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Comparative examination and flow characteristics of magnetohydrodynamic rotative flowing of second-grade liquid between two-oblique plane surfaces

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A Correction to this article was published on 16 April 2024

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Abstract

In this research article, the effect of rotating and second-grade fluid on an MHD Jeffery–Hamel flow (J–HF) has been investigated. Here, the MHD second-grade fluid theory has been used. The PDEs that represent this flow are transformed into ODEs, which are then solved using two separate methods: the 4th–5th-order Runge–Kutta Fehlberg technique with shooting methodology and the DTM technique. The impact of diverse physical factors, like rotational factor, Deborah, and Hartmann numbers, on the dimensionless rapidity \(F\) of the second-grade fluid and the wall frictional force factor is analyzed. Backflow is not detected in the lower part of the channel, according to the study. Additionally, the results show that the reverse flow disappears completely as the Hartmann number increases. Also, it is found that the Deborah quantity has less impact on the dimensionless velocity \(F\) of second-grade fluid nearby the down surface of the rotative diverging channel, but a significant increase in the thickener of the momentum boundary layer at the upper half of the channel is noticed with the rise in the magnitude of the Deborah number, hence signaling the beginning of the backflowing behavior. The current findings are contrasted to those of prior investigations and the HAM-built Mathematica package BVPh 2. The newly used analytical method shows high reliability, usefulness, and precision, as evidenced by the excellent agreement between DTM, HAM-BMP BVPh 2, and computational RKF45.

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Abbreviations

J–HF:

Jeffery–Hamel flow

CFD:

Computational fluid dynamics

BWCM:

Bernoulli wavelet collocation method

RKF-45:

4th–5th-order Runge–Kutta–Fehlberg

MHD:

Magnetohydrodynamic

SHAM:

Spectral homotopy analysis methodology

HAM:

Homotopy analysis methodology

DTM:

Differential transformation methodology

MHD-JHNF:

Magnetohydrodynamic Jeffery–Hamel nanofluid flow

HAM-BMP BVPh 2:

HAM-built Mathematica package BVPh 2

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Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA for funding this research work through the project number “NBU-FFR-2024-3021-01”. The authors are thankful to the Deanship of Graduate Studies and Scientific Research at University of Bisha for supporting this work through the Fast-Track Research Support Program.

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Authors and Affiliations

  1. Materials and Energy Engineering Laboratory (LMGE), Technology Department, Faculty of Technology, 20 Aout 1955 University of Skikda, PO Box 26, 21000, Skikda, Algeria

    Mohamed Kezzar

  2. Mechanical Engineering Department, University of 20 Aout 1955, El Hadaiek Road, B. O. 26, 21000, Skikda, Algeria

    Mohamed Kezzar & M. Slimane Tich Tich

  3. Drilling and MCP Department, University Kasdi Merbah, Ouargla, Algeria

    Abdelkader Khentout

  4. Mechanics of Materials and Plant Maintenance Research Laboratory (LR3MI), Mechanical Engineering Department, Faculty of Engineering, Badji Mokhtar University of Annaba (UBMA), PO Box 12, 23052, Annaba, Algeria

    Mohamed Rafik Sari

  5. Finance and Insurance Department, College of Business Administration, Northern Border University, 1321, Arar, Saudi Arabia

    Mohamed R. Eid

  6. Department of Mathematics, Faculty of Science, New Valley University, El-Kharga, 72511, Al-Wadi Al-Gadid, Egypt

    Mohamed R. Eid

  7. Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, 61922, Bisha, Saudi Arabia

    Essam M. Elsaid

Authors
  1. Mohamed Kezzar
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Correspondence to Mohamed R. Eid or Essam M. Elsaid.

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Appendices

Appendix A

See Table 

Table 4 Differential transformation operations
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4.

Appendix B

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Table 5 The first few components of the solution
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5.

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Kezzar, M., Khentout, A., Tich, M.S.T. et al. Comparative examination and flow characteristics of magnetohydrodynamic rotative flowing of second-grade liquid between two-oblique plane surfaces. J Therm Anal Calorim 149, 3645–3656 (2024). https://doi.org/10.1007/s10973-024-12917-y

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