Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (1): 127-140.doi: https://doi.org/10.1007/s10483-022-2807-8

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Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation

I. WAINI1,2, A. ISHAK2, I. POP3   

  1. 1. Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Durian Tunggal 76100, Malaysia;
    2. Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia;
    3. Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
  • 收稿日期:2021-07-08 修回日期:2021-11-07 发布日期:2021-12-24
  • 通讯作者: A. ISHAK, E-mail:anuar_mi@ukm.edu.my

Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation

I. WAINI1,2, A. ISHAK2, I. POP3   

  1. 1. Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Durian Tunggal 76100, Malaysia;
    2. Department of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia;
    3. Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
  • Received:2021-07-08 Revised:2021-11-07 Published:2021-12-24
  • Contact: A. ISHAK, E-mail:anuar_mi@ukm.edu.my

摘要: The magnetohydrodynamic (MHD) mixed convection flow past a shrinking vertical sheet with thermal radiation is considered. Besides, the effects of Cu-Al2O3 nanoparticles and dust particles are considered. The similarity variables reduce the governing equations to the similarity equations, which are then solved numerically. The outcome shows that, for the shrinking case, the solutions are not unique. The rate of heat transfer and the friction factor enlarge with increasing the values of the copper nanoparticle volume fraction as well as the magnetic parameter. Meanwhile, the assisting flow and the rise of the thermal radiation reduce these quantities. Two solutions are found, and the boundary layer separation is dependent on the mixed convection parameter.

关键词: dusty fluid, hybrid nanofluid, magnetohydrodynamic (MHD), mixed convection, shrinking sheet, thermal radiation, dual solution

Abstract: The magnetohydrodynamic (MHD) mixed convection flow past a shrinking vertical sheet with thermal radiation is considered. Besides, the effects of Cu-Al2O3 nanoparticles and dust particles are considered. The similarity variables reduce the governing equations to the similarity equations, which are then solved numerically. The outcome shows that, for the shrinking case, the solutions are not unique. The rate of heat transfer and the friction factor enlarge with increasing the values of the copper nanoparticle volume fraction as well as the magnetic parameter. Meanwhile, the assisting flow and the rise of the thermal radiation reduce these quantities. Two solutions are found, and the boundary layer separation is dependent on the mixed convection parameter.

Key words: dusty fluid, hybrid nanofluid, magnetohydrodynamic (MHD), mixed convection, shrinking sheet, thermal radiation, dual solution

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