TY  - JOUR
AU  - Hafeez, Abdul
AU  - Khan, Javed
AU  - Ying, Xiao
PY  - 2026
DA  - 2026/10/06
TI  - Artificial Neural Network-Based Modeling of Transient Bio-Convective Williamson Tri-Hybrid Nanofluid Flow with Gyrotactic Microorganisms over a Stretching Sheet
JO  - ICCK Journal of Applied Mathematics
T2  - ICCK Journal of Applied Mathematics
JF  - ICCK Journal of Applied Mathematics
VL  - 2
IS  - 4
SP  - 266
EP  - 282
DO  - 10.62762/JAM.2026.618998
UR  - https://www.icck.org/article/abs/JAM.2026.618998
KW  - tri-hybrid nanofluid
KW  - williamson fluid
KW  - neural network prediction
KW  - stretching sheet
KW  - gyrotactic microorganisms
KW  - activation energy
KW  - transient flow
AB  - In this paper, we study the unsteady magnetohydrodynamic (MHD) flow and the heat and mass transfer of a Williamson tri-hybrid nanofluid (THNF) composed of water and Al$_2$O$_3$, TiO$_2$ and Cu nanoparticles over a stretching sheet. The model incorporates thermal radiation, activation energy, chemical reaction, a heat source and the bioconvection of motile gyrotactic microorganisms. An artificial neural network (ANN) is employed for the predictive modeling of such THNF flows under these combined effects. Similarity transformations reduce the governing nonlinear partial differential equations (PDEs) to coupled ordinary differential equations (ODEs), which are solved numerically with a boundary-value-problem solver (SciPy solve_bvp). A feed-forward ANN is trained on the numerical dataset and validated through regression analysis, training convergence, comparison of numerical and predicted data, and error analysis, which results in an ANN with excellent predictive accuracy. The results show that the magnetic field, thermal radiation, Eckert number and heat source increase the temperature field, whereas the Williamson and unsteadiness parameters decrease the velocity profile. The concentration increases with the activation energy, whereas a stronger chemical reaction and a larger Schmidt number lower the concentration profile. Furthermore, the skin-friction coefficient, Nusselt number, Sherwood number and motile-microorganism density number are evaluated over a range of physical parameters. The proposed ANN-assisted framework is an efficient and reliable tool for analyzing and optimizing advanced THNF-based thermal systems.
SN  - 3068-5656
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Hafeez2026Artificial,
  author = {Abdul Hafeez and Javed Khan and Xiao Ying},
  title = {Artificial Neural Network-Based Modeling of Transient Bio-Convective Williamson Tri-Hybrid Nanofluid Flow with Gyrotactic Microorganisms over a Stretching Sheet},
  journal = {ICCK Journal of Applied Mathematics},
  year = {2026},
  volume = {2},
  number = {4},
  pages = {266-282},
  doi = {10.62762/JAM.2026.618998},
  url = {https://www.icck.org/article/abs/JAM.2026.618998},
  abstract = {In this paper, we study the unsteady magnetohydrodynamic (MHD) flow and the heat and mass transfer of a Williamson tri-hybrid nanofluid (THNF) composed of water and Al\$\_2\$O\$\_3\$, TiO\$\_2\$ and Cu nanoparticles over a stretching sheet. The model incorporates thermal radiation, activation energy, chemical reaction, a heat source and the bioconvection of motile gyrotactic microorganisms. An artificial neural network (ANN) is employed for the predictive modeling of such THNF flows under these combined effects. Similarity transformations reduce the governing nonlinear partial differential equations (PDEs) to coupled ordinary differential equations (ODEs), which are solved numerically with a boundary-value-problem solver (SciPy solve\_bvp). A feed-forward ANN is trained on the numerical dataset and validated through regression analysis, training convergence, comparison of numerical and predicted data, and error analysis, which results in an ANN with excellent predictive accuracy. The results show that the magnetic field, thermal radiation, Eckert number and heat source increase the temperature field, whereas the Williamson and unsteadiness parameters decrease the velocity profile. The concentration increases with the activation energy, whereas a stronger chemical reaction and a larger Schmidt number lower the concentration profile. Furthermore, the skin-friction coefficient, Nusselt number, Sherwood number and motile-microorganism density number are evaluated over a range of physical parameters. The proposed ANN-assisted framework is an efficient and reliable tool for analyzing and optimizing advanced THNF-based thermal systems.},
  keywords = {tri-hybrid nanofluid, williamson fluid, neural network prediction, stretching sheet, gyrotactic microorganisms, activation energy, transient flow},
  issn = {3068-5656},
  publisher = {Institute of Central Computation and Knowledge}
}