Research Article
Triple Solutions with Stability Analysis of MHD Mixed
Convection Flow of Micropolar Nanofluid with Radiation Effect
Hazoor Bux Lanjwani,
1
Muhammad Saleem Chandio,
1
M. Imran Anwar,
2
Amnah S. Al-Johani,
3
Ilyas Khan ,
4
and Md. Nur Alam
5
1
University of Sindh, Jamshoro, Pakistan
2
University of Sargodha, Pakistan
3
Mathematics Department, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
4
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
5
Department of Mathematics, Pabna University of Science & Technology, Pabna-6600, Bangladesh
Correspondence should be addressed to Ilyas Khan; i.said@mu.edu.sa and Md. Nur Alam; nuralam.pstu23@gmail.com
Received 16 October 2021; Revised 30 January 2022; Accepted 22 February 2022; Published 11 April 2022
Academic Editor: Raghvendra Bohara
Copyright © 2022 Hazoor Bux Lanjwani et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
This paper deals with two-dimensional steady boundary layer flow, heat, and mass transfer characteristics of micropolar nanofluid
past on exponentially stretching/shrinking surface. The effect of different physical parameters like magnetic field, buoyancy,
thermal radiation, and connective heat transfer are examined. Furthermore, similarity solutions are obtained by similarity
transformation on the governing system of partial differential equations. The shooting method with help of the Maple software
is used to achieve the numerical solutions of the equations. For the different ranges of the applied parameters, triple solutions
are obtained for both cases of the surface. In view of the triple solutions, stability analysis is performed by bvp4c in the
MATLAB software, where only first solution is found feasible which is discussed. The main findings of the first solution
indicate the skin friction, drag force, heat, and mass transfer rates are increasing for the λ >0 and decreasing for λ <0 as the K
is enhanced. The velocity profiles decrease with increase in magnetic, slip velocity, and suction parameters. The temperature
profiles increase with increase in magnetic, thermophoresis, thermal radiation, and Brownian motion parameters, whereas
concentration profiles reduce with increase in Schmitt number and Brownian motion.
1. Introduction
The study of non-Newtonian fluid flows have gained much
importance, because of the common Newtonian fluids may
not completely satisfy the properties of the fluid flow in
many industrial applications, examples of such fluids are
biological fluids, polymeric fluids, fluids containing addi-
tives, liquid crystals, and paint colloidal solutions. Moreover,
the class of the non-Newtonian fluids containing different
kinds of complex properties are Casson fluids, Maxwell
fluids, and micropolar fluids. The micropolar fluid intro-
duced by Eringen [1] possesses a microscopic effect due to
the microstructure and micromotion of particles present in
fluid. These microstructure particles are of different shapes
which rotate independently to the motion of the fluid perti-
cles (Anwar et al. [2]). The system of the micropolar fluid
flow equations contains a microrotating vector besides the
classical velocity vector. These fluids contain smaller rigid
particles which rotate about the centroid of volume particles
that predicts the flow behaviors at rotation and microscale
independently that is defined by a microrotation vector.
Therefore, micropolar fluids are very important in fluid
dynamics, especially in studying some flows around some
important surfaces such as stretching surfaces or shrinking
surfaces. In this regard, MHD micropolar fluid flow on the
inclined plate was investigated by Kasim et al. [3]. The
micropolar fluid flow on the inclined surface with different
physical parameters was also studied by Das [4]. Srinivasa-
charya and Bindu [5] examined the entropic generation of
the micropolar fluid with parallel plates on the inclined
Hindawi
Journal of Nanomaterials
Volume 2022, Article ID 3147696, 21 pages
https://doi.org/10.1155/2022/3147696