中国物理B ›› 2025, Vol. 34 ›› Issue (11): 114402-114402.doi: 10.1088/1674-1056/addcbc

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Finite element analysis of copper nanoparticles in Boger fluid: Effects of dynamic inter-particle spacing, nanolayer thermal conductivity, nanoparticles diameter, and thermal radiation over a stretching sheet

Qadeer Raza1,†, Xiaodong Wang(王晓东)1,2,‡, Tahir Mushtaq3, Bagh Ali4,†, and Nehad Ali Shah5   

  1. 1 School of Mathematics and Statistics, Xi'an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi'an 710129, China;
    2 Shenzhen Research Institute of Northwestern Polytechnical University, Shenzhen 518057, China;
    3 Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan;
    4 Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai-602105, Tamilnadu, India;
    5 Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
  • 收稿日期:2025-01-17 修回日期:2025-04-25 接受日期:2025-05-23 出版日期:2025-10-30 发布日期:2025-11-24
  • 通讯作者: Xiaodong Wang E-mail:xiaodongwang@nwpu.edu.cn
  • 基金资助:
    Project supported by the Fundamental Research Funds for the Central Universities (Grant No. D5000230061) and the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2025A1515011192).

Finite element analysis of copper nanoparticles in Boger fluid: Effects of dynamic inter-particle spacing, nanolayer thermal conductivity, nanoparticles diameter, and thermal radiation over a stretching sheet

Qadeer Raza1,†, Xiaodong Wang(王晓东)1,2,‡, Tahir Mushtaq3, Bagh Ali4,†, and Nehad Ali Shah5   

  1. 1 School of Mathematics and Statistics, Xi'an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi'an 710129, China;
    2 Shenzhen Research Institute of Northwestern Polytechnical University, Shenzhen 518057, China;
    3 Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari 61100, Pakistan;
    4 Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai-602105, Tamilnadu, India;
    5 Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
  • Received:2025-01-17 Revised:2025-04-25 Accepted:2025-05-23 Online:2025-10-30 Published:2025-11-24
  • Contact: Xiaodong Wang E-mail:xiaodongwang@nwpu.edu.cn
  • Supported by:
    Project supported by the Fundamental Research Funds for the Central Universities (Grant No. D5000230061) and the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2025A1515011192).

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摘要： This study explores the magnetohydrodynamic (MHD) boundary layer flow of a water-based Boger nanofluid over a stretching sheet, with particular focus on the influences of nanoparticle diameter, nanolayer effects, and thermal radiation. The primary aim is to examine how variations in nanoparticle size and nanolayer thickness affect the hydrothermal behavior of the nanofluid. The model also incorporates the contributions of viscous dissipation and Joule heating within the heat transfer equation. The governing momentum and energy equations are converted into dimensionless partial differential equations (PDEs) using appropriate similarity variables and are numerically solved using the finite element method (FEM) implemented in MATLAB. Extensive validation of this method confirms its reliability and accuracy in numerical solutions. The findings reveal that increasing the diameter of copper nanoparticles significantly enhances the velocity profile, with a more pronounced effect observed at wider inter-particle spacings. A higher solvent volume fraction leads to decreased velocity and temperature distributions, while a greater relaxation time ratio improves velocity and temperature profiles due to the increased elastic response of the fluid. Moreover, enhancements in the magnetic parameter, thermal radiation, and Eckert number lead to an elevation in temperature profiles. Furthermore, higher nanolayer thickness reduces the temperature profile, whereas particle radius yields the opposite outcome.

关键词: finite element method, Boger nanofluid, thermal radiation, nanoparticles diameter, nanolayer thermal conductivity, inter-particle spacing

Abstract: This study explores the magnetohydrodynamic (MHD) boundary layer flow of a water-based Boger nanofluid over a stretching sheet, with particular focus on the influences of nanoparticle diameter, nanolayer effects, and thermal radiation. The primary aim is to examine how variations in nanoparticle size and nanolayer thickness affect the hydrothermal behavior of the nanofluid. The model also incorporates the contributions of viscous dissipation and Joule heating within the heat transfer equation. The governing momentum and energy equations are converted into dimensionless partial differential equations (PDEs) using appropriate similarity variables and are numerically solved using the finite element method (FEM) implemented in MATLAB. Extensive validation of this method confirms its reliability and accuracy in numerical solutions. The findings reveal that increasing the diameter of copper nanoparticles significantly enhances the velocity profile, with a more pronounced effect observed at wider inter-particle spacings. A higher solvent volume fraction leads to decreased velocity and temperature distributions, while a greater relaxation time ratio improves velocity and temperature profiles due to the increased elastic response of the fluid. Moreover, enhancements in the magnetic parameter, thermal radiation, and Eckert number lead to an elevation in temperature profiles. Furthermore, higher nanolayer thickness reduces the temperature profile, whereas particle radius yields the opposite outcome.

Key words: finite element method, Boger nanofluid, thermal radiation, nanoparticles diameter, nanolayer thermal conductivity, inter-particle spacing

中图分类号:  (Thermal radiation)

  • 44.40.+a
44.30.+v (Heat flow in porous media) 47.11.Fg (Finite element methods) 52.30.Cv (Magnetohydrodynamics (including electron magnetohydrodynamics)) 47.50.-d (Non-Newtonian fluid flows)