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Open AccessArticle

Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition

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School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Malaysia
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KCAET Khairpur Mirs, Sindh Agriculture University, Tandojam Sindh 70060, Pakistan
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Department of Mathematics and Social Sciences, Sukkur IBA University, Sukkur 65200, 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, Cankaya University, Ankara 06790, Turkey
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan
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Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
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Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 74; https://doi.org/10.3390/sym12010074
Received: 30 November 2019 / Revised: 23 December 2019 / Accepted: 24 December 2019 / Published: 2 January 2020
(This article belongs to the Special Issue Symmetry in Newtonian and Non-Newtonian Fluids)
The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative). View Full-Text
Keywords: micropolar nanofluid; inclined plane; dual solutions; stability analysis micropolar nanofluid; inclined plane; dual solutions; stability analysis
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MDPI and ACS Style

Lund, L.A.; Omar, Z.; Khan, U.; Khan, I.; Baleanu, D.; Nisar, K.S. Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition. Symmetry 2020, 12, 74.

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