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Electromagnetohydrodynamic unsteady blood flow with ternary nanoparticles in a vertical irregular peristaltic flow: an exact treatment

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Abstract

It is believed that the use of nanoparticles to assist the blood is one of the most essential strategies to combat cancer cells that are located inside the human body. This is accomplished by enclosing the cancer cells and subjecting the regions that are affected to heat, which kills the cells and makes it possible to dispose of them in a different manner. This study offers a mathematical depiction of the flow of blood that is supported by various nanoparticles (gold-Au, iron oxide-Fe3O4, and carbon nanotube particles-SWCNTs) as it travels through a vertical artery with varied undulation while being subjected to electric and magnetic fields. The modeling process was done by a set of nonlinear partial differential equations using the Poisson–Boltzmann equation and the momentum in both directions in addition to the heat equation. Some dimensionless parameters are used to linearize the system before being solved exactly with the assistance of Mathematica software. The hypothesis that the artery ripple is irregular, and that the artery is exposed to both magnetic and electric fields, in addition to using three different types of nanoparticles, represents a novelty of this work. The impact of these factors on the flow and streamlines inside the artery is observed by a set of graphs. The results tend to an augmentation in the transversal velocity may be seen in relation to the rise in nanoparticle concentration and the Grashof number, as opposed to the impact of the magnetic field, particularly in the context of unsteady flow. Moreover, the presence of irregularities in the artery leads to an increase in both longitudinal velocity and temperature while simultaneously diminishing the waviness of both parameters.

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Abbreviations

\({a}_{0}\) :

Breadth of the artery \((\mathrm{m})\)

\({B}_{0}\) :

Transverse magnetic strength (A m−1)

\(Cp\) :

Specific heat (J kg−1 K−1)

\(e\) :

Electronic charge

\(E\) :

Electric field

\({E}_{\mathrm{x}}\) :

Longitudinal uniform electric field (V m−1)

\(m\) :

Electro-osmotic number

\({n}_{0}\) :

Ion density

\(P\) :

Pressure (Kg m−1s−2)

\(Q\) :

Heat generation parameter

\(t\) :

Time (s)

\(T\) :

Temperature (\(\mathrm{K}\))

\({T}_{\mathrm{a}}\) :

Absolute temperature (\(\mathrm{K}\))

\(\mathrm{U}\) :

Axial velocity (m s−1)

\(V\) :

Transverse velocity (m s−1)

\({z}_{0}\) :

Valence

\(\alpha\) :

Electro-osmotic velocity

\(\beta\) :

Irregularity parameter

\(\delta\) :

Wave number (m−1)

\(\varepsilon\) :

Wave amplitude ratio

\({\epsilon }_{0}\) :

Solution’s permittivity constant (H m−1)

\(k\) :

Debye–Hückel parameter

\({k}_{\mathrm{B}}\) :

Boltzmann constant (J K−1)

\(\mu\) :

Dynamic viscosity (Ns m−2)

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\rho\) :

Density (Kg m−3)

\({\rho }_{0}\) :

Net charge density (C m−3)

\(\phi\) :

Nanoparticles volume fraction

\(\overline{\phi }\) :

EDL potential function

Gr :

Grashof number

\(M\) :

Magnetic parameter

\(\mathrm{Pr}\) :

Prandtl number

\(\mathrm{Re}\) :

Reynolds number

\(f\) :

Fluid base

\(\mathrm{nf}\) :

Nanofluid

\(\mathrm{hnf}\) :

Hybrid nanofluid

\(\mathrm{thnf}\) :

Ternary hybrid nanofluid

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Acknowledgements

Researchers would like to thank the Deanship of Scientific Research, Qassim University, for funding the publication of this project.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, University of Bisha, P.O. Box 344, 61922, Bisha, Saudi Arabia

    Essam M. Elsaid

  2. Basic Sciences Department, El Gazeera High Institute for Engineering and Technology, Cairo, Egypt

    Essam M. Elsaid

  3. Department of Mathematics, College of Science and Arts, Qassim University, Alnbhaniah, Saudi Arabia

    A. A. M. Sayed

  4. Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt

    A. A. M. Sayed

  5. Basic Engineering Sciences Department, Faculty of Engineering at Benha, Benha University, Cairo, Egypt

    Mohamed S. Abdel-wahed

  6. Civil and Environmental Department, College of Engineering and Design, Kingdome University, Riffa, Kingdom of Bahrain

    Mohamed S. Abdel-wahed

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  1. Essam M. Elsaid
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Elsaid, E.M., Sayed, A.A.M. & Abdel-wahed, M.S. Electromagnetohydrodynamic unsteady blood flow with ternary nanoparticles in a vertical irregular peristaltic flow: an exact treatment. J Therm Anal Calorim 148, 14163–14181 (2023). https://doi.org/10.1007/s10973-023-12598-z

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