Computational Analysis of Natural Convection Heat Transfer in Nanofluids Under a Uniform Magnetic Field Using Levenberg–Marquardt Backpropagation Neural Networks

This study examines heat transfer by natural convection between two infinitely parallel plates in hybrid nanofluids under a homogeneous magnetic field. It seeks to evaluate how well LMBNs predict nonlinear magnetoconvective flows. Using a similarity variable-based mathematical model, the governing partial differential equations are converted to ordinary differential equations. Using the traditional fourth-order Runge–Kutta approach, these equations are then solved numerically to provide reference data. A thorough study examines how temperature and velocity profiles are affected by several crucial dimensionless factors, including the Brownian motion parameter, squeezing number, Hartmann number, Schmidt number, and Eckert number. Results show that while raising the Hartmann number from 1 to 3 lowers the maximum velocity by almost 22%, raising the Eckert number from 0.1 to 0.5 increases the peak temperature by around 18%. With regression correlations exceeding 0.9999, the LMBNN model has prediction errors as low as 10⁻¹¹ to 10⁻¹², showing better accuracy than standard numerical interpolation techniques. The originality of this study comes from combining traditional numerical analysis with LMBNN training to produce a really accurate, data-driven surrogate model for nanofluid flows under magnetoconvection. This hybrid computational technique provides an effective instrument for forecasting heat transfer behavior in magnetic field-affected engineering applications.