Integrated artificial intelligence and non-similar analysis for forced convection of radially magnetized ternary hybrid nanofluid of Carreau-Yasuda fluid model over a curved stretching surface

The current study investigates the boundary layer flow of Carreau-Yasuda (C-Y) ternary hybrid nanofluid model in a porous medium across curved surface stretching at linear rate under the influence of applied radial magnetic field. $A{l}_2{O}_3$, $F{e}_3{O}_4$ and $\mathrm{Si}{O}_2$ are nanoparticles and ethylene glycol is considered as base fluid. The effects of viscous dissipation and ohmic heating are present in the energy equation. The governing partial differential equation (PDEs) is nondimensionalized using non-similarity transformations. They can be treated as ordinary differential equations (ODEs) using local non-similarity method and solutions are obtained via bvp4c MATLAB tools. The results are evaluated by introducing computational intelligence approach utilizing the AI-based Levenberg–Marquardt scheme with a backpropagation neural network (LMS-BPNN) to investigate flow stability. The authors intend to use AI-based LMS-BPNN is to optimize the behavior of the hybrid nanofluid (HNF) flow of Carreau-Yasuda fluid across a stretching curved sheet. Initial/reference solutions are obtained through bvp4c function (an embedded MATLAB function designed to solve systems of ODEs) by systematically adjusting input parameters as demonstrated in Scenarios 1–5. There are three options to divide the numerical data: 80% for training, 10% for testing, and an additional 10% for validation. The LMS-BPNN is used for approximate solutions of Scenario 1–5. The efficiency and reliability of LMS-BPNN are validated through fitness curves based on correlation index (R), error, and regression analysis. The velocity and temperature profiles asymptotically satisfy boundary conditions of Scenario 1–5 with LMS-BPNN.