A Mathematical Model of Blood Flow in Merging Veins under a Magnetic Resonance Imaging Influence



Abstract Views
207

Downloads
194

Citations

Share

##plugins.themes.bootstrap3.article.sidebar##

Submitted Apr 11, 2021
Published Jun 22, 2021
10.24018/ejmath.2021.2.3.35

Abstract viewed = 207 times

Table of Contents

##plugins.themes.bootstrap3.article.main##

Venous blood flow through the superior and inferior vena cavae and via a merger to the right atrium of the heart is investigated. Based on the Newtonian assumption for blood, the model is developed using Boussinesq’s approximation for the continuity, momentum, energy, and mass diffusion equations, which are non-linear partial differential equations. The governing equations are non-dimensionalized and solved by the regular perturbation technique. Expressions for the concentration, temperature, and velocity are obtained, analyzed, and presented graphically and quantitatively, and discussed. The results show that an increase in the magnetic field strength and conflux angle produce fluctuations in the flow velocity.

Keywords: merging flow, venous blood, resonance imaging influence

References

  1. D.M. Wooton, and D.N. Ku, (1999). Fluid mechanics of vascular systems, diseases and thrombosis. Annual Review Biomedical Engineering, 299-329.
     Google Scholar
  2. H. Badre, S.C.R. Dennis, and F.T. Smith. (1985). Numerical and asymptotic solutions for merging flow through a channel with an upstream splitter plate. Journal of Fluid Mechanics, 156, 63-81.
     Google Scholar
  3. J.K. Krijger, and B. Hillen. (1990). Steady two-dimensional merging flow from two channels into a single channel. Applied Scientific Research, 47(3), 233-246.
     Google Scholar
  4. Ayushi Nakano, Yusuhiko Sugii, Mobomu Minamiyano (2005). Velocity profiles of pulsatile blood flow in arteries with bifurcation and confluence in rat mesentery measured by particle image velocimetry. Bifurcation and Confluence, JSME International Journal Series C, 48 (4), 444-452. Doi 10.1299/jsmec 48.444.
     Google Scholar
  5. T. Ishikawa, H. Fujiwara, N. Matsuki, T. Yoshimoto, Y. Imai, H. Ueno, and T. Yamaguchi (2011). Asymmetry of blood flow and cancer cell adhesion in a micro-channel with symmetric bifurcation and confluence, Biomedical Micro-devices, 13, 159-167.
     Google Scholar
  6. D. Pinho, D. Bento, and R. Lima. (2014) studied the effect of cell-free layer on the velocity profiles in blood flow in a micro-channel with bifurcation and confluence, Material Science, Corpus ID: 137708448.
     Google Scholar
  7. A.A. Siddiqui. (2013). Numerical Simulation of an asymmetric merging flow in a rectangular channel, arXiv: 1308.0805 (Physics).
     Google Scholar
  8. Siddiqui, A.A. (2016), Numerical simulation of asymmetric merging flow in a rectangular channel. World Journal of Mechanics. 6, 118-130. http://dx.doi.org/10.4236/wjm.2016.64010.
     Google Scholar
  9. A.A. Siddiqui, S. Ahmad, and M. Aqeel (2018), Influence of magnetic field on the merging flow of Powell-Eying fluids: an exact solution, Journal of Mechanica, 53(9), 2287-2298.
     Google Scholar
  10. M. Tadjfar, and F.T. Smith. (2004). Direct simulation and modeling of basic 3-dimensional bifurcating tube flow, Journal Fluid Mechanics. 519: 1-32.
     Google Scholar
  11. A.R. Bestman. (1991). Global models for the biomechanics of green plants, part 1. International Journal of Energy Research. 19: 677– 684.
     Google Scholar
  12. Erwin Kreyzig. Advanced Engineering Mathematics, John Wiley and Sons, Incorporation, New Delhi, India, 1983.
     Google Scholar