Numerical framework for investigating MHD heat and mass transfer in nanofluid flow over 2-D boundary layers in a porous medium: A variation of parameters method approach

• Conducts an in-depth analysis of MHD heat and mass transfer in nanofluid flow through porous media, emphasizing Brownian motion, thermophoresis, and heat effects to uncover key factors affecting nanofluid behavior in engineering contexts. • Demonstrates the effectiveness of combining the Variation of Parameters Method (VPM) with the Levenberg-Marquardt Neural Network Scheme (LMNNS) to solve complex differential equations with enhanced precision and adaptability. • Provides valuable insights into heat and mass transfer processes, showcasing the intricate interactions between thermal dynamics and material diffusion within advanced fluid systems. This article presents a comprehensive investigation into the laminar viscosity, radiation impact and viscous dissipation in the context of Magnetohydrodynamics (MHD) heat and mass transfer nanofluid flow over 2-D boundary layers in a porous medium. The research explores the role of Brownian motion, thermophoresis, and heat in shaping fluid flow patterns. By applying appropriate transformations, the governing nonlinear partial differential equations are transformed into ordinary differential equations (ODEs). Solutions for the obtained boundary layer ODEs are acquired by using the Variation of Parameters method (VPM) which is a well-established and effective technique fir this purpose. The proposed method utilizes multiplier as a tool to reduce computational efforts. To deal with the produced flow equations, Levenberg-Marquardt neural network strategy (LMNNS) is implemented with variation of parameters. A dataset is first created for various scenarios. The behaviors of involved significant parameters are presented over chart obtained using the variation of parameter involved. To estimate results for diverse instances, a training, validation, and testing process is carried out by using the intelligent computing algorithm nftool. The model is studied using gradient analysis, regression, mean squared error (MSE) and histogram studies with the help of the solver designed as LMNNS. The conclusions are supported by tabular and graphical analyses. The physical characteristics associated with magnetic parameter, thermophoresis parameter, pressure gradient parameter, permeability parameter, Lewis number, Eckert number, Brownian motion parameter, and Prandtl number are visually displayed to facilitate easy observation and analysis.