Abstract
The effects of a velocity slip and an external magnetic field on the flow of biomagnetic fluid (blood) through a stenosed bifurcated artery are investigated by using ANSYS FLUENT. Blood is regarded as a non-Newtonian power-law fluid, and the magnetization and electrical conductivity are considered in the mathematical model. The no-slip condition is replaced by the first-order slip condition. The slip boundary condition and magnetic force are compiled in the solver by the user-defined function (UDF). Numerical solutions are obtained by the finite volume method based on a nonuniform grid structure. The accuracy and efficiency of the solver are verified through a comparison with the literature. The results are presented graphically for different parameter values, and the effects of the magnetic number, the magnetic source position, the vascular obstruction ratio, the slip parameter, and the power-law index on the flow and temperature fields are illustrated.
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Abbreviations
- d :
-
arterywidth
- c p :
-
specific heat
- u s :
-
slip velocity
- p :
-
pressure
- k :
-
thermal conductivity
- n :
-
power-law index
- σ :
-
electrical conductivity
- M :
-
magnetization
- B :
-
magnetic induction
- (a,b):
-
magnetic source position
- d min :
-
minimum diameter of stenosis
- u, v :
-
velocity components along x-and y-axes
- U 0 :
-
fluid average velocity at inlet
- ρ :
-
biomagnetic fluid density
- T w :
-
temperature at arterial walls
- T f :
-
fluid temperature at inlet
- µ 0 :
-
magnetic permeability of vacuum
- H :
-
magnetic field strength
- H 0 :
-
magnetic field strength at point (a, 0)
- Nu :
-
Nusselt number
- τ 1 :
-
wall shear stress
- q :
-
wall heat flux
- β :
-
velocity slip coefficient
- M n :
-
magnetic number
- L R :
-
recirculation length
- C p :
-
pressure coefficient
- Re :
-
Reynolds number
- Cf:
-
local skin friction coefficient
- A :
-
vascular obstruction ratio
- β* :
-
dimensionless velocity slip coefficient
- Ls:
-
position of separation point
- L r :
-
position of reattachment point.
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Citation: XU, Y. X., ZHU, J., ZHENG, L. C., and SI, X. H. Non-Newtonian biomagnetic fluid flow through a stenosed bifurcated artery with a slip boundary condition. Applied Mathematics and Mechanics (English Edition), 41(11), 1611–1630 (2020) https://doi.org/10.1007/s10483-020-2657-9
Project supported by the Fundamental Research Funds for the Central Universities of China (No. FRF-BR-18-008B)
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Xu, Y., Zhu, J., Zheng, L. et al. Non-Newtonian biomagnetic fluid flow through a stenosed bifurcated artery with a slip boundary condition. Appl. Math. Mech.-Engl. Ed. 41, 1611–1630 (2020). https://doi.org/10.1007/s10483-020-2657-9
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DOI: https://doi.org/10.1007/s10483-020-2657-9