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Open AccessArticle

Magnetohydrodynamic (MHD) Flow of Micropolar Fluid with Effects of Viscous Dissipation and Joule Heating Over an Exponential Shrinking Sheet: Triple Solutions and Stability Analysis

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School of Quantitative Sciences, Universiti Utara Malaysia, 06010 Sintok, Kedah
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KCAET Khairpur Mirs, Sindh Agriculture University, Tandojam Sindh 70060, Pakistan
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
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Department of Mathematics and Statistics, Institute of Southern Punjab (ISP), Multan 60700, Pakistan
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Centre of Excellence for Research in Engineering Materials, King Saud University, P.O. Box-800, Riyadh 11421, Saudi Arabia
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Electrochemistry and Corrosion Laboratory, Department of Physical Chemistry, National Research Centre, El-Behoth St. 33, Dokki, Cairo 12622, Egypt
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Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 142; https://doi.org/10.3390/sym12010142
Received: 3 December 2019 / Revised: 29 December 2019 / Accepted: 7 January 2020 / Published: 10 January 2020
(This article belongs to the Special Issue Symmetry in Newtonian and Non-Newtonian Fluids)
A numerical study was carried out to examine the magnetohydrodynamic (MHD) flow of micropolar fluid on a shrinking surface in the presence of both Joule heating and viscous dissipation effects. The governing system of non-linear ordinary differential equations (ODEs) was obtained from the system of partial differential equations (PDEs) by employing exponential transformations. The resultant equations were transformed into initial value problems (IVPs) by shooting technique and then solved by the Runge–Kutta (RK) method. The effects of different parameters on velocity, angular velocity, temperature profiles, skin friction coefficient, and Nusselt number were obtained and demonstrated graphically. We observed that multiple solutions occurred in certain assortments of the parameters for suction on a surface. The stability analysis of solutions was performed, and we noted that the first solution was stable while the remaining two solutions were not. The results also showed that the velocity of the fluid increased as the non-Newtonian parameter rose in all solutions. Furthermore, it was detected that the temperature of fluid rose at higher values of the Eckert number in all solutions. View Full-Text
Keywords: triple solutions; micropolar fluid; shrinking; stability analysis triple solutions; micropolar fluid; shrinking; stability analysis
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MDPI and ACS Style

Lund, L.A.; Omar, Z.; Khan, I.; Raza, J.; Sherif, E.-S.M.; Seikh, A.H. Magnetohydrodynamic (MHD) Flow of Micropolar Fluid with Effects of Viscous Dissipation and Joule Heating Over an Exponential Shrinking Sheet: Triple Solutions and Stability Analysis. Symmetry 2020, 12, 142.

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