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<p>This study investigates the unsteady two-dimensional flow dynamics of Casson–Carreau tri-hybrid nanofluids containing gyrotactic microorganisms, with temperature-dependent thermophysical properties and radiative effects over flat and slendering sheets. The flow is influenced by magnetohydrodynamics, thermophoresis, Brownian motion, and bio-convection. To efficiently solve the governing nonlinear differential equations, a hybrid artificial neural network optimized using the water cycle algorithm is proposed. The water cycle algorithm, an established optimization method inspired by natural hydrological processes, is employed to fine-tune the artificial neural network parameters, enhancing prediction accuracy for velocity, temperature, concentration, and microorganism distribution. The hybrid WCA-ANN approach uses collocation-based discretization to evaluate residuals but avoids full-domain meshing or iterative matrix solvers, thereby reducing computational load. The WCA efficiently adjusts ANN masses and biases, accelerating convergence while preserving accuracy. Compared to traditional solvers like the finite difference method, the WCA-ANN framework offers enhanced flexibility and speed in solving multi-physics problems with complex boundary layers. The results show that increasing the variable concentration diffusivity (0–0.4), nanoparticle volume fraction (2%–5%), and temperature-dependent thermal conductivity (0.1–3.5) significantly improve heat and mass transfer rates. Additionally, the density of motile microorganisms increases with higher motile microorganism diffusion coefficients (0.2–0.4). The study underscores the effect of flat surfaces on flow behavior, highlighting the role of variable diffusivity and thermal conductivity in heat and mass transfer.</p>

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Optimized ANN approach for unsteady heat transfer and flow of Casson–Carreau tri-hybrid nanofluids with temperature-dependent properties

  • 期刊论文

  • 发表日期：

    2025年9月6日

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  • Faisal,
  • Jia Wantao,
  • Aroosa Ramzan,
  • Sohaib Arshad Mayo

摘要

This study investigates the unsteady two-dimensional flow dynamics of Casson–Carreau tri-hybrid nanofluids containing gyrotactic microorganisms, with temperature-dependent thermophysical properties and radiative effects over flat and slendering sheets. The flow is influenced by magnetohydrodynamics, thermophoresis, Brownian motion, and bio-convection. To efficiently solve the governing nonlinear differential equations, a hybrid artificial neural network optimized using the water cycle algorithm is proposed. The water cycle algorithm, an established optimization method inspired by natural hydrological processes, is employed to fine-tune the artificial neural network parameters, enhancing prediction accuracy for velocity, temperature, concentration, and microorganism distribution. The hybrid WCA-ANN approach uses collocation-based discretization to evaluate residuals but avoids full-domain meshing or iterative matrix solvers, thereby reducing computational load. The WCA efficiently adjusts ANN masses and biases, accelerating convergence while preserving accuracy. Compared to traditional solvers like the finite difference method, the WCA-ANN framework offers enhanced flexibility and speed in solving multi-physics problems with complex boundary layers. The results show that increasing the variable concentration diffusivity (0–0.4), nanoparticle volume fraction (2%–5%), and temperature-dependent thermal conductivity (0.1–3.5) significantly improve heat and mass transfer rates. Additionally, the density of motile microorganisms increases with higher motile microorganism diffusion coefficients (0.2–0.4). The study underscores the effect of flat surfaces on flow behavior, highlighting the role of variable diffusivity and thermal conductivity in heat and mass transfer.