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Hybrid/mono-carbon nanotubes–water flow in a peristaltic curved channel with viscous dissipation

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Abstract

Investigation of peristaltic motion of a hybrid/mono-carbon nanotube–water flow through a curved channel is carried out in this work. This work meets a lot of engineering and bioapplications such as the motion of the food through the digestive tract and the pumping of the urine from the kidney to the bladder and the pumping systems in the engineering field. The model is described by a set of partial differential equations, this system is transformed to a dimensionless system in terms of which is solved in two steps, the stream function is solved analytically with the assistance of the Mathematica program, and the heat equation is solved numerically using fifth-order Runge–Kutta method. The impact of the channel curvature, amplitude ratio, and the nanoparticle concentration on the pumping and trapping phenomenon is presented and discussed in detail. As concluded from the study, the hybrid type of nanoparticles raises the pressure gradient at the upper and the lower walls as well as the heat transfer decreases due to the presence of two types of nanotubes.

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Abbreviations

\(\bar{ X}\) :

Cartesian coordinate along the transversal direction \(\left( m \right)\)

\(\bar{R},\) :

Cartesian coordinate along the radial direction \(\left( m \right)\)

\(\bar{U}\) :

Transversal velocity \(\left( {m/s} \right)\)

\(\bar{V}\) :

Radial velocity \(\left( {m/s} \right)\)

\(\bar{ T}_{0}\) :

The lower-wall temperature \(\left( K \right)\)

\(\bar{ T}_{1}\) :

The upper-wall temperature \(\left( K \right)\)

\(\bar{a}\) :

Channel width \(\left( m \right)\)

\(\bar{b }\) :

Amplitude \(\left( m \right)\)

λ:

Wavelength \(\left( m \right)\)

c :

Speed \(\left( {m/s} \right)\)

\(\bar{R}^{*}\) :

Channel radius \(\left( m \right)\)

\(\bar{t}\) :

Time (sec)

\(z\) :

Heat transfer coefficient

\(\bar{Q}\) :

Flow rate volume

\(\bar{H}\) :

Sinusoidal function at the wall

\(\psi\) :

Stream function

\(x\) :

Dimensionless coordinate along the transversal direction \(\left( { = \frac{{2\pi \bar{x}}}{\lambda }} \right)\)

\(r\) :

Dimensionless coordinate along the radial direction \(\left( { = \frac{{\bar{r}}}{{\bar{a}}}} \right)\)

\(u\) :

Dimensionless transversal velocity \(\left( { = \frac{{\bar{u}}}{c}} \right)\)

\(v\) :

Dimensionless radial velocity \(\left( { = \frac{{\bar{v}}}{c}} \right)\)

\(\theta\) :

Dimensionless temperature \(\left( { = \frac{{\bar{T} - \bar{T}_{1} }}{{\bar{T}_{0} - \bar{T}_{1} }}} \right)\) \(\left( - \right)\)

\(\phi\) :

Nanoparticles volume fraction \(\left( - \right)\)

\(\rho\) :

Fluid density \(\left( {{\text{kg}}/{\text{m}}^{3} } \right)\)

\(\mu\) :

Dynamic viscosity \(\left( {{\text{Ns}}/{\text{m}}^{2} } \right)\)

\(\nu\) :

Kinematic viscosity \(\left( {m^{2} /s} \right)\)

\(k\) :

Thermal conductivity \(\left( {{\text{W}}/{\text{m}}.K} \right)\)

\(\rho c_{p}\) :

Volumetric heat capacity \(\left( {{\text{J}}/{\text{m}}^{3} .{\text{K}}} \right)\)

K :

Curvature parameter, \(k = \frac{{\bar{R}^{*} }}{{\bar{a}}}\)

\(\delta\) :

Wavenumber, \(\delta = \frac{{2\pi \bar{a} }}{\lambda }\)

\(Br\) :

Brinkman number, \(Br = \frac{{c^{2} \mu_{f} }}{{k_{f} \left( {\bar{T}_{0} - \bar{T}_{1} } \right)}}\)

\(\epsilon\) :

Amplitude ratio \(= \frac{{\bar{b}}}{{\bar{a}}}\)

\(P\) :

Dimensionless pressure \(\left( { = \frac{{2\pi \bar{a}^{2} }}{\lambda \mu c}\bar{p} } \right)\left( - \right)\)

\(t\) :

Dimensionless time period \(\left( { = \frac{{2\pi c \bar{t}}}{\lambda }} \right)\)

\(f\) :

Fluid phase

\(nf\) :

Nanofluid

\(s\) :

