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# Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis

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School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Kedah
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KCAET Khairpur Mir’s & FAE, Sindh Agriculture University, Tandojam 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 Computer Science, Beirut Arab University, 115020 Beirut, Lebanon
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Department of Software, Sejong University, Seoul 05006, Korea
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Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi Arabia
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Author to whom correspondence should be addressed.
Energies 2019, 12(24), 4617; https://doi.org/10.3390/en12244617
Received: 28 October 2019 / Revised: 20 November 2019 / Accepted: 28 November 2019 / Published: 5 December 2019
(This article belongs to the Special Issue Fluid Flow and Heat Transfer Ⅱ)
In this study, first-order slip effect with viscous dissipation and thermal radiation in micropolar fluid on a linear shrinking sheet is considered. Mathematical formulations of the governing equations of the problem have been derived by employing the fundamental laws of conservations which then converted into highly non-linear coupled partial differential equations (PDEs) of boundary layers. Linear transformations are employed to change PDEs into non-dimensional ordinary differential equations (ODEs). The solutions of the resultant ODEs have been obtained by using of numerical method which is presented in the form of shootlib package in MAPLE 2018. The results reveal that there is more than one solution depending upon the values of suction and material parameters. The ranges of dual solutions are , and no solution is where $S c i$ is the critical values of $S$ . Critical values have been obtained in the presence of dual solutions and the stability analysis is carried out to identify more stable solutions. Variations of numerous parameters have been also examined by giving tables and graphs. The numerical values have been obtained for the skin friction and local Nusselt number and presented graphically. Further, it is observed that the temperature and thickness of the thermal boundary layer increase when thermal radiation parameter is increased in both solutions. In addition, it is also noticed that the fluid velocity increases in the case of strong magnetic field effect in the second solution. View Full-Text
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MDPI and ACS Style

Lund, L.A.; Omar, Z.; Khan, I.; Kadry, S.; Rho, S.; Mari, I.A.; Nisar, K.S. Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis. Energies 2019, 12, 4617. https://doi.org/10.3390/en12244617

AMA Style

Lund LA, Omar Z, Khan I, Kadry S, Rho S, Mari IA, Nisar KS. Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis. Energies. 2019; 12(24):4617. https://doi.org/10.3390/en12244617

Chicago/Turabian Style

Lund, Liaquat A., Zurni Omar, Ilyas Khan, Seifedine Kadry, Seungmin Rho, Irshad A. Mari, and Kottakkaran S. Nisar 2019. "Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis" Energies 12, no. 24: 4617. https://doi.org/10.3390/en12244617

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