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Impact of Curvature-Dependent Channel Walls on Peristaltic Flow of Newtonian Fluid Through a Curved Channel with Heat Transfer

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Abstract

The basic idea of the present article is to model and study the aspects of curvature-dependent channel walls on peristalsis of laminar viscous material flow through a curved geometry. Mathematical modeling for such flow configuration is being presented for the first time. Lubrication theory assumptions are used for mathematical modeling of the problem. Moreover, the numerical method is used to solve the resulting system of equation. The impacts of different flow quantities on the heat transfer rate, velocity and temperature profiles are discussed via graphs. Results indicate that the curvature parameter considerably influences the mechanical and thermal aspects of the flow and hence must be included in the modeling of flows through curved a channel.

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References

  1. Latham, T.W.: Fluid Motion in a Peristaltic Pump. MIT, Cambridge (1966)

    Google Scholar 

  2. Shapiro, A.H.; Jaffrin, M.Y.; Weinberg, S.L.: Peristaltic pumping with long wave length at low Reynolds number. J. Fluid Mech. 37, 799 (1969)

    Article  Google Scholar 

  3. Burn, J.C.; Parkes, T.: Peristaltic motion. J. Fluid Mech. 29, 731–743 (1967)

    Article  Google Scholar 

  4. Mishra, M.; Ramachandra Rao, A.: Peristaltic transport of Newtonian fluid in an asymmetric channel. Z. Angew. Math. Phys. 54, 532–550 (2003)

    Article  MathSciNet  Google Scholar 

  5. Hayat, T.; Wang, Y.; Siddiqui, A.M.; Hutter, K.: Peristaltic motion of Johnson–Segalman fluid in a planar channel. Math. Problems Eng. 1, 1–23 (2003)

    Article  MathSciNet  Google Scholar 

  6. Hayat, T.; Wang, Y.; Hutter, K.; Asghar, S.; Siddiqui, A.M.: Peristaltic transport of an Oldroyd-b fluid in a planar channel. Math. Problems Eng. (2004). https://doi.org/10.1155/S1024123X04405043

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. Hayat, T.; Abbasi, F.M.; Ahmad, B.; Alsaedi, A.: Peristaltic transport of Carreau–Yasuda fluid in a curved channel with slip effects. PLoS ONE 15(4), e95070 (2014)

    Article  Google Scholar 

  9. Xiao-Jun, Y.: A new integral transform with an application in heat-transfer problem. Therm. Sci. 20, 677–681 (2016)

    Article  Google Scholar 

  10. Ali, N.; Javid, K.; Sajid, M.; Zaman, A.; Hayat, T.: Numerical simulations of Oldroyd 8-constant fluid flow and heat transfer in a curved channel. Int. J. Heat Mass Transf. 94, 500–508 (2016)

    Article  Google Scholar 

  11. Xiao-Jun, Y.; Feng, G.: A new technology for solving diffusion and heat equations. Therm. Sci. 21, 133–140 (2017)

    Article  Google Scholar 

  12. Rashad, A.M.; Rashidi, M.M.; Lorenzini, G.; Ahmed, S.E.; Aly, A.M.: Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium saturated with Cu-water nanofluid. Int. J. Heat Mass Transf. 104, 878–889 (2017)

    Article  Google Scholar 

  13. Yang, X.J.; Machado, J.A.T.: A new fractional operator of variable order: application in the description of anomalous diffusion. Physica A 481, 276–283 (2017)

    Article  MathSciNet  Google Scholar 

  14. Rashad, A.M.: Unsteady nanofluid flow over an inclined stretching surface with convective boundary condition and anisotropic slip impact. Int. J. Heat Technol. 35, 82–90 (2017)

    Article  Google Scholar 

  15. Nagaraju, G.; Srinivas, J.; Murthy, J.V.R.; Rashad, A.M.: Entropy generation analysis of the MHD flow of couple stress fluid between two concentric rotating cylinders with porous lining. Heat Transf. Asian Res. 46, 316–330 (2017)

    Article  Google Scholar 

  16. Yang, X.J.: A new integral transform operator for solving the heat-diffusion problem. Appl. Math. Lett. 64, 193–197 (2017)

    Article  MathSciNet  Google Scholar 

  17. Rashad, A.M.; Sivasankaran, S.; Mansour, M.A.; Bhuvaneswari, M.: Magneto-convection of nanofluids in a lid-driven trapezoidal cavity with internal heat generation and discrete heating. Numer. Heat Transf. Part A: Appl. 71, 1223–1234 (2017)

