This study examines the boundary layer flow of a Casson nanofluid over an inclined extending surface, addressing the critical issue of heat and mass transmission in nanofluid applications. The research is motivated by the need to understand the thermal efficiencies of fluid fluxes influenced by Brownian motion and thermophoresis, particularly in the presence of Soret and Dufour effects. To tackle this complex problem, we employ the Buongiorno model to analyze the nonlinear dynamics of Casson nanofluid flow within an inclined channel, focusing on the intensified boundary layer's critical flow parameters. An innovative approach utilizing Artificial Neural Networks (ANNs) is introduced to solve the intricate nonlinear differential equations governing the heat transfer and flow characteristics of Casson nanofluids. The bvp4c built-in MATLAB function is utilized to assess the performance of the acquired current physical model across various scenarios, and a correlation of the results with a reference data set is conducted to verify the validity and efficiency of the proposed algorithm. This method demonstrates a high level of efficiency and accuracy, achieving a mean squared error in the range of 10−9 to 10−10. The results of this research not only enhance computational efficiency but also improve solution accuracy, making significant contributions to the understanding of coupled heat and mass transfer phenomena. The findings have broad applications across various industries, including biomedical devices, lubrication, energy systems, food processing, and cooling for electronics, where nanofluid flows are prevalent. The inclusion of Soret and Dufour effects further enriches the applicability of this analysis, providing valuable insights into the complex interactions within nanofluid systems. The effect of specific physical parameters is stated in terms of energy, velocity, and mass configuration; the velocity outline decreases with an increase in magnetic parameter. The concentration profile is lowered by an increase in the chemical reaction parameter and thermophoresis factor. As the Brownian motion factor rises, mass diffusion shows increases.
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