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Numerical study of Hall effects on the peristaltically induced motion of a viscous fluid through a non-uniform regime: An application to the medical science

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Abstract.

Impacts of Hall current (potential) on the peristaltically induced motion of a magneto-hydrodynamics (MHD) viscous incompressible fluid is analysed in a curved geometry. This study is novel in term of integrating numerically the Hall effects with peristaltic propulsive phenomena bounded within the curved regime. The usage of these electro-kinetically controlled devices in the modern era of bio-medical industries makes this study relatively new and interesting. Firstly, the governing equations are modelled in a curvilinear coordinates system. Secondly, these equations are transformed into a dimensionless system of equations by using dimensionless variables under long-wavelength and low-Reynold-number assumptions. The numerical solution of these governing equations is obtained with the appropriate boundary conditions (BCs) by using the BVP4C technique. The significant influences of several embedded physical parameters such as the curvature parameter, Hartmann number, Hall parameter in the velocity profile, pumping and trapping phenomena's are argued expansively through graphs. It is visible that the effects of the Hall current are dominant over the boundary layer (BL) phenomena for large values of the Hall parameter. Moreover, comparison among the straight channel and the curvedchannel is also highlighted. Furthermore, the validation of the numerical code is given at some particular values of the curvature parameter through numeric tables.

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References

  1. E.H. Hall, Am. J. Math. 2, 287 (1879)

    Article  Google Scholar 

  2. M. Turkyilmazoglu, Eur. J. Mech. B 65, 184 (2017)

    Article  MathSciNet  Google Scholar 

  3. M. Turkyilmazoglu, Eur. Phys. J. Plus 129, 120 (2014)

    Article  Google Scholar 

  4. M. Turkyilmazoglu, Int. J. Heat Mass Transfer 85, 609 (2015)

    Article  Google Scholar 

  5. L.F. Shampine, J. Kierzenka, M.W. Reichelt, Solving boundary value problems for ordinary differential equations in MATLAB with BVP4C (2000)

  6. T. Cebeci, H. Keller, J. Comput. Phys. 7, 289 (1971)

    Article  ADS  Google Scholar 

  7. W.M. Bayliss, E.H. Starling, J. Physiol. 24, 99 (1899)

    Article  Google Scholar 

  8. Y.C. Fung, C.S. Yih, J. Appl. Mech. 35, 669 (1968)

    Article  ADS  Google Scholar 

  9. F. Yin, Y.C. Fung, J. Appl. Mech. 36, 579 (1969)

    Article  ADS  Google Scholar 

  10. M. Li, J.G. Brasseur, J. Fluid Mech. 248, 129 (1993)

    Article  ADS  Google Scholar 

  11. S. Takabatake, K. Ayukawa, J. Fluid Mech. 122, 439 (1982)

    Article  ADS  Google Scholar 

  12. S. Takabatake, K. Ayukawa, A. Mori, J. Fluid Mech. 193, 269 (1988)

    Article  ADS  Google Scholar 

  13. T.D. Brown, T.K. Hung, J. Fluid Mech. 83, 249 (1977)

    Article  ADS  Google Scholar 

  14. T.K. Hung, T.D. Brown, J. Fluid Mech. 73, 77 (1976)

    Article  ADS  Google Scholar 

  15. T. Hayat, N. Ali, Appl. Math. Mod. 32, 761 (2008)

    Article  Google Scholar 

  16. S. Srinivas, R. Gayathri, Appl. Math. Comput. 215, 185 (2009)

    MathSciNet  Google Scholar 

  17. K.S. Mekheimer, Y. Abd Elmaboud, Physica A 372, 1657 (2008)

    Google Scholar 

  18. S. Asghar, Q. Hussain, T. Hayat, Math. Comput. Appl. 18, 198 (2013)

    MathSciNet  Google Scholar 

  19. A. Ebaid, Phys. Lett. A 372, 4493 (2008)

    Article  ADS  Google Scholar 

  20. K.K. Raju, R. Devanathan, Rheol. Acta 13, 944 (1974)

    Article  Google Scholar 

  21. A.M. Siddiqui, W.H. Schwarz, J. Non-Newtonian Fluid Mech. 53, 257 (1994)

    Article  Google Scholar 

  22. S. Asghar, T. Minhas, A. Ali, Chin. Phys. B 24, 054702 (2014)

    Article  Google Scholar 

  23. T. Hayat, N. Ahmed, N. Ali, Commun. Nonlinear Sci. Numer. Simul. 13, 1581 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  24. T. Hayat, A. Afsar, N. Ali, Math. Comput. Model. 47, 380 (2008)

    Article  Google Scholar 

  25. T. Hayat, N. Saleem, N. Ali, Commun. Nonlinear Sci. Numer. Simul. 15, 2407 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  26. O.A. Beg, M.M. Rashidi, Int. J. Appl. Math. Mech. 9, 22 (2013)