    Article  Google Scholar 

  18. Yang, X.J.; Gao, F.; Ju, Y.; Zhou, H.: Fundamental solutions of the general fractional-order diffusion equations. Math. Methods Appl. Sci. 41, 9312–9320 (2018)

    Article  MathSciNet  Google Scholar 

  19. Prakash, J.; Ramesh, K.; Tripathi, D.; Kumar, R.: Numerical simulation of heat transfer in blood flow altered by electroosmosis through tapered micro-vessels. Microvasc. Res. 118, 162–172 (2018)

    Article  Google Scholar 

  20. Tripathi, D.; Bhushan, S.; Beg, O.A.: Unsteady viscous flow driven by the combined effects of peristalsis and electro-osmosis. Alex. Eng. J. 57, 1349–1359 (2018)

    Article  Google Scholar 

  21. Armaghani, T.; Rashad, A.M.; Vahidifar, O.; Mishra, S.R.; Chamkha, A.J.: Effects of discrete heat source location on heat transfer and entropy generation of nanofluid in an open inclined L-shaped cavity. Int. J. Numer. Methods Heat Fluid Flow 29, 1363–1377 (2019)

    Article  Google Scholar 

  22. Yang, X.J.; Feng, Y.; Cattani, C.; Inc, M.: Fundamental solutions of anomalous diffusion equations with the decay exponential kernel. Math. Methods Appl. Sci. 42, 4054–4060 (2019)

    Article  MathSciNet  Google Scholar 

  23. Kumar, K.G.; Ramesh, G.K.; Gireesha, B.J.; Rashad, A.M.: On stretched magnetic flow of Carreau nanofluid with slip effects and nonlinear thermal radiation. Nonlinear Eng. 8, 340–349 (2019)

    Article  Google Scholar 

  24. Liu, J.; Xiao-Jun, Y.; Feng, Y.: On integrability of the time fractional nonlinear heat conduction equation. J. Geom. Phys. 144, 190–198 (2019)

    Article  MathSciNet  Google Scholar 

  25. Hayat, T.; Aslam, N.; Khan, M.I.; Khan, M.I.; Alsaedi, A.: Physical significance of heat generation/absorption and Soret effects on peristalsis flow of pseudoplastic fluid in an inclined channel. J. Mol. Liq. 275, 599–615 (2019)

    Article  Google Scholar 

  26. Ogulu, A.; Abbey, T.M.: Simulation of heat transfer on an oscillatory blood flow in an indented porous artery. Int. Commun. Heat 32, 983–989 (2005)

    Article  Google Scholar 

  27. Srinivas, S.; Kothandapani, M.: Peristaltic transport in an asymmetric channel with heat transfer. Int. J. Heat Mass Transf. 35, 514–522 (2008)

    Article  Google Scholar 

  28. Ramananmurthy, J.V.; Parsad, K.M.; Narla, V.K.: Unsteady peristaltic transport in curved channel. Phys. Fluid 25, 1903 (2013)

    Article  Google Scholar 

  29. Hina, S.; Mustafa, M.; Hayat, T.: Peristaltic motion of Jhon–Segalman fluid in a curved channel with slip conditions. PLoS ONE 4(12), e114168 (2014)

    Article  Google Scholar 

  30. Shehzad, S.A.; Abbasi, F.M.; Hayat, T.; Alsaadi, F.; Mousa, G.: Peristalsis in curved channel with slip condition and radial magnetic field. Int. J. Heat Mass Transf. 91, 562–569 (2015)

    Article  Google Scholar 

  31. Abbasi, F.M.; Saba, S.A.: Shehzad, Heat transfer analysis for peristaltic flow of Carreau-Yasuda fluid through a curved channel with radial magnetic field. Int. J. Heat Mass Transf. 115, 777–783 (2017)

    Article  Google Scholar 

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Acknowledgements

Authors acknowledge the support of Higher Education Commission (HEC) of Pakistan via Project 7395/Federal/NRPU/R&D/HEC/2017.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

    Saba & Fahad Munir Abbasi

  2. Department of Mathematics, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    Sabir Ali Shehzad

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  1. Saba
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  2. Fahad Munir Abbasi
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  3. Sabir Ali Shehzad
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Correspondence to Sabir Ali Shehzad.

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Saba, Abbasi, F.M. & Shehzad, S.A. Impact of Curvature-Dependent Channel Walls on Peristaltic Flow of Newtonian Fluid Through a Curved Channel with Heat Transfer. Arab J Sci Eng 45, 9037–9044 (2020). https://doi.org/10.1007/s13369-020-04653-w

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  • DOI: https://doi.org/10.1007/s13369-020-04653-w

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