A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian flui...

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Bibliographic Details
Published in:Transport in porous media 2017-10, Vol.120 (1), p.239-254
Main Authors: Sharma, Bhupesh Dutt, Yadav, Pramod Kumar
Format: Article
Language:English
Subjects:
Blood flow
Blood vessels
Boundary layer transition
Civil Engineering
Classical and Continuum Physics
Constrictions
Earth and Environmental Science
Earth Sciences
Erythrocytes
Flow velocity
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Mathematical models
Newtonian fluids
Permeability
Plasmas (physics)
Rapid prototyping
Shear flow
Shear stress
Thickness
Wall shear stresses
Yield stress
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Summary:In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.
ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-017-0918-9