Skip to main content
SpringerLink
Log in

Impact of Cattaneo-Christov heat flux on electroosmotic transport of third-order fluids in a magnetic environment

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

In the case of steady flow of a fluid under the combined influence of external electric and magnetic fields, the fluid moves forward by forming an axial momentum boundary layer. With this end in view a study has been performed here to investigate the problem of entropy generation during electroosmotically modulated flow of a third-order electrically conducting fluid flowing on a microchannel bounded by silicon-made parallel plates under the influence of a magnetic field, by paying due consideration to the steric effect. The associated mechanism of heat transfer has also been duly taken care of, by considering Cattaneo-Christov heat flux. A suitable finite difference scheme has been developed for the numerical procedure. A detailed study of the velocity and temperature distributions has been made by considering their variations with respect to different physical parameters involved in the problem. The results of numerical computation have been displayed graphically. The computational work has been carried out by considering blood as the working fluid, with the motivation of exploring some interesting phenomena in the context of hemodynamical flow in micro-vessels. Among other variables, parametric variations of the important physical variables, viz. i) skin friction and ii) Nusselt number have been investigated. The study confirms that the random motion of the fluid particles can be controlled by a suitable adjustment of the intensity of an externally applied magnetic field in the transverse direction. It is further revealed that the Nusselt number diminishes, as the Prandtl number gradually increases; however, a steady increase in the Nusselt number occurs with increase in thermal relaxation. Entropy generation is also found to be enhanced with increase in Joule heating. The results of the present study have also been validated in a proper manner.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Lyklema, Fundamentals of Interface and Colloid Science (Academic Press, 2000)

  2. H. Lowe, W. Ehrfeld, Electrochem. Acta 44, 3679 (1997)

    Article  Google Scholar 

  3. O. Worz, K.P. Jackel, T. Richter, A. Wold, Chem. Eng. Sci. 56, 1029 (2001)

    Article  Google Scholar 

  4. S.V. Gokhale, R.K. Tayal, V.K. Jayaraman, B.D. Kulkarni, Int. J. Chem. Reactor Eng. 3, 1 (2005)

    Article  Google Scholar 

  5. J. Koo, C. Kleinstreuer, Int. J. Heat Mass Transfer 47, 3159 (2004)

    Article  Google Scholar 

  6. J. Chen, M. Chu, K. Koulajian, X.Y. Wu, A. Giacca, Y. Sun, Biomed. Microdevices 11, 1251 (2009)

    Article  Google Scholar 

  7. D. Bhattaa, A.A. Michel, M. Marti Villalba, G.D. Emmerson, I.J.G. Sparrow, E.A. Perkins, M.B. McDonnell, R.W. Ely, G.A. Cartwright, Biosens. Bioelectron. 30, 78 (2011)

    Article  Google Scholar 

  8. D.R. Arifin, L.Y. Yeo, J.R. Friend, Biomicrofluidics 1, 014103 (2007)

    Article  Google Scholar 

  9. P. Abhimanyu, P. Kaushik, P.K. Mondal, S. Chakaraborty, Journal of Non-Newtonian Fluid Mechanics 231, 56 (2016)

    Article  MathSciNet  Google Scholar 

  10. S. Chandra, J.C. Misra, J. Mol. Liq. 224(A), 818 (2016)

    Article  Google Scholar 

  11. J.C. Misra, S. Chandra, H. Herwig, J. Hydrodyn. 27, 350 (2015)

    Article  ADS  Google Scholar 

  12. Z. Tan, J. Liu, Phys. Lett. A 381, 2573 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  13. J.C. Misra, S. Chandra, G.C. Shit, P.K. Kundu, Appl. Math. Mech. 35, 749 (2014)

    Article  Google Scholar 

  14. J.C. Misra, S. Chandra, Cent. Eur. J. Phys. 12, 274 (2014)

    Google Scholar 

  15. J.C. Misra, S. Chandra, J. Hydrodyn. 25, 309 (2013)

    Article  ADS  Google Scholar 

  16. J.C. Misra, G.C. Shit, S. Chandra, P.K. Kundu, Appl. Math. Comput. 217, 7932 (2011)

    MathSciNet  Google Scholar 

  17. J.R. Kelner, M.S. Roos, P.R. Brakeman, T.F. Budinger, Magn. Reson. Med. 16, 139 (1990)

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  19. Y. Kinouchi, H. Yamaguchi, T.S. Tenforde, Bioelectromagnetics 17, 21 (1996)

