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Modeling and analysis of MHD two-phase blood flow through a stenosed artery having temperature-dependent viscosity

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Abstract.

Present paper deals with MHD two-phase blood flow through a stenosed inclined artery with viscous dissipation, Joule heating and k -th-order chemical reaction. The two layered model of blood flow is considered in which core and plasma regions have temperature-dependent viscosity and constant viscosity, respectively. Elliptic shaped stenosis is considered for both core and plasma regions, separately. A continuous behaviour is assumed at interface of both core and plasma regions of blood flow with a no slip condition at the wall of the artery. Governing coupled non-linear partial differential equations are solved using a numerical technique named as single shooting method. The quantitative profile analysis is done for velocity, temperature, concentration of blood flow over an entire arterial segment. The effects of various parameters on flow characteristics for two-phase blood flow through stenosed artery are presented with the help of graphs. Current findings are in a good agreement with the findings of previous recent research studies.

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References

  1. J.H. Barbee, G.R. Cokelet, Microvasc. Res. 3, 6 (1971)

    Google Scholar 

  2. D.A. Fedosov, B. Caswell, A.S. Popel, G.E. Karniadakis, Microcirculation 17, 615 (2010)

    Google Scholar 

  3. R. Fahraeus, T. Lindqvist, Am. J. Physiol.-Legacy Content 96, 562 (1931)

    Google Scholar 

  4. R. Chebbi, J. Biol. Phys. 41, 313 (2015)

    Google Scholar 

  5. G.R. Cokelet, H.L. Goldsmith, Circul. Res. 68, 1 (1991)

    Google Scholar 

  6. M. Sharan, A.S. Popel, Biorheology 38, 415 (2001)

    Google Scholar 

  7. A. Medvedev, V. Fomin, Dokl. Phys. 56, 610 (2011)

    Google Scholar 

  8. Y. Çinar, A.M. Senyol, K. Duman, Am. J. Hypertension 14, 433 (2001)

    Google Scholar 

  9. K. Hooman, H. Gurgenci, Int. J. Heat Mass Transfer 51, 1139 (2008)

    Google Scholar 

  10. K. Torrance, D. Turcotte, J. Fluid Mech. 47, 113 (1971)

    ADS  Google Scholar 

  11. S. Siddiqa, S. Naqvi, N. Begum, S. Awan, M. Hossain, Int. J. Therm. Sci. 132, 457 (2018)

    Google Scholar 

  12. S. Siddiqa, S. Naqvi, M. Hossain, N. Massarotti, A. Mauro, J. Mol. Liq. 248, 616 (2017)

    Google Scholar 

  13. C.J. Cooper, T.P. Murphy, D.E. Cutlip, K. Jamerson, W. Henrich, D.M. Reid, D.J. Cohen, A.H. Matsumoto, M. Steffes, M.R. Jaff et al., New England J. Med. 370, 13 (2014)

    Google Scholar 

  14. W.J. Jean, I. Al-Bitar, D.L. Zwicke, S.C. Port, D.H. Schmidt, T.K. Bajwa, Catheter. Cardiovasc. Diag. 32, 8 (1994)

    Google Scholar 

  15. K.S. Mekheimer, M. El Kot, Acta Mech. Sin. 24, 637 (2008)

    ADS  MathSciNet  Google Scholar 

  16. S. Kamangar, G. Kalimuthu, I. Anjum Badruddin, A. Badarudin, N. Salman Ahmed, T. Khan, Sci. World J. 2014, 354946 (2014)

