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<p>The nanofluid’s thermal potential is remarkable and provides many dynamical applications in nuclear cooling, extrusion&#xa0;processes,&#xa0;solar&#xa0;collectors,&#xa0;thermal&#xa0;systems, and heating and cooling devices. Due to these motivations, this research examines an unsteady electrically conducting free convective Jeffrey-type nanofluid (graphene nanoparticles distributed in polyvinyl alcohol (PVA)/water) flow over a heated moving plate in a porous medium. The key motivation of recent work is to evaluate how fractional calculus, especially the newly developed Prabhakar fractional operator, having the Mittag–Leffler function in its kernel with three different parameters, can more precisely explain the memory as well as hereditary characteristics of nanofluid (NF) flows in complex media, thereby contributing a deeper perception into energy transport mechanisms. The fractional governing equations are designed by employing the Prabhakar derivative and solved with the Laplace technique. The key findings show that the momentum and temperature profiles rise with larger estimations of the solar radiation parameter. The velocity and thermal fields go down while enlarging the Prandtl number. Among base fluids, water-based NF shows higher thermal behaviour as compared to PVA-based nanofluid. These results can be used to advance the efficiency of heat exchangers, solar collectors, photovoltaic–thermal networks, and other industrial and engineering processes by increasing heat transfer and energy absorption.</p>

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Comprehensive investigation of fractional jeffrey-type graphene-based nanofluid flow: significance of magnetic field, porosity, and mittag–leffler function

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Qasim Ali,
  • Muhammad Amir,
  • Muhammad Farman,
  • Ahmed Sayed M. Metwally,
  • Hijaz Ahmad

摘要

The nanofluid’s thermal potential is remarkable and provides many dynamical applications in nuclear cooling, extrusion processes, solar collectors, thermal systems, and heating and cooling devices. Due to these motivations, this research examines an unsteady electrically conducting free convective Jeffrey-type nanofluid (graphene nanoparticles distributed in polyvinyl alcohol (PVA)/water) flow over a heated moving plate in a porous medium. The key motivation of recent work is to evaluate how fractional calculus, especially the newly developed Prabhakar fractional operator, having the Mittag–Leffler function in its kernel with three different parameters, can more precisely explain the memory as well as hereditary characteristics of nanofluid (NF) flows in complex media, thereby contributing a deeper perception into energy transport mechanisms. The fractional governing equations are designed by employing the Prabhakar derivative and solved with the Laplace technique. The key findings show that the momentum and temperature profiles rise with larger estimations of the solar radiation parameter. The velocity and thermal fields go down while enlarging the Prandtl number. Among base fluids, water-based NF shows higher thermal behaviour as compared to PVA-based nanofluid. These results can be used to advance the efficiency of heat exchangers, solar collectors, photovoltaic–thermal networks, and other industrial and engineering processes by increasing heat transfer and energy absorption.