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<p>The field of nanotechnology is advancing at an impressive pace, leading to the growing popularity of research on nanofluids. The groundbreaking innovation of nanofluids has had a revolutionary impact on the domains of science and engineering. The aim of this analysis is to establish a sophisticated mathematical framework for the 3D Darcy–Forchheimer dynamics by considering an elongated convectively heated permeable channel with magnetic effects and convective heat transfer. The proposed flow model produces highly nonlinear steady-state Navier–Stokes coupled PDEs, with associated convective boundary conditions imposed at the stretching surface. The governing flow expressions are reduced to dimensionless forms using standard transformation variables to streamline the evaluation process. These dimensionless ODEs are then solved analytically using a built-in algorithm in a programming platform, with a convergence analysis conducted for various flow fields. Graphical illustrations are employed to enhance the understanding of relevant flow parameters. Additionally, tables are presented to demonstrate the influence of drag force and heat transfer rates. Ultimately, this investigation has significant implications for the utilization of nanofluids in manufacturing applications, particularly in geothermal and geophysical systems, storage devices, and various other fields.</p>

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A mathematical model for three dimensional magnetohydrodynamic thermal nanofluid flow over a permeable Darcy-Forchheimer medium with chemical reaction and activation energy effects

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Haroon Ur Rasheed,
  • Waris Khan,
  • Marouan Kouki,
  • Hakim AL Garalleh,
  • Afnan Al Agha

摘要

The field of nanotechnology is advancing at an impressive pace, leading to the growing popularity of research on nanofluids. The groundbreaking innovation of nanofluids has had a revolutionary impact on the domains of science and engineering. The aim of this analysis is to establish a sophisticated mathematical framework for the 3D Darcy–Forchheimer dynamics by considering an elongated convectively heated permeable channel with magnetic effects and convective heat transfer. The proposed flow model produces highly nonlinear steady-state Navier–Stokes coupled PDEs, with associated convective boundary conditions imposed at the stretching surface. The governing flow expressions are reduced to dimensionless forms using standard transformation variables to streamline the evaluation process. These dimensionless ODEs are then solved analytically using a built-in algorithm in a programming platform, with a convergence analysis conducted for various flow fields. Graphical illustrations are employed to enhance the understanding of relevant flow parameters. Additionally, tables are presented to demonstrate the influence of drag force and heat transfer rates. Ultimately, this investigation has significant implications for the utilization of nanofluids in manufacturing applications, particularly in geothermal and geophysical systems, storage devices, and various other fields.