Numerical Investigation of Heat and Mass Transfer in Micropolar Nanofluid Flows over an Inclined Surface with Stochastic Numerical Approach

This paper examines the impacts of heat radiation and Soret effects on nanofluid flow in a micropolar magnetohydrodynamic (MHD) framework over an inclined sheet that is stretching. This issue is critical for applications in biomedical engineering, sophisticated cooling systems, and chemical reactions where accurate fluid flow and heat transfer control are required. Brownian diffusion and thermophoretic motion effects are included in the model. Similarity transformations are utilized to transform the system of partial differential equations (PDEs) into a set of ordinary differential equations (ODEs) in order to tackle this intricate challenge. These ODEs are solved using the Levenberg–Marquardt backpropagation (LMB) optimization technique. Utilizing a dataset produced by MATLAB’s “bvp4c” solver, the results are verified. To assess the LMB algorithm’s correctness, a number of statistical tools are used, such as curve fitting, performance plots, regression measures, and histograms. The best measures of performance in the form of mean square errors (MSEs) are obtained as 2.7164E - 09 , 1.0276E - 08 , 1.217E - 08 , 1.3125E - 08 , 2.9218E - 08 , 1.0184E - 09 , 2.874E - 10, and 3.6039E - 10 against 373 , 1000 , 1000 , 1000 , 134 , 660 , 133, ,and 648 iterations. The comparative analysis verifies the validity of the suggested solver, showing absolute errors ranging from E - 10 to E - 03 for all significant parameter findings. According to quantitative studies, there is a noticeable damping effect when the magnetic component is increased since it lowers the fluid velocity. On the other hand, fluid velocity is improved when the material parameter is increased. Furthermore, as the Lewis number increases, the concentration profile diminishes, emphasizing its impact on mass transfer rates. Thermal diffusion, the hallmark of the Soret effect, significantly alters concentration gradients, which are essential for industrial process optimization. These results show the originality of our methodology by offering a thorough examination of the interactions among magnetic fields, material characteristics, and diffusion effects in nanofluid flow. By mathematically describing the ways in which these parameters affect flow and heat transfer, this study goes above and beyond earlier research, providing important new information for the design and optimization of systems that depend on micropolar MHD flows.