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<p>This study explores the steady, two-dimensional laminar boundary layer flow of an incompressible Casson fluid containing tri-hybrid nanoparticles (gold, silver, and copper oxide) over a curved stretching surface. The governing equations, derived from the Navier–Stokes framework, are reduced to a system of ordinary differential equations (ODEs) via similarity transformations. These ODEs are solved numerically using the Runge-Kutta-Fehlberg 4–5th order method, incorporating the effects of a uniform magnetic field, Darcy-Forchheimer porous medium resistance, internal heat source, chemical reaction, velocity slip, and thermal relaxation modeled by the Cattaneo-Christov equation. The results reveal that tri-hybrid nanofluids significantly enhance thermal and mass transfer compared to conventional and hybrid nanofluids. As the unsteadiness parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41939_2025_940_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation> increases from 0.1 to 0.3, the Nusselt number is enhanced by approximately 1.36% for the tri-hybrid nanofluid, 1.34% for the hybrid nanofluid, and 1.29% for the nanofluid, while the Sherwood number remains nearly constant. Non-Fourier heat conduction, represented by the Cattaneo-Christov model, has a pronounced effect on thermal profiles, particularly at high thermal relaxation times. Additionally, surface curvature intensifies both heat and mass transport, highlighting its importance in biomedical applications involving curved biological geometries. The numerical findings show strong agreement with existing literature, confirming the model’s reliability. An Artificial Neural Network (ANN) model was trained on the RKF-generated dataset to predict the Nusselt number across varying physical parameters. The ANN predictions closely matched the numerical results, validating its effectiveness as a rapid and accurate surrogate model for estimating heat transfer performance in complex nanofluid systems.</p>

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Artificial neural network-based prediction of casson tri-hybrid nanofluid flow over a curved stretching surface: application to drug delivery

  • 期刊论文

  • 发表日期：

    2025年6月22日

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  • M. N. Pooja,
  • Gunisetty Ramasekhar,
  • S. K. Narasimhamurthy

摘要

This study explores the steady, two-dimensional laminar boundary layer flow of an incompressible Casson fluid containing tri-hybrid nanoparticles (gold, silver, and copper oxide) over a curved stretching surface. The governing equations, derived from the Navier–Stokes framework, are reduced to a system of ordinary differential equations (ODEs) via similarity transformations. These ODEs are solved numerically using the Runge-Kutta-Fehlberg 4–5th order method, incorporating the effects of a uniform magnetic field, Darcy-Forchheimer porous medium resistance, internal heat source, chemical reaction, velocity slip, and thermal relaxation modeled by the Cattaneo-Christov equation. The results reveal that tri-hybrid nanofluids significantly enhance thermal and mass transfer compared to conventional and hybrid nanofluids. As the unsteadiness parameter \(\omega \) ω increases from 0.1 to 0.3, the Nusselt number is enhanced by approximately 1.36% for the tri-hybrid nanofluid, 1.34% for the hybrid nanofluid, and 1.29% for the nanofluid, while the Sherwood number remains nearly constant. Non-Fourier heat conduction, represented by the Cattaneo-Christov model, has a pronounced effect on thermal profiles, particularly at high thermal relaxation times. Additionally, surface curvature intensifies both heat and mass transport, highlighting its importance in biomedical applications involving curved biological geometries. The numerical findings show strong agreement with existing literature, confirming the model’s reliability. An Artificial Neural Network (ANN) model was trained on the RKF-generated dataset to predict the Nusselt number across varying physical parameters. The ANN predictions closely matched the numerical results, validating its effectiveness as a rapid and accurate surrogate model for estimating heat transfer performance in complex nanofluid systems.