. 2022 Dec 25;14(1):48.

doi: 10.3390/mi14010048.

Numerical Investigation of Darcy-Forchheimer Hybrid Nanofluid Flow with Energy Transfer over a Spinning Fluctuating Disk under the Influence of Chemical Reaction and Heat Source

Muhammad Riaz Khan¹, Aisha M Alqahtani², Sharifah E Alhazmi³, Mohamed Abdelghany Elkotb^{4

5}, Maawiya Ould Sidi⁶, Haifaa F Alrihieli⁷, Elsayed Tag-Eldin⁸, Mansour F Yassen^{9

10}

Affiliations

¹ Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan.
² Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia.
³ Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 21955, Saudi Arabia.
⁴ Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia.
⁵ Mechanical Engineering Department, College of Engineering, Kafrelsheikh University, Kafr Elsheikh 33516, Egypt.
⁶ RT-M2A Laboratory, Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka 42421, Saudi Arabia.
⁷ Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia.
⁸ Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt.
⁹ Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia.
¹⁰ Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt.

PMID: 36677110
PMCID: PMC9863586
DOI: 10.3390/mi14010048

Numerical Investigation of Darcy-Forchheimer Hybrid Nanofluid Flow with Energy Transfer over a Spinning Fluctuating Disk under the Influence of Chemical Reaction and Heat Source

Muhammad Riaz Khan et al. Micromachines (Basel). 2022.

. 2022 Dec 25;14(1):48.

doi: 10.3390/mi14010048.

Authors

Muhammad Riaz Khan¹, Aisha M Alqahtani², Sharifah E Alhazmi³, Mohamed Abdelghany Elkotb^{4

5}, Maawiya Ould Sidi⁶, Haifaa F Alrihieli⁷, Elsayed Tag-Eldin⁸, Mansour F Yassen^{9

10}

Affiliations

¹ Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan.
² Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia.
³ Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 21955, Saudi Arabia.
⁴ Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia.
⁵ Mechanical Engineering Department, College of Engineering, Kafrelsheikh University, Kafr Elsheikh 33516, Egypt.
⁶ RT-M2A Laboratory, Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka 42421, Saudi Arabia.
⁷ Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia.
⁸ Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt.
⁹ Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia.
¹⁰ Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt.

PMID: 36677110
PMCID: PMC9863586
DOI: 10.3390/mi14010048

Abstract

The present computational model is built to analyze the energy and mass transition rate through a copper and cobalt ferrite water-based hybrid nanofluid (hnf) flow caused by the fluctuating wavy spinning disk. Cobalt ferrite (CoFe₂O₄) and copper (Cu) nanoparticles (nps) are incredibly renowned in engineering and technological research due to their vast potential applications in nano/microscale structures, devices, materials, and systems related to micro- and nanotechnology. The flow mechanism has been formulated in the form of a nonlinear set of PDEs. That set of PDEs has been further reduced to the system of ODEs through resemblance replacements and computationally solved through the parametric continuation method. The outcomes are verified with the Matlab program bvp4c, for accuracy purposes. The statistical outputs and graphical evaluation of physical factors versus velocity, energy, and mass outlines are given through tables and figures. The configuration of a circulating disk affects the energy transformation and velocity distribution desirably. In comparison to a uniform interface, the uneven spinning surface augments energy communication by up to 15%. The addition of nanostructured materials (cobalt ferrite and copper) dramatically improves the solvent physiochemical characteristics. Furthermore, the upward and downward oscillation of the rotating disc also enhances the velocity and energy distribution.

Keywords: MHD; PCM; chemical reaction; heat source; hybrid nanofluid; wavy fluctuating disk.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

**Figure 1**
The hybrid nanofluid flow over a fluctuating disk.

**Figure 2**
The behavior of primary velocity $f (η)$ against copper $ϕ_{1} = ϕ_{C u}$ nanoparticles.

**Figure 3**
The behavior of primary velocity $f (η)$ against cobalt ferrite $ϕ_{2} = ϕ_{F e_{2} O_{4}}$ nanoparticles.

**Figure 4**
The behavior of primary velocity $f (η)$ against disk fluctuation term S.

**Figure 5**
The behavior of primary velocity $f (η)$ against porosity parameter $λ$ .

**Figure 6**
The behavior of primary velocity $f (η)$ against Forchhemier number Fr.

**Figure 7**
The behavior of secondary velocity $h (η)$ against injection term $+ β$ .

**Figure 8**
The behavior of secondary velocity $h (η)$ against suction term $- β$ .

**Figure 9**
The behavior of secondary velocity $h (η)$ against disk term $ω$ .

**Figure 10**
The nature of energy $θ (η)$ field against copper $ϕ_{1}$ nanoparticles.

**Figure 11**
The nature of energy $θ (η)$ field against cobalt ferrite $ϕ_{2}$ nanoparticles.

**Figure 12**
The nature of energy $θ (η)$ field against the thermal energy ratio coefficient $γ$ .

**Figure 13**
The nature of energy $θ (η)$ versus heat absorption/generation term $ℏ$ .

**Figure 14**
The nature of concentration $Φ (η)$ profile versus the Schmidt number Sc.

**Figure 15**
The nature of concentration $Φ (η)$ profile versus the chemical reaction Kr.

See this image and copyright information in PMC

References

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1. Sabu A.S., Mackolil J., Mahanthesh B., Mathew A. Reiner-Rivlin nanomaterial heat transfer over a rotating disk with distinct heat source and multiple slip effects. Appl. Math. Mech. 2021;42:1495–1510. doi: 10.1007/s10483-021-2772-7. - DOI
1. Li Y.X., Muhammad T., Bilal M., Khan M.A., Ahmadian A., Pansera B.A. Fractional simulation for Darcy-Forchheimer hybrid nanoliquid flow with partial slip over a spinning disk. Alex. Eng. J. 2021;60:4787–4796. doi: 10.1016/j.aej.2021.03.062. - DOI

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Numerical Investigation of Darcy-Forchheimer Hybrid Nanofluid Flow with Energy Transfer over a Spinning Fluctuating Disk under the Influence of Chemical Reaction and Heat Source

Affiliations

Numerical Investigation of Darcy-Forchheimer Hybrid Nanofluid Flow with Energy Transfer over a Spinning Fluctuating Disk under the Influence of Chemical Reaction and Heat Source

Authors

Affiliations

Abstract

Conflict of interest statement

Figures

References

LinkOut - more resources

Full Text Sources