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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

Author

Listed:
  • Liaquat Ali Lund

    (School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Kedah
    KCAET Khairpur Mir’s & FAE, Sindh Agriculture University, Tandojam 70060, Pakistan)

  • Zurni Omar

    (School of Quantitative Sciences, Universiti Utara Malaysia, Sintok 06010, Kedah)

  • Ilyas Khan

    (Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam)

  • Seifedine Kadry

    (Department of Mathematics and Computer Science, Beirut Arab University, 115020 Beirut, Lebanon)

  • Seungmin Rho

    (Department of Software, Sejong University, Seoul 05006, Korea)

  • Irshad Ali Mari

    (KCAET Khairpur Mir’s & FAE, Sindh Agriculture University, Tandojam 70060, Pakistan)

  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi Arabia)

Abstract

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 S ≥ S c i , i = 0 , 1 , 2 and no solution is S < S c i 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.

Suggested Citation

  • Liaquat Ali Lund & Zurni Omar & Ilyas Khan & Seifedine Kadry & Seungmin Rho & Irshad Ali Mari & Kottakkaran Sooppy Nisar, 2019. "Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis," Energies, MDPI, vol. 12(24), pages 1-17, December.
  • Handle: RePEc:gam:jeners:v:12:y:2019:i:24:p:4617-:d:294433
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    Citations

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    Cited by:

    1. Stanford Shateyi & Hillary Muzara, 2020. "On Numerical Analysis of Carreau–Yasuda Nanofluid Flow over a Non-Linearly Stretching Sheet under Viscous Dissipation and Chemical Reaction Effects," Mathematics, MDPI, vol. 8(7), pages 1-24, July.
    2. Qian Wang & Shiwei Ge & Weidong Cao & Shanshan Yu & Zijie Liao, 2023. "Study of Arc Interruption Characteristics under Rated Current in Low Voltage Circuit Breakers," Energies, MDPI, vol. 16(10), pages 1-12, May.
    3. Shabbir Ahmad & Kashif Ali & Sohail Ahmad & Jianchao Cai, 2021. "Numerical Study of Lorentz Force Interaction with Micro Structure in Channel Flow," Energies, MDPI, vol. 14(14), pages 1-18, July.

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