    Article  Google Scholar 

  20. O. Aydin, A. Kaya, Appl. Math. Model. 33, 4086 (2009)

    Article  Google Scholar 

  21. A. Sinha, J.C. Misra, ASME J. Heat Transf. 136, 112701 (2014)

    Article  Google Scholar 

  22. A. Sinha, J.C. Misra, J. Mech. 30, 491 (2014)

    Article  Google Scholar 

  23. J.C. Misra, A. Sinha, Heat Mass Transf. 49, 617 (2013)

    Article  ADS  Google Scholar 

  24. J.C. Misra, A. Sinha, Spec. Top. Rev. Porous Media Int. J. 4, 147 (2013)

    Article  Google Scholar 

  25. J.C. Misra, S. Chandra, G.C. Shit, P.K. Kundu, J. Mech. Med. Biol. 13, 1350013 (2013)

    Article  Google Scholar 

  26. A. Sinha, J.C. Misra, Appl. Math. Mech. 33, 649 (2012)

    Article  Google Scholar 

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

    Article  Google Scholar 

  28. J.C. Misra, A. Sinha, G.C. Shit, Int. J. Biomath. 4, 207 (2011)

    Article  MathSciNet  Google Scholar 

  29. J.C. Misra, G.C. Shit, S. Chandra, P.K. Kundu, J. Eng. Math. 59, 91 (2011)

    Article  Google Scholar 

  30. J.C. Misra, A. Sinha, G.C. Shit, Appl. Math. Mech. 31, 1405 (2010)

    Article  Google Scholar 

  31. J.C. Misra, G.C. Shit, J. Appl. Mech., Trans. ASME (USA) 76, 06106 (2009)

    Google Scholar 

  32. J.C. Misra, G.C. Shit, Appl. Math. Comput. 210, 350 (2009)

    MathSciNet  Google Scholar 

  33. J.C. Misra, S. Maiti, G.C. Shit, J. Mech. Med. Biol. 8, 507 (2008)

    Article  Google Scholar 

  34. J.C. Misra, A. Sinha, J. Hydrodyn. 27, 647 (2015)

    Article  ADS  Google Scholar 

  35. J.C. Misra, S. Chandra, J. Hydrodyn. 25, 309 (2013)

    Article  ADS  Google Scholar 

  36. J.C. Misra, G.C. Shit, S. Chandra, P.K. Kundu, J. Eng. Math. 59, 91 (2011)

    Article  Google Scholar 

  37. J.C. Misra, B. Pal, A.S. Gupta, Math. Models Methods Appl. Sci. 8, 1323 (1998)

    Article  MathSciNet  Google Scholar 

  38. T. Hayat, M. Imtiaz, A. Alsaedi, S. Almezal, J. Mag. Magn. Mater. 401, 296 (2016)

    Article  ADS  Google Scholar 

  39. M. Mustafa, AIP Adv. 5, 047109 (2015)

    Article  ADS  Google Scholar 

  40. S. Han, L. Zheng, C. Li, X. Zhang, Appl. Math. Lett. 38, 87 (2014)

    Article  MathSciNet  Google Scholar 

  41. M. Ciarletta, B. Straughan, Mech. Res. Commun. 37, 445 (2010)

    Article  Google Scholar 

  42. A. Sarkar, P.K. Kundu, Eur. Phys. J. Plus 132, 534 (2017)

    Article  Google Scholar 

  43. F.A. Soomro, R.U. Haq, Z.H. Khan, Q. Zhang, Eur. Phys. J. Plus 132, 412 (2017)

    Article  Google Scholar 

  44. C. Sulochana, G.P. Ashwinkumber, N. Sandeep, Eur. Phys. J. Plus 132, 387 (2017)

    Article  Google Scholar 

  45. M.I. Afridi, M. Qasim, S. Shafie, Eur. Phys. J. Plus 132, 404 (2017)

    Article  Google Scholar 

  46. R.J. Moreau, Magnetohydrodynamics (Springer, 1990)

  47. K. Ayun, M.Y. Khan, M. Asraf, J. Ahmad, Q. M-Ul-Hassan, Eur. Phys. J. Plus 132, 552 (2017)

    Article  Google Scholar 

  48. R.F. Probstein, Physicochemical Hydrodynamics (Wiley, New York, 1994)

  49. R.J. Hunter, Zeta Potential in Colloid Science: Principles and Applications (Academic Press, London, 1981)

  50. S. Sarkar, S. Ganguly, P. Dutta, Int. J. Heat Mass Transer 104, 1325 (2017)

    Article  Google Scholar 

  51. S.A. Shehzad, T. Hussain, T. Hayat, M. Ramzan, A. Alsaedi, J. Cent. South Univ. 22, 360 (2015)

    Article  Google Scholar 

  52. V. Lakshmikantham, A.S. Vatsala, Generalized Quasilinearization for Nonlinear Problems (Mathematics and Its Applications) (Kluwer Academic, Dordrecht, 1998)

  53. J.C. Misra, A. Sinha, B. Mallick, Physica A 470, 330 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  54. L.H. Thomas, Elliptic Problems in Linear Difference Equations over a Network, Watson Sci. Comput. Lab. Rept. (Columbia University, New York, 1949)

  55. A. Bejan, ASME J. Heat Transf. 101, 718 (1979)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Healthcare Science and Technology, Indian Institute of Engineering Science and Technology, Shibpur, 711103, Howrah, India

    J. C. Misra, B. Mallick & A. Roy Chowdhury

  2. Department of Mathematics, Yogoda Satsanga Palpara Mahavidyalaya, 721457, Purba Medinipur, India

    A. Sinha

Authors
  1. J. C. Misra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Mallick
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Sinha
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Roy Chowdhury
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Misra, J.C., Mallick, B., Sinha, A. et al. Impact of Cattaneo-Christov heat flux on electroosmotic transport of third-order fluids in a magnetic environment. Eur. Phys. J. Plus 133, 195 (2018). https://doi.org/10.1140/epjp/i2018-12002-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2018-12002-6

Search

Navigation