Novel design of artificial intelligence-based neural networks for the dynamics of magnetized chemically reactive Darcy–Forchheimer nanofluid flow

This study explores the intricate interaction of thermal radiation, chemical reactions, Brownian motion, and thermophoresis on heat and mass transfer within a magnetic nanofluid, flowing over a porous stretching surface. Current models in the literature are limited in their ability to account for the complex dynamics governing this process, particularly with respect to nonlinear variations in fluid momentum, temperature, and mass diffusion. To overcome these limitations, we propose an enhanced approach utilizing the Darcy–Forchheimer fluidic model (DFM), which integrates these nonlinear effects and addresses both momentum and mass diffusion. Our model is distinct in its application of artificial intelligence neural networks (AI-NN) alongside the Levenberg–Marquardt method (LMM), offering a more sophisticated computational solution than traditional numerical methods. The fluidic motion is governed by partial differential equations (PDEs) and these mathematical equations are then reproduced by converting them into dimensionless ordinary differential equations (ODEs) along with support parameters to control the motion and diffusion of mass if fluid. Computational solutions are derived utilizing artificial intelligence neural network (AI-NN) with Levenberg–Marquardt method (LMM), enabling an analysis of the effects of thermophysical factors such as source of heat \((\lambda )\) $(\lambda )$ , magnetic effect parameter \((M)\) $(M)$ , Schmidt number \((Sc)\) $(Sc)$ , chemical reaction effect \(({c}_{\text{r}})\) $(c_{\text{r}})$ , Brownian motion parameter \(({N}_{\text{b}})\) $(N_{\text{b}})$ , thermophoresis effect \({(N}_{\text{t}})\) ${(N}_{\text{t}})$ , radiation number \((Rd)\) $(Rd)$ , and thermal buoyancy number \((\alpha )\) $(\alpha )$ . The dataset generated for the governing system of Darcy–Forchheimer fluidic model (DFM) is applied to extract the approximate solutions through Mathematica and MATLAB techniques. The findings demonstrate the significant impact of these parameters on velocity, temperature, and mass concentration, with variations observed across 14 different scenarios. The study’s computational framework, validated through regression analysis, error histograms, and fitness functions, ensures high accuracy, with mean squared error (MSE) values clearly represented. This novel approach offers a promising alternative to existing models, enhancing the understanding of heat and mass transfer in magnetized nanofluids. Performance analysis is made on the bases of variety of scenarios taken for velocity \(\left( {f^{\prime } \left( \eta \right)} \right)\) $\left(f^{\prime }\left(\eta \right)\right)$ , temperature \(\left( {\theta \left( \eta \right)} \right)\) $\left(\theta \left(\eta \right)\right)$ , and concentration of mass \(\left(\phi \left(\eta \right)\right)\) $\left(\varphi ,\left(\eta \right)\right)$ which ranged from \({10}^{-14}\) ${10}^{-14}$ to \({10}^{-9}\) ${10}^{-9}$ . Regression analysis \(\left(RA\right)\) $\left(R,A\right)$ , error histogram \(\left(EH\right)\) $\left(E,H\right)$ , and fitness state of function \((FF)\) $(FF)$ stood responsible for validation and accuracy of the AI-NN LMM demonstrating MSE graphically.