Deep Learning Approach for Power Law Fluid Flow and Heat Transfer Over a Nonlinear Moving Porous Wedge in a Darcy–Forchheimer Medium
Wajiha Waheed, Irfan Mustafa, Sami Ul Haq, Abuzar Ghaffari, Muhammad Asif Javed
Abstract
ABSTRACT This study explores the effects of a spatially varying magnetic field on the flow and heat transfer of a power‐law non‐Newtonian fluid past a stretchable porous wedge within a Darcy–Forchheimer porous medium. A mathematical framework is developed by extending the Navier–Stokes and energy equations, incorporating the Cauchy stress tensor for power‐law fluids, Darcy's law, Forchheimer's inertial correction, and Lorentz force effects. The governing partial differential equations are transformed into a system of nonlinear ordinary differential equations via a local non‐similar transformation, treating dimensionless parameters as streamwise independent. The resulting system is solved using a finite difference method (FDM) in MATLAB, generating 200 data points for velocity, temperature, skin friction, and Nusselt number. These results are further employed to train a supervised artificial intelligence model based on the Levenberg‐Marquardt Scheme–Artificial Neural Network (LMS‐ANN), with 70% of data used for training and 15% each for validation and testing. Comparative analysis demonstrates excellent agreement between FDM and LMS‐ANN, achieving mean squared errors as low as 2.6 × 10 −7 for skin friction and 6.6 × 10 −8 for Nusselt number. The study confirms that Darcy–Forchheimer effects significantly enhance velocity and heat transfer, establishing the LMS‐ANN framework as a reliable and efficient predictive tool.