Analysis of MHD-driven copper nanofluids flow through porous non-uniform channels using artificial neural network integrated computational scheme

Abstract

Nanoparticles’ geometric properties could significantly improve heat transfer in nanofluids, which are crucial for many engineering and industrial applications. This study explores heat transfer capabilities of magnetohydrodynamics (MHD)-influenced copper-based nanofluid flow through convergent-divergent channels by integrating the critical roles of interparticle spacing and nanoparticle radius. In this analysis, a mathematical model is developed that comprises of partial differential equations (PDEs), which account for momentum, heat and concentration under multifaceted factors. The governing system of PDEs is transformed into ordinary differential systems and then solved using the bvp4c solver scheme. By taking advantage of bvp4c data, an Artificial Neural Network (ANN) based on multilayers is employed. The proposed ANN model demonstrated superior predictive capability, achieving the best validation performance of 4.3084 × 10−10, with a corresponding gradient of 9.9799 × 10−8. In addition, the error histogram indicated a performance level of –4.0 × 10−6, while the regression analysis yielded a correlation coefficient of 1.0, which confirms excellent agreement between the predicted and target outputs. Velocity profile decreases due to larger opening angle decreases nanofluid velocity for both small and large interparticle spacing and radii due to the geometric expansion effects. In contrast, augmented values of magnetic parameter enhance velocity through the Lorentz force, whereas higher porosity suppresses velocity by reducing the permeability of medium. © 2026 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.