Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2014, Article ID 915640, 9 pages
http://dx.doi.org/10.1155/2014/915640
Research Article

Computational Dynamics of Arterial Blood Flow in the Presence of Magnetic Field and Thermal Radiation Therapy

1Center for Research in Computational and Applied Mechanics, University of Cape Town, Rondebosch 7701, South Africa
2Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa

Received 24 March 2014; Accepted 31 March 2014; Published 22 April 2014

Academic Editor: Raseelo Joel Moitsheki

Copyright © 2014 T. Chinyoka and O. D. Makinde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Ogulu and A. R. Bestman, “Deep heat muscle treatment a mathematical model—I,” Acta Physica Hungarica, vol. 73, no. 1, pp. 3–16, 1993. View at Publisher · View at Google Scholar · View at Scopus
  2. A. Ogulu and A. R. Bestman, “Deep heat muscle treatment a mathematical model—II,” Acta Physica Hungarica, vol. 73, no. 1, pp. 17–27, 1993. View at Publisher · View at Google Scholar · View at Scopus
  3. T.-C. Shih, H.-L. Liu, and A. T.-L. Horng, “Cooling effect of thermally significant blood vessels in perfused tumor tissue during thermal therapy,” International Communications in Heat and Mass Transfer, vol. 33, no. 2, pp. 135–141, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. S. A. Sapareto and W. C. Dewey, “Thermal dose determination in cancer therapy,” International Journal of Radiation Oncology Biology Physics, vol. 10, no. 6, pp. 787–800, 1984. View at Google Scholar · View at Scopus
  5. C. Damianou and K. Hynynen, “Focal spacing and near-field heating during pulsed high temperature ultrasound therapy,” Ultrasound in Medicine and Biology, vol. 19, no. 9, pp. 777–787, 1993. View at Publisher · View at Google Scholar · View at Scopus
  6. J. van der Zee, “Heating the patient: a promising approach?” Annals of Oncology, vol. 13, no. 8, pp. 1173–1184, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. W. Levin, M. D. Sherar, B. Cooper, R. P. Hill, J. W. Hunt, and F.-F. Liu, “Effect of vascular occlusion on tumour temperatures during superficial hyperthermia,” International Journal of Hyperthermia, vol. 10, no. 4, pp. 495–505, 1994. View at Google Scholar · View at Scopus
  8. R. B. Roemer, “The local tissue cooling coefficient: a unified approach to thermal washout and steady-state perfusion calculations,” International Journal of Hyperthermia, vol. 6, no. 2, pp. 421–430, 1990. View at Google Scholar · View at Scopus
  9. H. H. Pennes, “Analysis of tissue and arterial blood temperatures in the resting human forearm,” Journal of Applied Physiology, vol. 1, no. 2, pp. 93–122, 1948. View at Google Scholar · View at Scopus
  10. O. I. Craciunescu and S. T. Clegg, “Pulsatile blood flow effects on temperature distribution and heat transfer in rigid vessels,” Journal of Biomechanical Engineering, vol. 123, no. 5, pp. 500–505, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Siegel and M. Perlmutter, “Heat transfer for pulsating laminar duct flow,” Journal of Heat Transfer, vol. 8, pp. 111–116, 1962. View at Google Scholar
  12. J. C. Chato, “Heat transfer to blood vessels,” Journal of Biomechanical Engineering, vol. 102, no. 2, pp. 110–118, 1980. View at Google Scholar · View at Scopus
  13. T. C. Shih, H. S. Kou, and W. L. Lin, “Effect of effective tissue conductivity on thermal dose distributions of living tissue with directional blood flow during thermal therapy,” International Communications in Heat and Mass Transfer, vol. 29, no. 1, pp. 115–126, 2002. View at Publisher · View at Google Scholar · View at Scopus
  14. M. C. Kolios, A. E. Worthington, D. W. Holdsworth, M. D. Sherar, and J. W. Hunt, “An investigation of the flow dependence of temperature gradients near large vessels during steady state and transient tissue heating,” Physics in Medicine and Biology, vol. 44, no. 6, pp. 1479–1497, 1999. View at Publisher · View at Google Scholar · View at Scopus