Solid particles

References

  1. J.C. Burns, T. Parkes, Peristaltic motion. J. Fluid Mech. 29, 731–743 (1967)

    Article  ADS  Google Scholar 

  2. T.F. Zien, S. Ostrach, A long-wave approximation to peristaltic motion. J. Biomech. 3, 63–75 (1970)

    Article  Google Scholar 

  3. K.K. Raju, R. Devanathan, Peristaltic motion of a non-Newtonian fluid. Rheol. Acta 11, 170–178 (1972)

    Article  Google Scholar 

  4. N. Ali, M. Sajid, Z. Abbasa, T. Javed, Non-Newtonian fluid flow induced by peristaltic waves in a curved channel. Eur. J. Mech. B/Fluids 29, 387–394 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  5. N. Ali, M. Sajid, T. Javed, Z. Abbas, Heat transfer analysis of peristaltic flow in a curved channel. Int. J. Heat Mass Transf. 53, 3319–3325 (2010)

    Article  Google Scholar 

  6. A. Alireza, K. Sadeghy, S. Sadeqi, Peristaltic flow of non-newtonian fluids through curved channels: a numerical study. Ann. Trans. Nordic Rheol. Soc. 21, 163–170 (2013)

    Google Scholar 

  7. N. Ali, M. Sajid, T. Javed, Z. Abbas, An analysis of peristaltic flow of a micropolar fluid in a curved channel. Chin. Phys. Lett. 28(1), 014704 (2011)

    Article  ADS  Google Scholar 

  8. S. Noreen, T. Hayat, A. Alsaedi, Flow of MHD Carreau fluid in a curved channel. Appl. Bionics Biomech. 10, 29–39 (2013)

    Article  Google Scholar 

  9. A.M. Abd-All, S.M. Abo-Dahab, R.D. Al-Simery, Effect of rotation on peristaltic flow of a micropolar fluid through a porous medium with an external magnetic field. J. Magn. Magn. Mater. 348, 33–43 (2013)

    Article  ADS  Google Scholar 

  10. T. Hayat, S. Hina, A.A. Hendi, S. Asghar, Effect of wall properties on the peristaltic flow of a third-grade fluid in a curved channel with heat and mass transfer. Int. J. Heat Mass Transf. 54, 5126–5136 (2011)

    Article  Google Scholar 

  11. S. Hina, T. Hayat, A. Alsaedi, Heat and mass transfer effects on the peristaltic flow of Johnson-Segalman fluid in a curved channel with compliant walls. Int. J. Heat Mass Transf. 55, 3511–3521 (2012)

    Article  Google Scholar 

  12. S. Hina, M. Mustafa, T. Hayat, A. Alsaedi, Peristaltic flow of pseudoplastic fluid in a curved channel with wall properties. J. Appl. Mech. 80(2), 024501 (2013)

    Article  ADS  Google Scholar 

  13. S. Hina, M. Mustafa, T. Hayat, F.E. Alsaadi, Peristaltic motion of third-grade fluid in curved channel. Appl. Math. Mech. -Engl. Ed. 35(1), 73–84 (2014)

    Article  MathSciNet  Google Scholar 

  14. A. Sinha, G.C. Shit, N.K. Ranjit, Peristaltic transport of MHD flow and heat transfer in an asymmetric channel: Effects of variable viscosity, velocity-slip and temperature jump. Alex. Eng. J. 54, 691–704 (2015)

    Article  Google Scholar 

  15. T. Hayat, Quratulain, M. Rafiq, Fuad Alsaadi and M.Ayub, Soret and Dufour effects on peristaltic transport in curved channel with radial magnetic field and convective conditions. J. Magn. Magn. Mater. 405, 358–369 (2016)

  16. M. Ali Abbas, Y.Q. Bai, M.M. Bhatti, M.M. Rashidi, Three-dimensional peristaltic flow of hyperbolic tangent fluid in a non-uniform channel having flexible walls. Alex. Eng. J. 55, 653–662 (2016)

    Article  Google Scholar 

  17. M. Rashid, K. Ansar, S. Nadeem, Effects of induced magnetic field for peristaltic flow of Williamson fluid in a curved channel. Phys. A 553, 123979 (2020)

    Article  MathSciNet  Google Scholar 

  18. R. Ahmed, N. Ali, K. Al-Khaled, S.U. Khan, I. Tlili, Finite difference simulations for non-isothermal hydromagnetic peristaltic flow of a bio-fluid in a curved channel: Applications to physiological systems. Comput. Methods Progr. Biomed. 195, 105672 (2020)

