Mathematical model for bingham flow properties of blood in uniform tapered tube

Document Type : Research Paper

Authors

1 Department of Mathematics, Buddha Institute of Technology, GIDA, Gorakhpur (U.P.)-273209, India

2 North Eastern Hill University

Abstract

The stenosis and non-Newtonian property of the fluid in the blood flow represent the behavior of Herschel-Buckley fluid.
In a tapered tube model all the vessels which carry blood towards the tissues are considered as long and its one end slowly tapering cones rather than cylinders. Since the blood flow consist of two regions in which one is central region, consist of concentrated blood cells and its behavior is non-Newtonian and other region is periph-eral layer of plasma which represent the Newtonian behavior of fluid motion. In present paper, we have considered the Bingham fluid
model and study the flow of blood in a uniform tapered tube and obtained conditions and its variation in various graphs for shear stress and pressure gradient.

Keywords

References

[1] P. Bagchi, Mesoscale simulation of blood flow in small vessels, Journal of Bio-physics 92(6), (2007), 1858 1877.
[2] G. Bugliarello and J. Sevilla, Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes, Biorheology, 7(2), (1970), 85107.
[3] W. Y. Chan, Simulation of Arterial Stenosis Incorporating Fluid Structural In-teraction and Non-newtonian Blood Flow, Masters Thesis, RMIT University,Australia, (2006).
[4] S. E. Charm and G. S. Kurland, Blood flow in non-uniform tapered capillaries tubes, Biorheology, 4(4), (1967).
[5] P. Chaturani and R. N. Pralhad, Blood flow in tapered tube with bio-rheological applications, Biorheology, 22(4), (1985), 303-314.
[6] P. Chaturani and V. Palanisamy, Casson fluid model for pulsatile flow of blood with periodic body acceleration, Biorheology, 27(5), (1990), 619 630.
[7] F. Jiannong and R. G. Owens, Numerical simulation of pulsatile blood flow using a new constitutive model, Biorheology, 43(5), (2006), 637 660.
[8] S. Kumar and S. Kumar, A mathematical model for newtonian and non-newtonian flow through tapered tubes, Indian Journal of Biomechanics, Special Issue (NCBM 7-8), (2009), 191-195.
[9] S. Oka, Pressure development in a non-newtonian flow through a tapered tube, Biorheology, 10(2), (1973), 207-212.
[10] V. Pappu and P. Bagchi, Hydrodynamic interaction between erythrocytes and leukocytes affects rheology of blood in microvessels, Biorheology, 44(3), (2007),191-215.
[11] A. R. Pries and Secomb, Resistance to blood flow in vivo, from poiseuille to the in vivo viscosity law, Biorheology, 34(4), (1997), 369-373.
[12] K. Sakamoto, R. Sunaga, K. Nakamara and Y. Sato, Study of the relation between fluid distribution change in tissue and impedance change in during hemodialysis by frequency characteristics of the flowing blood, Annals N. Y.
Acad. Sci., 873(1), (1999), 77-88.
[13] N. L. Singh and J. Kumar, Mathematical study of steady blood flow in narrow vessel with plasma layer near the wall, Indian Journal Theoretical Physics, 50,(2002), 155-160.
[14] J. R. Womersley, Method for the calculation of velocity rate of flow and viscous drug in the areries when the pressure gradient is known, J. Physiol, 127(3),(1955), 553-563.
Journal of Hyperstructures
Volume 12, Issue 2
2023
Pages 375-386

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