  15. J. Creeze and J. J. W. Lagendijk, “Temperature uniformity during hyperthermia: the impact of large vessels,” Physics in Medicine and Biology, vol. 37, no. 6, pp. 1321–1337, 1992. View at Publisher · View at Google Scholar · View at Scopus
  16. H. W. Cho and J. M. Hyun, “Numerical solutions of pulsating flow and heat transfer characteristics in a pipe,” International Journal of Heat and Fluid Flow, vol. 11, no. 4, pp. 321–330, 1990. View at Google Scholar · View at Scopus
  17. S. Y. K. Seo Young Kim, B. H. K. Byung Ha Kang, and J. M. H. Jae Min Hyun, “Heat transfer in the thermally developing region of a pulsating channel flow,” International Journal of Heat and Mass Transfer, vol. 36, no. 17, pp. 4257–4266, 1993. View at Google Scholar · View at Scopus
  18. J. Prakash, O. D. Makinde, and A. Ogulu, “Magnetic effect on oscillatory blood flow in a constricted tube,” Botswana Journal of Technology, vol. 13, no. 1, pp. 45–50, 2004. View at Google Scholar
  19. O. D. Makinde, “Analysis of non-newtonian reactive flow in a cylindrical pipe,” Journal of Applied Mechanics, Transactions ASME, vol. 76, no. 3, pp. 1–5, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. T. Chinyoka, Y. Y. Renardy, M. Renardy, and D. B. Khismatullin, “Two-dimensional study of drop deformation under simple shear for Oldroyd-B liquids,” Journal of Non-Newtonian Fluid Mechanics, vol. 130, no. 1, pp. 45–56, 2005. View at Publisher · View at Google Scholar · View at Scopus
  21. T. Chinyoka, “Computational dynamics of a thermally decomposable viscoelastic lubricant under shear,” Journal of Fluids Engineering, Transactions of the ASME, vol. 130, no. 12, Article ID 121201, 7 pages, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. T. J. Pedley, Fluid Dynamics of Large Blood Vessel, Cambridge Press, Cambridge, UK, 1980.
  23. L. Pauling and C. D. Coryell, “The magnetic properties and structure of hemoglobin, oxyhemoglobin and carbonmonoxyhemoglobin,” Proceedings of the National Academy of Sciences of the United States of America, vol. 22, pp. 210–216, 1936. View at Google Scholar
  24. A. R. Rao and K. S. Deshikachar, “Physiological-type flow in a circular pipe in the presence of a transverse magnetic field,” The Journal of the Indian Institute of Science, vol. 68, pp. 247–260, 1988. View at Google Scholar
  25. K. Haldar and S. N. Ghosh, “Effect of a magnetic field on blood flow through an indented tube in the presence of erythrocytes,” Indian Journal of Pure and Applied Mathematics, vol. 25, no. 3, pp. 345–352, 1994. View at Google Scholar
  26. P. Cheng, “Two dimensional radiating gas flow by a moment method,” The American Institute of Aeronautics and Astronautics, vol. 2, pp. 1662–1664, 1964. View at Google Scholar
  27. M. M. Lih, Transport Phenomenon in Medicine and Biology, John Wiley and Sons, New York, NY, USA, 1969.
  28. T. Chinyoka, “Poiseuille flow of reactive Phan-Thien-Tanner liquids in 1D channel flow,” Journal of Heat Transfer, vol. 132, no. 11, Article ID 111701, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. T. Chinyoka, “Suction-injection control of shear banding in non-isothermal and exothermic channel flow of Johnson-Segalman liquids,” Journal of Fluids Engineering, Transactions of the ASME, vol. 133, no. 7, Article ID 071205, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. I. E. Ireka and T. Chinyoka, “Non-isothermal flow of a Johnson-Segalman liquid in a lubricated pipe with wall slip,” Journal of Non-Newtonian Fluid Mechanics, vol. 192, pp. 20–28, 2013. View at Google Scholar
  31. T. Chinyoka, S. Goqo, and B. I. Olajuwon, “Computational analysis of gravity driven flow of a variable viscosity viscoelastic fluid down an inclined plane,” Computers & Fluids, vol. 84, no. 15, pp. 315–326, 2013. View at Google Scholar