Citation :

D. Vidhya, P. Umadevi, R. Jeevitha, A. Sathya Kala, K. Sharmilaa, "HAM-Driven Physics-Informed Neural Operator for Stratified Radiative Oldroyd-B/Maxwell Nanofluid Flow with Gyrotactic Bioconvection," International Journal of Mechanical Engineering, vol. 13, no. 8, pp. 113-130, 2026. Crossref, https://doi.org/10.14445/23488360/IJME-V13I8P110

Abstract

For the purpose of simulating stratified radiative Oldroyd-B/Maxwell nanofluid flow induced by gyrotactic microorganisms, this research suggests a new HAM-guided Physics-Informed Neural Operator (HAM-PINO). Nanoparticle concentration diffusion, Rosseland thermal radiation transport, and microorganism conservation laws are coupled with the governing nonlinear viscoelastic momentum equations. The suggested approach incorporates Homotopy Analysis Method convergence-control parameters into operator learning, in contrast to traditional PINNs that are unstable under strong viscoelastic and radiative couplings. This leads to fast convergence across regimes with multiple parameters and stable residual evolution. According to numerical benchmarking, the HAM-PINO solver outperforms the following: RKF45, shooting, DeepONet, FNO, and Transformer-PINO, with a relative L_2-error of 4.2×10^ (-6). The technical results show that as the radiation increases, the heat transfer improves, and the Nusselt number goes up from 1.90 to 2.65. On the other hand, the skin friction goes up from 0.42 to 0.59 due to viscoelastic relaxation. Under stratified stability, the transfer rates of microorganisms also rise. When it comes to bio-nanofluid transport systems that involve multiple physics, HAM-PINO provides a computational operator framework that is both efficient and scalable.

Keywords

Physics-Informed Neural Operator, Homotopy Analysis Method, Heat transfer, Nanoparticle concentration diffusion, Oldroyd - B/Maxwell nanofluid flow.

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