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<p>The present investigation deals with the study of thermo-fluidic behavior of copper–alumina/water (Cu–Al<sub>2</sub>O<sub>3</sub>/H<sub>2</sub>O) HNF over a permeable stretching sheet with the influence of Darcy–Forchheimer drag. The synergistic dispersion of different NFs in the base liquid greatly enhances the overall thermal conductivity of the base liquid. So, hybrid nanofluids are attractive candidates for applications such as precision coating, polymer processing and microscale heat management. The research model assumes thermal conductivity, Prandtl number and viscosity to describe realistic thermophysical behavior. The flow controlling nonlinear PDEs are transformed into the corresponding ODEs by using the similarity transformations and solved by two approaches, i.e., SCMLW (Spectral Collocation Method with Legendre Wavelets) and bvp4c solver that allow the direct validation of the results. The present study has important applications in polymer extrusion, porous heat exchangers, geothermal systems, microelectronic cooling, aerospace thermal management, biomedical devices, and packed-bed reactors where efficient heat transfer and porous medium transport are essential. The numerical results reveal that increasing the Darcy–Forchheimer number from Fr = 0.1 to 1.5 enhances the fluid velocity and reduces the thermal boundary layer thickness, while the skin friction coefficient decreases from approximately − 0.116 to − 0.153 due to nonlinear inertial drag effects. It is also observed that the hybrid nanofluid retains thermal energy for a longer duration compared to mono nanofluids, indicating superior heat transfer capability. Unlike previous studies that often assume constant properties or neglect nonlinear inertial drag, the present work includes viscous dissipation and validates results using both SCMLW and MATLAB’s bvp4c solver, providing reliable benchmark solutions and new insights into coupled momentum and heat transfer phenomena.</p>

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Analysis of Cu–Al2O3/H2O hybrid nanofluid and heat transfer flow over a stretching porous surface under Darcy–Forchheimer resistance

  • 期刊论文

  • 发表日期：

    2026年6月27日

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  • Satyabrat Kar,
  • Bharat Keshari Swain

摘要

The present investigation deals with the study of thermo-fluidic behavior of copper–alumina/water (Cu–Al2O3/H2O) HNF over a permeable stretching sheet with the influence of Darcy–Forchheimer drag. The synergistic dispersion of different NFs in the base liquid greatly enhances the overall thermal conductivity of the base liquid. So, hybrid nanofluids are attractive candidates for applications such as precision coating, polymer processing and microscale heat management. The research model assumes thermal conductivity, Prandtl number and viscosity to describe realistic thermophysical behavior. The flow controlling nonlinear PDEs are transformed into the corresponding ODEs by using the similarity transformations and solved by two approaches, i.e., SCMLW (Spectral Collocation Method with Legendre Wavelets) and bvp4c solver that allow the direct validation of the results. The present study has important applications in polymer extrusion, porous heat exchangers, geothermal systems, microelectronic cooling, aerospace thermal management, biomedical devices, and packed-bed reactors where efficient heat transfer and porous medium transport are essential. The numerical results reveal that increasing the Darcy–Forchheimer number from Fr = 0.1 to 1.5 enhances the fluid velocity and reduces the thermal boundary layer thickness, while the skin friction coefficient decreases from approximately − 0.116 to − 0.153 due to nonlinear inertial drag effects. It is also observed that the hybrid nanofluid retains thermal energy for a longer duration compared to mono nanofluids, indicating superior heat transfer capability. Unlike previous studies that often assume constant properties or neglect nonlinear inertial drag, the present work includes viscous dissipation and validates results using both SCMLW and MATLAB’s bvp4c solver, providing reliable benchmark solutions and new insights into coupled momentum and heat transfer phenomena.