    Article  Google Scholar 

  19. M. Javed, N. Imran, A. Arooj and M. Sohail, Meta-analysis on homogeneous-heterogeneous reaction effects in a sinusoidal wavy curved channel, Chemical Physics Letters 763 (2021) 138200

  20. M.S. Abdel-Wahed, Nonlinear Rosseland thermal radiation and magnetic field effects on flow and heat transfer over a moving surface with variable thickness in a nanofluid. Can. J. Phys. 95(3), 267–273 (2017)

    Article  ADS  Google Scholar 

  21. A. Ebaid, E.H. Aly, Exact analytical solution of the peristaltic nanofluids flow in an asymmetric channel with flexible walls and slip condition: application to the cancer treatment. Comput Math Methods Med. 2013, 825376 (2013)

    MathSciNet  MATH  Google Scholar 

  22. F.M. Abbasi, T. Hayat, B. Ahmad, G.-Q. Chen, Slip effects on mixed convective peristaltic transport of copper-water nanofluid in an inclined channel. PLoS ONE 9(8), e105440 (2014). https://doi.org/10.1371/journal.pone.0105440

    Article  ADS  Google Scholar 

  23. T. Hayat, M. Shafique, A. Tanveer, A. Alsaedi, Radiative peristaltic flow of jeffrey nanofluid with slip conditions and joule heating. PLoS ONE 11(2), e0148002 (2016). https://doi.org/10.1371/journal.pone.0148002

    Article  Google Scholar 

  24. N.S. Akbar, A.W. Butt, Ferromagnetic effects for peristaltic flow of Cu–water nanofluid for different shapes of nanosize particles. Appl. Nanosci. 6, 379–385 (2016)

    Article  ADS  Google Scholar 

  25. M.S. Abdel-wahed, Magnetohydrodynamic Ferro-Nano fluid flow in a semi-porous curved tube under the effect of hall current and nonlinear thermal radiative. J. Magn. Magn. Mater. 474, 347–354 (2019)

    Article  ADS  Google Scholar 

  26. S. Nadeem, I. Shahzadi, Mathematical analysis for peristaltic flow of two-phase nanofluid in a curved channel. Commun. Theor. Phys. 64, 547–554 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  27. I. Shahzadi, S. Nadeem, F. Rabiei, Simultaneous effects of single-wall carbon nanotube and effective variable viscosity for peristaltic flow through annulus having permeable walls. Results Phys. 7, 667–676 (2017)

    Article  ADS  Google Scholar 

  28. N.S. Akbar, A.W. Butt, Carbon nanotubes analysis for the peristaltic flow in a curved channel with heat transfer. Appl. Math. Comput. 259, 231–241 (2015)

    MathSciNet  MATH  Google Scholar 

  29. V.K. Narla, D. Tripathi, O.A. Bég, Electro-osmotic nanofluid flow in a curved microchannel. Chin. J. Phys. 67, 544–558 (2020)

    Article  MathSciNet  Google Scholar 

  30. A. Saleem, S. Akhtar, F.M. Alharbi, S. Nadeem, M. Ghalambaz, A. Issakhov, Physical aspects of peristaltic flow of hybrid nano fluid inside a curved tube having ciliated wall. Results Phys. 19, 103431 (2020)

    Article  Google Scholar 

  31. E.M. Elsaid, M.S. Abdel-wahed, Mixed convection hybrid-nanofluid in a vertical channel under the effect of thermal radiative flux. Case Stud. Thermal Eng. 25, 100913 (2021)

    Article  Google Scholar 

  32. E.M. Elsaid, M.S. Abdel-wahed, Impact of hybrid nanofluid coolant on the boundary layer behavior over a moving cylinder: Numerical case study. Case Stud. Thermal Eng. 25, 100951 (2021)

    Article  Google Scholar 

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Acknowledgements

The authors would like to express their sincere thanks to the reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. Basic Sciences Department, Faculty of Engineering at Benha, Benha University, Cairo, Egypt

    M. S. Abdel-wahed

  2. Basic Sciences Department, Faculty of Engineering, BADR University in Cairo BUC, Cairo, Egypt

    M. S. Abdel-wahed

  3. Physics and Engineering Mathematics Department, Faculty of Engineering at Mataria, Helwan University, Cairo, Egypt

    A. Y. Sayed

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Correspondence to M. S. Abdel-wahed.

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Abdel-wahed, M.S., Sayed, A.Y. Hybrid/mono-carbon nanotubes–water flow in a peristaltic curved channel with viscous dissipation. Eur. Phys. J. Plus 136, 979 (2021). https://doi.org/10.1140/epjp/s13360-021-01958-z

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