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Effects of Catheter, Stenosis and Thrombosis in Non-Newtonian Blood Flow Through Narrow Arteries with Clinical Applications: A Mathematical Model

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Abstract

This study analyses the rheological characteristics of non-Newtonian Carreau fluid model for nanoparticles suspended flow of blood through constricted arteries in the presence of stenosis, thrombosis and catheters. Analytical expressions, such as, velocity distribution, temperature, pressure gradient, wall shear stress and resistive impedance to flow are obtained by implementing the perturbation method and through the extensive use of MATLAB and MATHEMATICA programming tools, the results are presented graphically and tabularly. It is found that temperature of the fluid lessens with the increase in stenosis shape parameter and depth of stenosis which results in the reduction of flow of blood in the artery. It is discovered that a rise in Weissenberg number results in the decrease of fluid’s velocity and skin friction. The magnitude of resistance to blood flow reduces with the upsurge of flow rate and stenosis shape parameter and the reverse character is recognized when Weissenberg number, the depth and axial displacement of blood clot increases. When the angioplasty catheter of radius 0.3 is inserted to the clear the constrictions in the artery, the resistance to flow surges considerably in the range of 6.75–8.78 when the stenosis position extends in the axial direction from 0.1 to 0.3. It is also recorded that when the catheter guidewire radius is 0.18, the pressure gradient in blood flow is found to vary in the range of 1.21–1.43 when the axial variable z varies from 0.2 to 0.8 and it decreases from 1.36 to 1.32 when the blood clot position displaces from 0.2 to 0.6.

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Abbreviations

L:

Length of the artery

R:

Non-stenotic radius of outer tube

K :

Thermal conductivity

T :

Temperature

S :

Stress tensor

Q:

Flow rate

Gr:

Grashof number

We:

Weissenberg number

\(\left( {{\bar{r}},{\bar{z}}} \right) \) :

Cylindrical Coordinates

\(\left( {{\bar{u}},{\bar{w}}} \right) \) :

Radial, Axial velocity

\(n\left( { \ge 2} \right) \) :

Multiple stenosis shape parameter

\(q/\frac{{\partial p}}{{\partial z}}\) :

Pressure gradient

a:

Location of the stenosis

b:

Length of the stenosis

c:

Catheter radius

m:

Power law index

\(\delta \) :

Maximum stenotic depth

g:

Gravity

p:

Fluid’s pressure

\(\Pi \) :

Second invariant of stress tensor

\(\eta \) :

Outer wall of artery

\(\epsilon \) :

Inner wall of artery

\(\beta \) :

Dimensionless heat source or sink parameter

\(\theta \) :

Temperature

\(\zeta \) :

Maximum height attained by the clot

\(\gamma \) :

Thermal expansion coefficient

\(\rho \) :

Density

\(\mu \) :

Viscosity

\(\phi \) :

Nanofluid volume fraction

nf:

Nanofluid

f:

Base fluid

s:

Metallic nanoparticles

d:

Displacement

\({c_p}\) :

Heat capacity

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Authors and Affiliations

  1. Applied Mathematics and Economics Programme Area, School of Applied Sciences and Mathematics, Universiti Teknologi Brunei, Jalan Tungku Link, Gadong, Bandar Seri Begawan, BE1410, Brunei Darussalam

    S. Afiqah Wajihah, D. S. Sankar & Atulya K. Nagar

  2. School of Mathematics Computer Science and Engineering, Liverpool Hope University, Hope Park, Liverpool, L16 9JD, UK

    S. Afiqah Wajihah, D. S. Sankar & Atulya K. Nagar

Authors
  1. S. Afiqah Wajihah
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  2. D. S. Sankar
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  3. Atulya K. Nagar
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Contributions

AWS perceived the research problem, formulated it as mathematical model and contributed in obtaining the analytical solutions and also take part in develo** MATLAB code for generating data for plotting the graphs and then analyzing the results. DSS contributed in obtaining the expressions for rheological quantities and involved in generating the data for plotting the graphs through MATLAB programming and analysed and validated the results. AKN analysed and validated the results. All authors read and approved the final manuscript.

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Correspondence to D. S. Sankar.

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Wajihah, S.A., Sankar, D.S. & Nagar, A.K. Effects of Catheter, Stenosis and Thrombosis in Non-Newtonian Blood Flow Through Narrow Arteries with Clinical Applications: A Mathematical Model. Int. J. Appl. Comput. Math 8, 136 (2022). https://doi.org/10.1007/s40819-022-01335-z

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