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Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two‐Phase Model

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  • Abeer Alhashash
  • Habibis Saleh

Abstract

In this study, the free convection of nanofluids between a rectangular enclosure and a sinusoidal cylinder is numerically analyzed using the finite element method (FEM). Two‐phase Buongiorno’s formulation was used to model the fluid layer, and Brinkman‐Forchheimer equation was used to formulate the porous layer. The enclosure has a low temperature, while the cylinder is maintained at a high temperature. The governing equations are expressed in PDEs and converted into weak formulations (Galerkin FEM). In numerical simulations, the average concentration, the amplitude of undulated cylinder, the number of undulated, and the Rayleigh number are investigated. It is observed that the homogeneous nanofluid model could be valid for low heating intensity with higher waviness frequency and/or higher amplitude. The higher the alumina concentration, the higher the heat transfer rate. The heat transfer rate can be boosted by up to 13% by suspending 1% alumina particles. The heat transfer enhancement decreases with increasing the amplitude and/or increasing the waviness number.

Suggested Citation

  • Abeer Alhashash & Habibis Saleh, 2023. "Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two‐Phase Model," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:8426825
    DOI: 10.1155/2023/8426825
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    References listed on IDEAS

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    1. Ammar I. Alsabery & Tahar Tayebi & Ali J. Chamkha & Ishak Hashim, 2018. "Effects of Non-Homogeneous Nanofluid Model on Natural Convection in a Square Cavity in the Presence of Conducting Solid Block and Corner Heater," Energies, MDPI, vol. 11(10), pages 1-27, September.
    2. Pensiri Sompong & Supot Witayangkurn, 2014. "Numerical Study of Natural Convection in a Heated Enclosure with Two Wavy Vertical Walls Using Finite Element Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Pensiri Sompong & Supot Witayangkurn, 2014. "Numerical Study of Natural Convection in a Heated Enclosure with Two Wavy Vertical Walls Using Finite Element Method," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, May.
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