Citation: Khan, M.S.; Mei, S.;
Shabnam; Ali Shah, N.; Chung, J.D.;
Khan, A.; Shah, S.A. Steady
Squeezing Flow of
Magnetohydrodynamics Hybrid
Nanofluid Flow Comprising Carbon
Nanotube-Ferrous Oxide/Water with
Suction/Injection Effect.
Nanomaterials 2022, 12, 660. https://
doi.org/10.3390/nano12040660
Academic Editors: Simone Morais
and Konstantinos Spyrou
Received: 23 December 2021
Accepted: 8 February 2022
Published: 16 February 2022
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nanomaterials
Article
Steady Squeezing Flow of Magnetohydrodynamics Hybrid
Nanofluid Flow Comprising Carbon Nanotube-Ferrous
Oxide/Water with Suction/Injection Effect
Muhammad Sohail Khan
1
, Sun Mei
1,
*, Shabnam
1
, Nehad Ali Shah
2
, Jae Dong Chung
2
, Aamir Khan
3,
*
and Said Anwar Shah
4
1
School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China;
sohailkhan8688@gmail.com (M.S.K.); shabnam8688@gmail.com (S.)
2
Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea;
nehadali199@yahoo.com (N.A.S.); jdchung@sejong.ac.kr (J.D.C.)
3
Department of Mathematics and Statistics, University of Haripur, Haripur 22620, KPK, Pakistan
4
Department of Basic Sciences and Islamiat, University of Engineering and Technology Peshawar,
Peshawar 25120, KPK, Pakistan; anwarshah@uetpeshawar.edu.pk
* Correspondence: sunm@ujs.edu.cn (S.M.); aamir.khan@uoh.edu.pk (A.K.)
Abstract: The main purpose of the current article is to scrutinize the flow of hybrid nanoliquid (ferrous
oxide water and carbon nanotubes) (CNTs + Fe
3
O
4
/H
2
O) in two parallel plates under variable
magnetic fields with wall suction/injection. The flow is assumed to be laminar and steady. Under a
changeable magnetic field, the flow of a hybrid nanofluid containing nanoparticles Fe
3
O
4
and carbon
nanotubes are investigated for mass and heat transmission enhancements. The governing equations
of the proposed hybrid nanoliquid model are formulated through highly nonlinear partial differential
equations (PDEs) including momentum equation, energy equation, and the magnetic field equation.
The proposed model was further reduced to nonlinear ordinary differential equations (ODEs) through
similarity transformation. A rigorous numerical scheme in MATLAB known as the parametric
continuation method (PCM) has been used for the solution of the reduced form of the proposed
method. The numerical outcomes obtained from the solution of the model such as velocity profile,
temperature profile, and variable magnetic field are displayed quantitatively by various graphs
and tables. In addition, the impact of various emerging parameters of the hybrid nanofluid flow is
analyzed regarding flow properties such as variable magnetic field, velocity profile, temperature
profile, and nanomaterials volume fraction. The influence of skin friction and Nusselt number are
also observed for the flow properties. These types of hybrid nanofluids (CNTs + Fe
3
O
4
/H
2
O) are
frequently used in various medical applications. For the validity of the numerical scheme, the
proposed model has been solved by another numerical scheme (BVP4C) in MATLAB.
Keywords: steady; hybrid nanofluid flow; variable magnetic field; parametric continuation method
(PCM); BV4C Schemes
1. Introduction
Heat transfer through the flow of fluid on the plate surface or on the surface of a
revolving disk is gaining incredible interest from researchers due to its many uses in
the aeronautical sciences and engineerings including chemical processes, thermal-energy-
producing systems, geothermal industry, gas turbine rotators, medical equipment, rotating
machinery, and computer storage. The squeezing flow produces by the motion of the
boundaries play a significant role in polymer processing, hydrodynamical machines, lubri-
cation equipment, etc. Due to its wide range of applications in many modern technologies,
it can be considered a good source of heat transmission. Researchers have also updated the
squeezing flow through the introduction of new ideas known as nanofluids. Nanofluids
Nanomaterials 2022, 12, 660. https://doi.org/10.3390/nano12040660 https://www.mdpi.com/journal/nanomaterials