, Alsaedi A (2012) Influence of wall properties on the peristaltic flow of a nanofluid: analytic and numerical solutions. Int J Heat Mass Transf 55:4871–4877

    Article  Google Scholar 

  93. Akbar NS, Nadeem S (2012) Peristaltic flow of a Phan-Thien-tanner nanofluid in a diverging tube. Heat Transf-Asian Res 41:10–22

    Article  Google Scholar 

  94. Mustafa M, Hina S, Hayat T, Alseadi A (2013) Slip effects on the peristaltic motion of nanofluid in a channel with wall properties. ASME J Heat Transf 135:041701-1-7

    Article  Google Scholar 

  95. Kleinstreuer C, Li J (2010) Chapter 5 Microfluidic devices in nanotechnology. Microfluidic devices for drug delivery. Wiley, New York

    Google Scholar 

  96. Gebhart B (1988) Buoyancy-induced flows and transport. Hemisphere, Washington

    MATH  Google Scholar 

  97. Bég OA, Bhargava R, Rawat S, Kahya E (2008) Numerical study of micropolar convective heat and mass transfer in a non-Darcy porous regime with Soret and Dufour diffusion. Emer J Eng Res 13:51–66

    Google Scholar 

  98. Bég OA, Prasad VR, Vasu B, Reddy NB, Li Q, Bhargava R (2011) Free convection heat and mass transfer from an isothermal sphere to a micropolar regime with Soret/Dufour effects. Int J Heat Mass Transf 54:9–18

    Article  MATH  Google Scholar 

  99. Prasad VR, Vasu B, Bég OA (2013) Thermo-diffusion and diffusion-thermo effects on free convection flow past a horizontal circular cylinder in a non-Darcy porous medium. J Porous Media 16:315–334

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Delhi, 110077, Delhi, India

    Dharmendra Tripathi

  2. Gort Engovation Research (Propulsion, Nanofluids and Biomechanics), Southmere Ave., BD73NU, Bradford, UK

    O. Anwar Bég

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  1. Dharmendra Tripathi
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  2. O. Anwar Bég
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Correspondence to Dharmendra Tripathi .

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  1. Banaras Hindu University, Varanasi, Uttar Pradesh, India

    S.K. Basu

  2. Banaras Hindu University, Varanasi, Uttar Pradesh, India

    Naveen Kumar

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Tripathi, D., Bég, O. (2014). Mathematical Modelling of Peristaltic Pumping of Nano-Fluids. In: Basu, S., Kumar, N. (eds) Modelling and Simulation of Diffusive Processes. Simulation Foundations, Methods and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-05657-9_4

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