Skip to main content
SpringerLink
Log in

Heat and mass transfer in magneto-biofluid flow through a non-Darcian porous medium with Joule effect

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

In the present study, a mathematical model for the hydromagnetic non-Newtonian biofluid flow in the non-Darcy porous medium with Joule effect is proposed. A uniform magnetic field acts perpendicularly to the porous surface. The governing nonlinear partial differential equations are transformed into linear ones which are solved numerically by applying the explicit finite difference method. The effects of various parameters, like Reynolds number and hydro-magnetic, Forchheimer, and Darcian parameters, Prandtl, Eckert, and Schmidt numbers, on the velocity, temperature, and concentration are presented graphically. The results of the study can find applications in surgical operations, industrial material processing, and various heat transfer processes.

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. H. H. Pennes, Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol., 1, No. 2, 93–122 (1948).

    Google Scholar 

  2. J. J. W. Lagendijk, The influence of blood flow in large vessels on the temperature distribution in hyperthermia, Phys. Med. Biol., 27, 17–23 (1982).

    Article  Google Scholar 

  3. J. C. Chato, Heat transfer to blood vessels, ASME J. Biomech. Eng., 102, 110–118 (1980).

    Article  Google Scholar 

  4. O. A. Bég and A. Sajid, CFD modeling of axisymmetric hemodynamics and heat transfer using ADINA, in: Technical Report of Biomechanics-III, Bradford University, Science Park, Listerhills, Bradford, UK (2002).

  5. M. C. Kolios, M. D. Sherar, and J. W. Hunt, Large blood vessel cooling in heated tissues: A numerical study, Phys. Med. Biol., 48, 4125–4134 (2003).

    Article  Google Scholar 

  6. S. Chakravarty and S. Sen, Dynamic response of heat and mass transfer in blood flow through stenosed bifurcated arteries, Korean–Austr. J., 17, No. 2, 47–62 (2005).

    Google Scholar 

  7. G. S. Barozzi and A. Dumas, Convective heat transfer coefficients in the circulation, J. Biomech. Eng., 113, 308–313 (1991).

    Article  Google Scholar 

  8. J. W. Baish, Heat transport by countercurrent blood vessels in the presence of an arbitrary pressure gradient, ASME J. Biomech. Eng., 112, 207 (1990).

    Article  Google Scholar 

  9. Z. S. Deng and J. Liu, Blood perfusion-based model for characterizing the temperature fluctuations in living tissue, Physica A: Stat. Mech. Appl., 300, 521–530 (2001).

    Article  MATH  Google Scholar 

  10. O. I. Craciiunescu and S. T. Clegg, Pulsatile blood flow effects on temperature distribution and heat transfer in rigid vessels, ASME J. Biomech. Eng., 123, No. 5, 500–505 (2001).

    Article  Google Scholar 

  11. L. Consiglieri, I. Santos, and D. Haemmerich, Theoretical analysis of the heat convection coefficient in large vessels and the significance for thermal ablative therapies, Phys. Med. Biol., 48, 4125–4134 (2003).

    Article  Google Scholar 

  12. R. V. Davalos, B. Rubinsky, and L. M. Mir, Theoretical analysis of the thermal effects during in-vivo tissue electroporation, Bioelectrochem. J., 61, 99–107 (2003).

    Article  Google Scholar 

  13. D. Shrivastava, B. McKay, and R. B. Romer, An analytical study of heat transfer in finite tissue with two blood vessels and uniform Dirichlet boundary conditions, ASME J. Heat Transf., 127, No. 2, 179–188 (2005).

    Article  Google Scholar 

  14. R. Skalak and S. Chien, Rheology of blood cells as soft tissues, Biorheology, 19, 453–461 (1982).

    Google Scholar 

  15. G. R. Cokelet, The rheology of human blood, in: Y. C. Fung (Ed.), Biomechanics – Its Foundations and Objectives, Prentice-Hall, Englewood Cliffs (1972), pp. 63–104.

    Google Scholar 

  16. T. Takeuchi, T. Mizuno, T. Higashi, A. Yamagishi, and M. Date, Orientation of red blood cells in high magnetic field, J. Magn. Mater., 140, 1462–1463 (1995).

