Citation: Khan, A.; Jamshed, W.; Eid,
M.R.; Pasha, A.A.; Tag El Din, E.S.M.;
Khalifa, H.A.E.-W.; Alharbi, S.K.
Unsteady Electro-Hydrodynamic
Stagnating Point Flow of Hybridized
Nanofluid via a Convectively Heated
Enlarging (Dwindling) Surface with
Velocity Slippage and Heat
Generation. Symmetry 2022, 14, 2136.
https://doi.org/10.3390/sym14102136
Academic Editors: Sergei
D. Odintsov and Ghulam Rasool
Received: 9 September 2022
Accepted: 10 October 2022
Published: 13 October 2022
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symmetry
S S
Article
Unsteady Electro-Hydrodynamic Stagnating Point Flow of
Hybridized Nanofluid via a Convectively Heated Enlarging
(Dwindling) Surface with Velocity Slippage and Heat Generation
Abbas Khan
1
, Wasim Jamshed
2,
* , Mohamed R. Eid
3,4
, Amjad Ali Pasha
5
, El Sayed M. Tag El Din
6
,
Hamiden Abd El-Wahed Khalifa
7,8
and Samaher Khalaf Alharbi
9
1
Department of Mathematics, University of Haripur, Haripur 22620, Pakistan
2
Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad 44000, Pakistan
3
Department of Mathematics, Faculty of Science, New Valley University, Al-Kharga 72511, Egypt
4
Department of Mathematics, Faculty of Science, Northern Border University, Arar 1321, Saudi Arabia
5
Aerospace Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia
6
Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt,
New Cairo 11835, Egypt
7
Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University,
Giza 13613, Egypt
8
Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia
9
Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass 51921, Saudi Arabia
* Correspondence: wasiktk@hotmail.com
Abstract: In (Al
2
O
3
-Cu/H
2
O) hybridized nanofluid (HYNF) is an unsteady electro-hydrodynamic
stagnation point flow. A stretchable (shrinkable) surface that was convectively heated was studied in
the past. In addition to the traditional nonslip surface, the heat generating (absorbing) and the velocity
slippage constraints are deliberated in this research. An obtained nonlinear scheme is resolved by
the homotopy analysis method. Governing parameters are the electric field parameters, that is,
the dimensionless parameters including the magnetic parameter, Prandtl quantity, heat generating
factor, Eckert quantity, and unsteady factor. We discuss in detail the effects of these variables on
the movement of problems and thermal transmission characteristics. Increasing the values of the
magneto and electric force parameters increased the temperature. Increasing the Prandtl number
lowered the temperature. For the Eckert parameter, an increase in temperature was recognized. The
symmetric form of the geometry model displayed improved the fluid flow by the same amount both
above and below the stagnation streamline, while it decreased the flow pressure by the same level.
The more heat source uses to increase the temperature of the HYNF over the entire area, the more
heat is supplied to the plate, but with a heat sink, the opposite effect is observed.
Keywords: hybridized nanofluid; unsteadiness stagnating point; velocity slippage; convective
boundary constraint; magnetic nanofluid; electric field; homotopy analysis method (HAM)
1. Introduction
Nanofluids have gained increasing attention due to their ability to recover heat transfer
efficiency in an assortment of industrial presentations, as well as the considerable upsurge
in the thermal conducting of the subsequent liquid. As a continuation of nanofluids, HYNFs
can be made by diffusing compound nano-powders or numerous types of nanomolecules in
the solution. HYNF is an innovative nanoliquid with two separate nanoparticles immersed
in the base fluid.
In recent years, many scholars have been involved in researching the heat transfer of
HYNF because HYNFs exhibit a higher heat transfer coefficient than conventional nanoflu-
ids. As a result, most heat transfer applications (e.g., machined coolants and HYNF) have
been explored to increase the thermal transmission coefficient of traditional nanoliquids.
Symmetry 2022, 14, 2136. https://doi.org/10.3390/sym14102136 https://www.mdpi.com/journal/symmetry