Insight into Unsteady Separated Stagnation Point Flow of Hybrid Nanofluids Subjected to an ElectroMagnetohydrodynamics Riga Plate
Abstract
:1. Introduction
2. Mathematical Formulation
 The term $\frac{\pi {j}_{0}{M}_{1}}{8{\rho}_{hnf}}\mathrm{exp}\left(\pi {y}_{1}/p\right)$ in the mathematical model is used to represent the electromagnetohydrodynamics effect from the Riga plate where ${M}_{1}=\frac{{M}_{0}\left(x{x}_{0}\left(t\right)\right)}{{\left({t}_{ref}\hspace{0.17em}\beta t\right)}^{2}}$ and ${y}_{1}=y/\sqrt{{t}_{ref}\hspace{0.17em}\beta t}$; ${j}_{0}$ is the electrodes’ current density, ${M}_{0}$ is a constant, ${t}_{ref}$ is the reference time (constant), $p$ is the width of magnets and electrodes, $\beta $ is the unsteadiness accelerating/decelerating parameter, $t$ is the time and ${x}_{0}\left(t\right)$ is the plate’s displacement.
 The velocity of free stream flow which align with the plate is ${u}_{e}\left(x,t\right)=\alpha \frac{\left(x{x}_{0}\left(t\right)\right)}{{t}_{ref}\beta t}+{u}_{0}\left(t\right)$; $\alpha $ is the acceleration parameter. Meanwhile, the velocity of the moving plate is ${u}_{0}\left(t\right)=\partial {x}_{0}\left(t\right)/\partial t\hspace{0.17em}.$
 The terms ${T}_{w}$ and ${T}_{\infty}$ respectively stand for surface and ambient temperatures.
 The sedimentation and aggregation effects are omitted by considering that the nanofluids are stable.
3. Stability Analysis
4. Results and Discussion
5. Conclusions
 The acceleration parameter enhances the skin friction and heat transfer coefficients for both hybrid nanofluids. However, the graphene–alumina/water has the maximum skin friction coefficient while copper–alumina/water has the maximum thermal coefficient for larger acceleration parameter.
 Upon the comparison of the hybrid and single nanofluids, the graphene–water has the maximum skin friction coefficient while alumina–water has the maximum heat transfer rate followed by graphene–water and copper–water nanofluids. This implies that the single nanofluids are a progressive heat transfer fluid and better than hybrid nanofluids for the case of unsteadiness decelerating flow.
 The increment of the decelerating parameter depreciates the velocity profile while the EMHD parameter accelerates the fluid velocity.
 Both decelerating and EMHD parameters reduce the temperature profile of the hybrid nanofluid by actively transmitting the fluid particle heat.
 The researchers can consider oil base fluid like ethylene glycol or combination of water and ethylene glycol.
 The researchers can consider magnetized hybrid nanofluid like magnetite–cobalt ferrite which actively operated under the magnetic field (EMHD) environment.
 The researchers can apply statistical data analysis like response surface methodology (RSM) and sensitivity analysis in investigating the significance of the physical parameters in this physical situation.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Properties  Water  Copper  Graphene  Alumina 

$\rho $$\left(\mathrm{kg}/{\mathrm{m}}^{3}\right)$  997.1  8933  2200  3970 
${C}_{p}$$\left(\mathrm{J}/\mathrm{kgK}\right)$  4179  385  790  765 
$k$$\left(\mathrm{W}/\mathrm{mK}\right)$  0.613  400  5000  40 
Properties  Correlations 

Thermal conductivity  ${k}_{hnf}=\left[\frac{\left(\frac{{\varphi}_{1}{k}_{1}+{\varphi}_{2}{k}_{2}}{{\varphi}_{hnf}}\right)2{\varphi}_{hnf}{k}_{f}+2\left({\varphi}_{1}{k}_{1}+{\varphi}_{2}{k}_{2}\right)+2{k}_{f}}{\left(\frac{{\varphi}_{1}{k}_{1}+{\varphi}_{2}{k}_{2}}{{\varphi}_{hnf}}\right)+{\varphi}_{hnf}{k}_{f}\left({\varphi}_{1}{k}_{1}+{\varphi}_{2}{k}_{2}\right)+2{k}_{f}}\right]{k}_{f}$ 
Heat capacity  ${\left(\rho {C}_{p}\right)}_{hnf}={\varphi}_{1}{\left(\rho {C}_{p}\right)}_{s1}+{\varphi}_{2}{\left(\rho {C}_{p}\right)}_{s2}+\left(1{\varphi}_{hnf}\right){\left(\rho {C}_{p}\right)}_{f}$ 
Density  ${\rho}_{hnf}={\varphi}_{1}{\rho}_{s1}+{\varphi}_{2}{\rho}_{s2}+\left(1{\varphi}_{hnf}\right){\rho}_{f}$ 
Dynamic viscosity  ${\mu}_{hnf}=\frac{{\mu}_{f}}{{\left(1{\varphi}_{hnf}\right)}^{2.5}};{\varphi}_{hnf}={\varphi}_{1}+{\varphi}_{2}$ 
${\mathit{f}}^{\u2033}\left(0\right)$  Present  Khashi’ie et al. [43]  Ahmad et al. [52] 
1.5394731  1.5394680  1.5394682 
$$\mathit{\beta}$$

$${\mathit{\gamma}}_{1}$$
 

First Solution  Second Solution  
−5.03  0.0487  −0.0486 
−5.031  0.0312  −0.0311 
−5.0315  0.0165  −0.0165 
−5.0316  0.0115  −0.0115 
−5.0318  0.0025  −0.0041 
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Khashi’ie, N.S.; Arifin, N.M.; Wahid, N.S.; Pop, I. Insight into Unsteady Separated Stagnation Point Flow of Hybrid Nanofluids Subjected to an ElectroMagnetohydrodynamics Riga Plate. Magnetochemistry 2023, 9, 46. https://doi.org/10.3390/magnetochemistry9020046
Khashi’ie NS, Arifin NM, Wahid NS, Pop I. Insight into Unsteady Separated Stagnation Point Flow of Hybrid Nanofluids Subjected to an ElectroMagnetohydrodynamics Riga Plate. Magnetochemistry. 2023; 9(2):46. https://doi.org/10.3390/magnetochemistry9020046
Chicago/Turabian StyleKhashi’ie, Najiyah Safwa, Norihan Md Arifin, Nur Syahirah Wahid, and Ioan Pop. 2023. "Insight into Unsteady Separated Stagnation Point Flow of Hybrid Nanofluids Subjected to an ElectroMagnetohydrodynamics Riga Plate" Magnetochemistry 9, no. 2: 46. https://doi.org/10.3390/magnetochemistry9020046