    Article  Google Scholar 

  17. E. E. Tzirtzilakis and G. B. Tanoudis, Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer, Int. J. Numer. Methods Heat Fluid Flow, 13, No. 7, 830– 848 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  18. V. C. Louckopoulos and E. E. Tzirtzilakis, Biomagnetic channel flow in spatially varying magnetic field, Int. J. Eng. Sci., 42, 571–590 (2004).

    Article  Google Scholar 

  19. A. R. A. Khaled and K. Vafai, The role of porous media in modeling flow and heat transfer in biological tissues, Int. J. Heat Mass Transfer, 26, No. 46, 4989–5003 (2003).

    Article  Google Scholar 

  20. A. Ogulu and E. Amos, Modeling pulsatile blood flow within a homogeneous porous bed in the presence of a uniform magnetic field and time-dependent suction, Int. Commun. Heat Mass Transfer, 34, 989–995 (2007).

    Article  Google Scholar 

  21. I. Pop and D. B. Ingham, Convective Heat Transfer: Mathematical and Numerical Modelling of Viscous Fluids and Porous Media, Pergamon, Oxford (2001).

    Google Scholar 

  22. L. Preziosi and A. Farina, On Darcy’s law for growing porous media, Int. J. Non-Linear Mech., 37, 485–491 (2002).

    Article  MATH  Google Scholar 

  23. W. J. Vankan, J. M. Huyghe, J. D. Janssen, A. Huson, W. J. D. Hacking, and W. Schrenner, Finite element analysis of blood flow through biological tissue, Int. J. Eng. Sci., 35, 375–385 (1997).

    Article  MATH  Google Scholar 

  24. S. Sorek and S. Sideman, A porous medium approach for modelling heart mechanics, Math. Biosci., 81, 14–32 (1986).

    Google Scholar 

  25. R. Bhargava, S. Rawat, H. S. Takhar, and O. A. Bég, Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel, Meccanica, 42, 247–262 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  26. R. C. Chaudhary, B. K. Sharma, and A. K. Jha, Radiation effect with simultaneous thermal and mass diffusion in MHD mixed convection flow from a vertical surface with ohmic heating, Rom. J. Phys., 51, No. 7–8, 715–727 (2006).

    Google Scholar 

  27. J. D. Hoffman, Numerical Methods for Engineers and Scientists, McGraw-Hill, New York (1992).

    MATH  Google Scholar 

  28. J. C. Chato, Heat transfer to blood vessels, ASME J. Biomech. Eng., 102, 110–118 (1980).

    Article  Google Scholar 

  29. J. W. Valvano, S. Nho, and G. T. Anderson, Analysis of the Weinbaum–Jiji model of blood flow in the canine kidney cortex for self-heated thermistors, ASME J. Biomech. Eng., 116, No. 2, 201–207 (1994).

    Article  Google Scholar 

  30. S. Gabrial, R. W. Lau, and C. Gabrial, The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues, Phys. Med. Biol., 41, 2271–2293 (2004).

    Article  Google Scholar 

  31. T. Bég and O. A. Bég, Chemically-decaying drug transport across membranes, in: Technical Report, Bradford University Science Park, Listerhills, Bradford, UK (2003).

  32. A. Sherman and E. W. Sutton, Magnetohydrodynamics, Evanston, IL, USA (1961).

  33. S. Rawat, R. Bhargava, O. Anwar Bég, P. Bhargava, and Ben R. Hughes, Pulsatile dissipative magneto-bio-rheological fluid flow and heat transfer in a non-Darcy porous medium channel: finite element modeling, Emirates J. Eng. Res., 14, No. 2, 77–90 (2009).

    Google Scholar 

  34. A. Dybbs and R. V. Edwards, A new look at porous media fluid mechanics: Darcy to Turbulent, Fundam. Transport Phenom. Porous Media, 82, 201–258 (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    B. K. Sharma

  2. Department of Chemical Engineering, Birla Institute of Technology and Science, Pilani, Rajasthan, India

    A. Mishra & S. Gupta

Authors
  1. B. K. Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. K. Sharma.

Additional information

Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 86, No. 3, pp. 717–725, July–August, 2013.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharma, B.K., Mishra, A. & Gupta, S. Heat and mass transfer in magneto-biofluid flow through a non-Darcian porous medium with Joule effect. J Eng Phys Thermophy 86, 766–774 (2013). https://doi.org/10.1007/s10891-013-0893-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-013-0893-0

Keywords

Search

Navigation