Data-efficient deep neural surrogates for simulating rotating non-Newtonian convective flows in anisotropic porous media under convective boundary conditions

This study develops a novel Physics-Informed Neural Network (PINN) framework for coupled flow and heat transfer in a rotating channel containing a power-law non-Newtonian fluid within an anisotropic porous medium. The proposed approach uniquely integrates Darcy-Brinkman-Forchheimer momentum transport, Coriolis-induced secondary flow, and realistic convective (Robin-type) thermal boundary conditions into a single PINN formulation, an aspect largely unexplored in existing literature. The model captures the complex interplay between rotation, anisotropic permeability, and non-Newtonian rheology, revealing that increasing the power-law index enhances axial transport and significantly improves heat transfer rates, while higher Biot numbers intensify wall heat removal. These coupled effects provide actionable design insights for optimizing thermal performance under rotating conditions. The framework is directly applicable to advanced engineering systems, including rotating heat exchangers, geothermal energy extraction, and porous cooling technologies, where conventional numerical methods face challenges due to strong multi-physics coupling. This work demonstrates that PINNs offer a robust and efficient alternative for accurately resolving such complex transport phenomena.