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A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip

Author

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  • Najiyah Safwa Khashi’ie

    (Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
    Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Durian Tunggal 76100, Melaka, Malaysia)

  • Norihan Md Arifin

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

  • Roslinda Nazar

    (School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 UKM, Selangor, Malaysia)

  • Ezad Hafidz Hafidzuddin

    (Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia)

  • Nadihah Wahi

    (Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia)

  • Ioan Pop

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

Abstract

The numerical study of nanofluid stagnation point flow coupled with heat and mass transfer on a moving sheet with bi-directional slip velocities is emphasized. A magnetic field is considered normal to the moving sheet. Buongiorno’s model is utilized to assimilate the mixed effects of thermophoresis and Brownian motion due to the nanoparticles. Zero nanoparticles’ flux condition at the surface is employed, which indicates that the nanoparticles’ fraction are passively controlled. This condition makes the model more practical for certain engineering applications. The continuity, momentum, energy and concentration equations are transformed into a set of nonlinear ordinary (similarity) differential equations. Using bvp4c code in MATLAB software, the similarity solutions are graphically demonstrated for considerable parameters such as thermophoresis, Brownian motion and slips on the velocity, nanoparticles volume fraction and temperature profiles. The rate of heat transfer is reduced with the intensification of the anisotropic slip (difference of two-directional slip velocities) and the thermophoresis parameter, while the opposite result is obtained for the mass transfer rate. The study also revealed the existence of non-unique solutions on all the profiles, but, surprisingly, dual solutions exist boundlessly for any positive value of the control parameters. A stability analysis is implemented to assert the reliability and acceptability of the first solution as the physical solution.

Suggested Citation

  • Najiyah Safwa Khashi’ie & Norihan Md Arifin & Roslinda Nazar & Ezad Hafidz Hafidzuddin & Nadihah Wahi & Ioan Pop, 2019. "A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip," Energies, MDPI, vol. 12(7), pages 1-19, April.
    • Handle: RePEc:gam:jeners:v:12:y:2019:i:7:p:1268-:d:219367
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    References listed on IDEAS

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    1. Haddad, Zoubida & Oztop, Hakan F. & Abu-Nada, Eiyad & Mataoui, Amina, 2012. "A review on natural convective heat transfer of nanofluids," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(7), pages 5363-5378.
    2. Sarkar, Jahar & Ghosh, Pradyumna & Adil, Arjumand, 2015. "A review on hybrid nanofluids: Recent research, development and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 43(C), pages 164-177.
    3. Nur Syazana Anuar & Norfifah Bachok & Ioan Pop, 2018. "A Stability Analysis of Solutions in Boundary Layer Flow and Heat Transfer of Carbon Nanotubes over a Moving Plate with Slip Effect," Energies, MDPI, vol. 11(12), pages 1-20, November.
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    Cited by:

    1. 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.
    2. 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.
    3. Iskandar Waini & Anuar Ishak & Ioan Pop, 2020. "Squeezed Hybrid Nanofluid Flow Over a Permeable Sensor Surface," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    4. Mikhail A. Sheremet, 2021. "Numerical Simulation of Convective-Radiative Heat Transfer," Energies, MDPI, vol. 14(17), pages 1-3, August.

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