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Sensitivity analysis for Rabinowitsch fluid flow based on permeable artery constricted with multiple stenosis of various shapes

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Abstract

The present work analyzes the non-Newtonian nature of blood flow through a stenosed artery by utilizing the Rabinowitsch fluid model. We explored the pseudoplastic nature of Rabinowitsch fluid as the blood has the shear-thinning characteristic. The artery is affected by various shapes (bell shape, W shape, elliptical shape) and multiple stenoses. It has permeable wall and slip effects on the boundary. The governing equations of the flow are processed in dimensionless form along with the assumptions of mild stenosis and solved analytically. A detailed graphical analysis of the analytically attained solution is provided. It is found that the flow velocity gets higher values in the narrowed region, and it overgrows in the stenotic region. Its behavior depicted near the axis of the channel reverses in the vicinity of the arterial wall for slip parameter and Darcy number. The local sensitivity analysis is utilized to assess the influence of significant physical parameters on the flow velocity. The slip parameter has a more substantial impact, and stenosis height has a more negligible effect on the flow velocity. The Darcy number is more effective than stenosis height and less influential than the slip parameter. The streamlines split into the contours in the stenotic region close to the boundary. The size of contours diminishes for a quick flow and increases for growing stenosis height and higher Darcy number. These contours have various shapes depending upon the shape of stenosis.

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All the authors declare that our manuscript fulfills all ethical standards of research.

Abbreviations

(\(\overline{r }, \overline{z }\)):

Cylindrical coordinates

(\(\stackrel{-}{u,}\overline{w }\)):

Radial and axial velocities

\(R (m)\) :

Non-stenotic radius of the artery

\({d}_{l}\) \((m)\) :

Position of stenosis (\(l=\mathrm{1,2},3\))

\({s}_{l}\) \((m)\) :

Width of stenosis (\(l=\mathrm{1,2},3\))

\(m\) :

Parametric constant

\(s (N{m}^{-2})\) :

Extra stress tensor

α :

Slip parameter

\({D}_{a}\) :

Darcy number

\(\rho (kg {m}^{-3})\) :

Density

\(\mu (Ns{m}^{-2})\) :

Dynamic viscosity

\({\delta }_{l}^{*}\) (m):

Maximum height of stenosis in dimensional form

PoI:

Parameter of interest

\(k\) :

Non-linearity factor of the model

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Acknowledgements

The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: 22UQU4330955DSR02.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Lahore, 54590, Pakistan

    M. Hasnain Shahzad & Aziz Ullah Awan

  2. Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk, 71491, Saudi Arabia

    N. Ameer Ahammad

  3. Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad, 44000, Pakistan

    Sohail Nadeem

  4. Department of Mathematics, Jamoum University College, Umm Al-Qura University, Mecca, 24382, Saudi Arabia

    Seham Ayesh Allahyani

  5. Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835, Egypt

    ElSayed M. Tag-ElDin

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  1. M. Hasnain Shahzad
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All the authors have contributed equally. The authors read and approved the final manuscript.

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Correspondence to Aziz Ullah Awan.

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Shahzad, M.H., Ahammad, N.A., Nadeem, S. et al. Sensitivity analysis for Rabinowitsch fluid flow based on permeable artery constricted with multiple stenosis of various shapes. Biomass Conv. Bioref. (2022). https://doi.org/10.1007/s13399-022-03311-5

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