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Triple Solutions of Carreau Thin Film Flow with Thermocapillarity and Injection on an Unsteady Stretching Sheet

Author

Listed:
  • Kohilavani Naganthran

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

  • Ishak Hashim

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

  • Roslinda Nazar

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

Abstract

Thin films and coatings which have a high demand in a variety of industries—such as manufacturing, optics, and photonics—need regular improvement to sustain industrial productivity. Thus, the present work examined the problem of the Carreau thin film flow and heat transfer with the influence of thermocapillarity over an unsteady stretching sheet, numerically. The sheet is permeable, and there is an injection effect at the surface of the stretching sheet. The similarity transformation reduced the partial differential equations into a system of ordinary differential equations which is then solved numerically by the MATLAB boundary value problem solver bvp4c. The more substantial effect of injection was found to be the reduction of the film thickness at the free surface and development of a better rate of convective heat transfer. However, the increment in the thermocapillarity number thickens the film, reduces the drag force, and weakens the rate of heat transfer past the stretching sheet. The triple solutions are identified when the governing parameters vary, but two of the solutions gave negative film thickness. Detecting solutions with the most negative film thickness is essential because it implies the interruption in the laminar flow over the stretching sheet, which then affects the thin film growing process.

Suggested Citation

  • Kohilavani Naganthran & Ishak Hashim & Roslinda Nazar, 2020. "Triple Solutions of Carreau Thin Film Flow with Thermocapillarity and Injection on an Unsteady Stretching Sheet," Energies, MDPI, vol. 13(12), pages 1-17, June.
  • Handle: RePEc:gam:jeners:v:13:y:2020:i:12:p:3177-:d:373549
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    References listed on IDEAS

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    1. Noor Saeed Khan & Taza Gul & Poom Kumam & Zahir Shah & Saeed Islam & Waris Khan & Samina Zuhra & Arif Sohail, 2019. "Influence of Inclined Magnetic Field on Carreau Nanoliquid Thin Film Flow and Heat Transfer with Graphene Nanoparticles," Energies, MDPI, vol. 12(8), pages 1-20, April.
    2. Rehman, Sajid & Rehman, Saeed Ur & Khan, Aamir & Khan, Zeeshan, 2020. "The effect of flow distribution on heat and mass transfer of MHD thin liquid film flow over an unsteady stretching sheet in the presence of variational physical properties with mixed convection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
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    Cited by:

    1. Kohilavani Naganthran & Roslinda Nazar & Zailan Siri & Ishak Hashim, 2021. "Entropy Analysis and Melting Heat Transfer in the Carreau Thin Hybrid Nanofluid Film Flow," Mathematics, MDPI, vol. 9(23), pages 1-19, November.
    2. Sumayyah Alabdulhadi & Sakhinah Abu Bakar & Anuar Ishak & Iskandar Waini & Sameh E. Ahmed, 2023. "Effect of Buoyancy Force on an Unsteady Thin Film Flow of Al 2 O 3 /Water Nanofluid over an Inclined Stretching Sheet," Mathematics, MDPI, vol. 11(3), pages 1-16, February.
    3. Mikhail A. Sheremet, 2021. "Numerical Simulation of Convective-Radiative Heat Transfer," Energies, MDPI, vol. 14(17), pages 1-3, August.

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