    Google Scholar 

  17. B. Tripathi, B.K. Sharma, AIP Conf. Proc. 1975, 030009 (2018)

    Google Scholar 

  18. M.M. Bhatti, A. Zeeshan, Biomed. Eng. Lett. 6, 242 (2016)

    Google Scholar 

  19. K. Buckenmaier, A. Pedersen, P. Sangiorgio, K. Scheffler, J. Clarke, B. Inglis, NeuroImage 186, 185 (2019)

    Google Scholar 

  20. J. Misra, A. Sinha, G. Shit, J. Mech. Med. Biol. 11, 547 (2011)

    Google Scholar 

  21. M. Bhatti, A. Zeeshan, R. Ellahi, N. Ijaz, J. Mol. Liq. 230, 237 (2017)

    Google Scholar 

  22. R. Ponalagusamy, R.T. Selvi, Meccanica 48, 2427 (2013)

    MathSciNet  Google Scholar 

  23. T. Hayat, S. Ayub, A. Tanveer, A. Alsaedi, J. Therm. Sci. Eng. Appl. 10, 031004 (2018)

    Google Scholar 

  24. B. Sharma, A. Mishra, S. Gupta, J. Eng. Phys. Thermophys. 86, 766 (2013)

    Google Scholar 

  25. R. Kumar, R. Kumar, S.A. Shehzad, M. Sheikholeslami, Int. J. Heat Mass Transfer 120, 540 (2018)

    Google Scholar 

  26. B. Sharma, M. Sharma, R. Gaur, A. Mishra, Int. J. Appl. Mech. Eng. 20, 385 (2015)

    Google Scholar 

  27. R. Chakraborty, R. Dey, S. Chakraborty, Int. J. Heat Mass Transfer 67, 1151 (2013)

    Google Scholar 

  28. O. Makinde, Chem. Eng. Commun. 198, 590 (2010)

    Google Scholar 

  29. B. Tripathi, B.K. Sharma, Int. J. Comput. Methods (2018) https://doi.org/10.1142/S0219876218501396

    MathSciNet  MATH  Google Scholar 

  30. S.C.O. Noutchie, Flow of a Newtonian fluid: The case of blood in large arteries, PhD Thesis (2009)

  31. R. Ponalagusamy, R.T. Selvi, Meccanica 50, 927 (2015)

    MathSciNet  Google Scholar 

  32. J.R. Womersley, J. Physiol. 127, 553 (1955)

    Google Scholar 

  33. R. Lamour, SIAM J. Sci. Comput. 18, 94 (1997)

    MathSciNet  Google Scholar 

  34. C. Michalik, R. Hannemann, W. Marquardt, Comput. Chem. Eng. 33, 1298 (2009)

    Google Scholar 

  35. S. Sharma, U. Singh, V. Katiyar, J. Magn. & Magn. Mater. 377, 395 (2015)

    ADS  Google Scholar 

  36. E. Tzirtzilakis, Phys. Fluids 17, 077103 (2005)

    ADS  MathSciNet  Google Scholar 

  37. R. Ellahi, M.M. Bhatti, K. Vafai, Int. J. Heat Mass Transfer 71, 706 (2014)

    Google Scholar 

  38. S. Srinivas, M. Kothandapani, Int. Commun. Heat Mass Transf. 35, 514 (2008)

    Google Scholar 

  39. B. Tripathi, B. Sharma, Int. J. Appl. Mech. Eng. 23, 767 (2018)

    Google Scholar 

  40. A. Zaman, N. Ali, O.A. Beg, M. Sajid, Int. J. Heat Mass Transfer 95, 1084 (2016)

    Google Scholar 

  41. M. El-Sayed, N. Eldabe, A. Ghaly, H. Sayed, Transp. Porous Media 89, 185 (2011)

    MathSciNet  Google Scholar 

  42. M. Sharan, B. Singh, P. Kumar, Appl. Math. Model. 21, 419 (1997)

    Google Scholar 

  43. M.M. Bhatti, A. Zeeshan, R. Ellahi, Comput. Biol. Med. 78, 29 (2016)

    Google Scholar 

  44. A. Rao, S. Sivaiah, R.S. Raju, J. Appl. Fluid Mech. 5, 63 (2012)

    Google Scholar 

  45. D.N. Ku, Annu. Rev. Fluid Mech. 29, 399 (1997)

    ADS  Google Scholar 

  46. N.A. Shah, D. Vieru, C. Fetecau, J. Magn. & Magn. Mater. 409, 10 (2016)

    ADS  Google Scholar 

  47. S. Majee, G. Shit, J. Magn. & Magn. Mater. 424, 137 (2017)

    ADS  Google Scholar 

  48. S. Rahman, R. Ellahi, S. Nadeem, Q.Z. Zia, J. Mol. Liq. 218, 484 (2016)

    Google Scholar 

  49. R. Ponalagusamy, S. Priyadharshini, Comput. Appl. Math. 37, 719 (2018)

    MathSciNet  Google Scholar 

  50. M. Dewhirst, B.L. Viglianti, M. Lora-Michiels, P.J. Hoopes, M.A. Hanson, Thermal dose requirement for tissue effect: experimental and clinical findings, in Thermal Treatment of Tissue: Energy Delivery and Assessment II, Vol. 4954 (ISOP, 2003) pp. 37--58

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science, Pilani, Pilani Campus, 333031, Rajasthan, India

    Bhavya Tripathi & Bhupendra Kumar Sharma

  2. Department of Bioscience, CASH, Mody University of Science and Technology, Lakshmangarh, 332311, Rajasthan, India

    Madhu Sharma

Authors
  1. Bhavya Tripathi
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  2. Bhupendra Kumar Sharma
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  3. Madhu Sharma
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Correspondence to Bhavya Tripathi.

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Tripathi, B., Sharma, B.K. & Sharma, M. Modeling and analysis of MHD two-phase blood flow through a stenosed artery having temperature-dependent viscosity. Eur. Phys. J. Plus 134, 466 (2019). https://doi.org/10.1140/epjp/i2019-12813-9

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