Open AccessA Mathematical Model of Blood Flow in Merging Veins under a Magnetic Resonance Imaging Influence
Author(s) -
W Okuyade,
T. M. Abbey,
M. E. Abbey,
D. M. Abbey
Publication year - 2021
Publication title -
european journal of mathematics and statistics
Language(s) - English
Resource type - Journals
ISSN - 2736-5484
DOI - 10.24018/ejmath.2021.2.3.35
Subject(s) - blood flow , magnetic field , magnetic resonance imaging , perturbation (astronomy) , partial differential equation , physics , inferior vena cava , mechanics , right atrium , flow (mathematics) , mathematical analysis , mathematics , classical mechanics , medicine , radiology , quantum mechanics
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.