    Google Scholar 

  27. Kh.S. Mekheimer, S.R. Komy, S.I. Abdelsalamd, Chin. Phys. B 22, 124702 (2013)

    Article  Google Scholar 

  28. N. Ali, Y. Wang, T. Hayat, M. Oberlack, Biorheology 45, 611 (2008)

    Google Scholar 

  29. N. Ali, Y. Wang, T. Hayat, M. Oberlack, Can. J. Phys. 87, 1047 (2009)

    Article  ADS  Google Scholar 

  30. N. Ali, T. Javed, Z. Naturforsch. 68a, 515 (2013)

    Article  ADS  Google Scholar 

  31. A.M. Abd-Alla, S.M. Abo-Dahab, A. Kilicman, J. Magn. & Magn. Mater. 384, 79 (2015)

    Article  ADS  Google Scholar 

  32. T. Hayat, Y. Wang, K. Hutter, S. Asghar, A.M. Siddiqui, Math. Prob. Eng. 4, 347 (2004)

    Article  Google Scholar 

  33. F.M. Abbasi, T. Hayat, B. Ahmad, G.Q. Chen, Z. Naturforsch. 69a, 451 (2014)

    Article  ADS  Google Scholar 

  34. T. Hayat, S. Bibi, M. Rafiq, A. Alsaedi, F.M. Abbasi, J. Magn. & Magn. Mater. 401, 733 (2016)

    Article  ADS  Google Scholar 

  35. K. Ramesha, M. Devakar, J. Magn. & Magn. Mater. 394, 335 (2015)

    Article  ADS  Google Scholar 

  36. W.R. Dean, Philos. Mag. 4, 208 (1927)

    Article  Google Scholar 

  37. W.R. Dean, Philos. Mag. 5, 673 (1928)

    Article  Google Scholar 

  38. H. Sato, T. Kawai, T. Fujita, M. Okabe, Trans. Jpn. Soc. Mech. Eng. B 66, 679 (2000)

    Article  Google Scholar 

  39. N. Ali, M. Sajid, T. Hayat, Z. Naturforsch. A 65a, 191 (2010)

    Article  ADS  Google Scholar 

  40. N. Ali, M. Sajid, T. Javed, Z. Abbas, Int. J. Heat Mass Transfer 53, 3319 (2010)

    Article  Google Scholar 

  41. N. Ali, K. Javid, M. Sajid, O.A. Beg, Comput. Methods Biomech. Biomed. Eng. 19, 614 (2016)

    Article  Google Scholar 

  42. S. Hina, T. Hayat, A. Alsaedi, Int. J. Heat Mass Transfer 55, 351 (2012)

    Google Scholar 

  43. S. Hina, M. Mustafa, T. Hayat, A. Alsaedi, ASME J. Appl. Mech. 80, 024501 (2013)

    Article  ADS  Google Scholar 

  44. T. Hayat, S. Hina, A.A. Hendi, S. Asghar, Int. J. Heat Mass Transfer 54, 5126 (2011)

    Article  Google Scholar 

  45. V.K. Narla, K.M. Prasad, J.V. Ramanamurthy, Chin. J. Eng. 2013, 582390 (2013)

    Article  Google Scholar 

  46. V. Ramesh Babu, S. Sreenadh, A.N.S. Srinivas, Ain Shams Eng. J. 9, 909 (2018)

    Article  Google Scholar 

  47. J.V. Ramanamurthy, K.M. Prasad, V.K. Narla, Phys. Fluids 25, 091903 (2013)

    Article  ADS  Google Scholar 

  48. A. Kalantari, K. Sadeghy, S. Sadeqi, Annu. Trans. Nordic Rheol. Soc. 21, 11155 (2013)

    Google Scholar 

  49. N. Ali, K. Javid, M. Sajid, O.A. Beg, Comput. Methods BioMech. BioMed. Eng. (2015) https://doi.org/10.1080/10255842.2015.1055257

  50. N. Ali, K. Javid, M. Sajid, A. Zaman, T. Hayat, Int. J. Heat Mass Transfer 94, 500 (2016)

    Article  Google Scholar 

  51. N. Ali, M. Sajid, Z. Abbas, T. Javed, Eur. J. Mech. B/Fluids 29, 387 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  52. N.B. Reddy, D. Bathaiah, Def. Sci. J. 32, 313 (1982)

    Article  Google Scholar 

  53. K. Chand, R. Kumar, Ind. J. Pure Appl. Phys. 50, 149 (2012)

    Google Scholar 

  54. T. Hayat, A. Bibi, H. Yasmin, B. Ahmad, J. Taiwan Inst. Chem. Eng. 58, 28 (2016)

    Article  Google Scholar 

  55. Z. Abbas, M. Naveed, M. Sajid, AIP Adv. 5, 107124 (2015)

    Article  ADS  Google Scholar 

  56. T.C. Papanastasiou, G.C. Georgiou, A.N. Alexandrou, Viscous fluid flow 532 (CRC Press, New York, 1999) p. 1606

  57. N. Ali, K. Javid, M. Sajid, T. Hayat, Meccanica 51, 1783 (2016)

    Article  MathSciNet  Google Scholar 

  58. N.S. Akbar, J. Bion. Eng. 12, 656 (2015)

    Article  Google Scholar 

  59. T. Hayat, S. Farooq, B. Ahmed, A. Alsaedi, Int. J. Heat Mass Transfer 106, 244 (2017)

    Article  Google Scholar 

  60. T. Hayat, S. Farooq, B. Ahmed, A. Alsaedi, Molliq (2018) https://doi.org/10.1016/j.molliq.2018.04.109

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Authors and Affiliations

  1. Department of Mathematics, Northern University, Nowshera, KPK, Pakistan

    Khurram Javid & Sehrish Khan

  2. Department of Mathematics & Statistics, International Islamic University, Islamabad, Pakistan

    Nasir Ali

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  1. Khurram Javid
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  2. Nasir Ali
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  3. Sehrish Khan
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Correspondence to Khurram Javid.

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Javid, K., Ali, N. & Khan, S. Numerical study of Hall effects on the peristaltically induced motion of a viscous fluid through a non-uniform regime: An application to the medical science. Eur. Phys. J. Plus 134, 395 (2019). https://doi.org/10.1140/epjp/i2019-12717-8

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