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Magnetohydrodynamics Flow Past a Moving Vertical Thin Needle in a Nanofluid with Stability Analysis

Author

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  • Siti Nur Alwani Salleh

    (Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia)

  • Norfifah Bachok

    (Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia)

  • Norihan Md Arifin

    (Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia)

  • Fadzilah Md Ali

    (Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43400, Selangor, Malaysia)

  • Ioan Pop

    (Department of Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania)

Abstract

In this study, we intend to present the dynamics of a system based on the model of convective heat and mass transfer in magnetohydrodynamics (MHD) flow past a moving vertical thin needle in nanofluid. The problem is formulated in mathematical form by using Buongiorno’s model with the modified boundary condition. The transformed boundary layer ordinary differential equations are solved numerically using the bvp4c function in MATLAB software. The effects of the involved parameters, including, Brownian motion, thermophoresis, magnetic field, mixed convection, needle size and velocity ratio parameter on the flow, heat and mass transfer coefficients are analyzed. The numerical results obtained for the skin friction coefficients, local Nusselt number and local Sherwood number, as well as the velocity, temperature and concentration profiles are graphically presented and have been discussed in detail. The study reveals that the dual solutions appear when the needle and the buoyancy forces oppose the direction of the fluid motion, and the range of the dual solutions existing depends largely on the needle size and magnetic parameter. The presence of the magnetic field in this model reduces the coefficient of the skin friction and heat transfer, while it increases the coefficient of the mass transfer on the needle surface. A stability analysis has been performed to identify which of the solutions obtained are linearly stable and physically relevant. It is noticed that the upper branch solutions are stable, while the lower branch solutions are not.

Suggested Citation

  • Siti Nur Alwani Salleh & Norfifah Bachok & Norihan Md Arifin & Fadzilah Md Ali & Ioan Pop, 2018. "Magnetohydrodynamics Flow Past a Moving Vertical Thin Needle in a Nanofluid with Stability Analysis," Energies, MDPI, vol. 11(12), pages 1-15, November.
    • Handle: RePEc:gam:jeners:v:11:y:2018:i:12:p:3297-:d:185587
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    References listed on IDEAS

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    1. Ishak, Anuar & Jafar, Khamisah & Nazar, Roslinda & Pop, Ioan, 2009. "MHD stagnation point flow towards a stretching sheet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3377-3383.
    2. Huminic, Gabriela & Huminic, Angel, 2012. "Application of nanofluids in heat exchangers: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(8), pages 5625-5638.
    3. Khairy Zaimi & Anuar Ishak & Ioan Pop, 2014. "Flow Past a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Two-Phase Model," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-6, November.
    4. Saidur, R. & Leong, K.Y. & Mohammad, H.A., 2011. "A review on applications and challenges of nanofluids," Renewable and Sustainable Energy Reviews, Elsevier, vol. 15(3), pages 1646-1668, April.
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    Cited by:

    1. Song, Ying-Qing & Hamid, Aamir & Khan, M. Ijaz & Gowda, R.J. Punith & Kumar, R. Naveen & Prasannakumara, B.C. & Khan, Sami Ullah & Khan, M. Imran & Malik, M.Y., 2021. "Solar energy aspects of gyrotactic mixed bioconvection flow of nanofluid past a vertical thin moving needle influenced by variable Prandtl number," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. A. J. Chamkha & A. M. Rashad & E. R. EL-Zahar & Hamed A. EL-Mky, 2019. "Analytical and Numerical Investigation of Fe 3 O 4 –Water Nanofluid Flow over a Moveable Plane in a Parallel Stream with High Suction," Energies, MDPI, vol. 12(1), pages 1-18, January.
    3. Najiyah Safwa Khashi’ie & Norihan Md Arifin & Ioan Pop, 2020. "Mixed Convective Stagnation Point Flow towards a Vertical Riga Plate in Hybrid Cu-Al 2 O 3 /Water Nanofluid," Mathematics, MDPI, vol. 8(6), pages 1-21, June.
    4. Anna Kraszewska & Janusz Donizak, 2021. "An Analysis of a Laminar-Turbulent Transition and Thermal Plumes Behavior in a Paramagnetic Fluid Subjected to an External Magnetic Field," Energies, MDPI, vol. 14(23), pages 1-23, November.
    5. Iskandar Waini & Anuar Ishak & Ioan Pop, 2020. "Hybrid Nanofluid Flow Past a Permeable Moving Thin Needle," Mathematics, MDPI, vol. 8(4), pages 1-18, April.
    6. Nur Adilah Liyana Aladdin & Norfifah Bachok, 2021. "Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
    7. Sumera Dero & Azizah Mohd Rohni & Azizan Saaban & Ilyas Khan, 2019. "Dual Solutions and Stability Analysis of Micropolar Nanofluid Flow with Slip Effect on Stretching/Shrinking Surfaces," Energies, MDPI, vol. 12(23), pages 1-20, November.

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