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Hall device impacts on ciliated pump-assisted blood flow of double-diffusion convection of nanofluid in a porous divergent channel

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Abstract

Motivated by bio-chemical systems and ciliated propulsion, we consider the steady laminar flow from a non-uniform wavy channel adjacent to a saturated porous medium which has been investigated analytically using an integration technique. A highly permeability domain is considered. We employed a sinusoidal complex wavy relation for the ciliated walls. A mathematical relation was used to convert the rheological equations from \(\big(\bar{X},\bar{\xi }\big)\) coordinate system to a \(\big(\bar{x},\bar{\xi }\big)\) dimensionless system. These rheological equations are simplified under two biological assumptions, one is creeping phenomena, and the second one is long-wavelength approximation. The solution of governing equations is obtained through Mathematica software 10.0 with the help of integration technique in a wave frame. The impacts of embedded hydro-mechanical parameters on the rheological features are studied. The boundary layer phenomena are obtained in the velocity profile under larger magnetic and porosity effects. The magnitude of pressure gradient is reduced under larger strength of magnetic and porosity effects. The cilia length parameter has a dynamic role in enhancement of the pressure gradient. The larger strength of the thermophoretic parameter has remarkable effects in augmentation of volumetric fraction, heat and mass transfer phenomena. The outcomes of current investigation are applicable in energy systems, manufacturing of ciliated micro-pumps, petroleum engineering, thermal augmentation of physiological and chemical fluids, and industrial magnetic materials processing.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha 61413, Saudi Arabia, for funding this work through research groups program under grant number R.G.P-1/234/42.

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Authors and Affiliations

  1. School of Science, Hunan City University, Yiyang, 413000, People’s Republic of China

    Ying-Qing Song

  2. Department of Mathematics, Northern University, Wattar-Wallai Road, Nowshera, 24110, KPK, Pakistan

    Khurram Javid

  3. Department of Mathematics, COMSATS University Islamabad, Sahiwal, 57000, Pakistan

    Sami Ullah Khan

  4. Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, 44000, Pakistan

    M. Ijaz Khan

  5. Qiuzhen College, Huzhou University, Huzhou, 313000, People’s Republic of China

    Tian-Chuan Sun

  6. CECOS University of IT and Emerging Sciences, Peshawar, Pakistan

    M. Imran Khan

  7. Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Kingdom of Saudi Arabia

    M. Y. Malik

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  1. Ying-Qing Song
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  2. Khurram Javid
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  3. Sami Ullah Khan
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  4. M. Ijaz Khan
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  5. Tian-Chuan Sun
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  6. M. Imran Khan
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  7. M. Y. Malik
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Correspondence to Tian-Chuan Sun or M. Imran Khan.

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Song, YQ., Javid, K., Khan, S.U. et al. Hall device impacts on ciliated pump-assisted blood flow of double-diffusion convection of nanofluid in a porous divergent channel. Eur. Phys. J. Plus 136, 667 (2021). https://doi.org/10.1140/epjp/s13360-021-01641-3

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