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Open AccessArticle

Dual Solutions and Stability Analysis of Magnetized Hybrid Nanofluid with Joule Heating and Multiple Slip Conditions

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School of Science, Guangdong University of Petrochemical Technology, Guangdong 525000, China
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Institute of Information and Communication Technology, University of Sindh Jamshoro, Sindh 76090, Pakistan
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Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam
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FAE, Sindh Agriculture University, Tandojam 70060, Pakistan
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Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
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Institute of Space Sciences, 077125 Magurele, Romania
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan
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Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
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Center of Excellence for Research in Engineering Materials (CEREM), King Saud University, P.O. Box 800, Al-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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Mechanical Design and Materials Department, Faculty of Energy Engineering, Aswan University, Aswan 81521, Egypt
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Author to whom correspondence should be addressed.
Processes 2020, 8(3), 332; https://doi.org/10.3390/pr8030332
Received: 15 February 2020 / Revised: 6 March 2020 / Accepted: 9 March 2020 / Published: 12 March 2020
(This article belongs to the Special Issue Rheological Study of Nanofluids)
This paper investigates the steady, two dimensional, and magnetohydrodynamic flow of copper and alumina/water hybrid nanofluid on a permeable exponentially shrinking surface in the presence of Joule heating, velocity slip, and thermal slip parameters. Adopting the model of Tiwari and Das, the mathematical formulation of governing partial differential equations was constructed, which was then transformed into the equivalent system of non-linear ordinary differential equations by employing exponential similarity transformation variables. The resultant system was solved numerically using the BVP4C solver in the MATLAB software. For validation purposes, the obtained numerical results were compared graphically with those in previous studies, and found to be in good agreement, as the critical points are the same up to three decimal points. Based on the numerical results, it was revealed that dual solutions exist within specific ranges of the suction and magnetic parameters. Stability analysis was performed on both solutions in order to determine which solution(s) is/are stable. The analysis indicated that only the first solution is stable. Furthermore, it was also found that the temperature increases in both solutions when the magnetic parameter and Eckert number are increased, while it reduces as the thermal slip parameter rises. Furthermore, the coefficient of skin friction and the heat transfer rate increase for the first solution when the magnetic and the suction parameters are increased. Meanwhile, no change is noticed in the boundary layer separation for the various values of the Eckert number in the heat transfer rate. View Full-Text
Keywords: hybrid nanofluid; Joule heating; slip conditions; dual solution; stability analysis hybrid nanofluid; Joule heating; slip conditions; dual solution; stability analysis
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MDPI and ACS Style

Yan, L.; Dero, S.; Khan, I.; Mari, I.A.; Baleanu, D.; Nisar, K.S.; Sherif, E.-S.M.; Abdo, H.S. Dual Solutions and Stability Analysis of Magnetized Hybrid Nanofluid with Joule Heating and Multiple Slip Conditions. Processes 2020, 8, 332.

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