Computational intelligence for MHD mixed convection Williamson fluid flow along a stretched surface under Dufour and Soret impacts

The importance of the Soret and Dufour influences upon this mixed convective flow of the Williamson fluid (SDE-MCFWF) along a stretched surface is investigated in this paper. The stiff highly nonlinear fluid flow system represented via partial differential equations is simplified and converted to simple fluid flow system in terms of ordinary differential equations. The resultant collection of ODEs is turned into a system of ODEs, which is then resolved using artificial neural networks back propagated using the Levenberg Marquardt technique (ANNB-LMT). To evaluate the recommended model's abilities, these obtained non-linear ODEs are solved by applying the ND-solve technique to get data sets from (ANNB-LMT). Error plots, regression tests, and the mean squared error guidance are used to further assess the correctness of the established outcomes for SDE-MCFWF. Tables and graphs demonstrate the trend of different physical factors on velocity, temperature, and concentration profiles, such as the curvature parameter, Prandtl number, magnetic field parameter, Dufour number, non-linear stretching parameter, Schmidt number, Porosity parameter, Brickman and Soret number. It shows that rise in Soret number causes the temperature to drop and the concentration profile to rise, but the Dufour number has the opposite effect. Using numerical simulations, the skin-friction coefficients, Sherwood number, and Nusselt number are studied. For rising levels of the Prandtl number and the power law stretching index, the skin friction coefficient and Nusselt number increase, whereas the Dufour number and curvature parameter drop. Higher Dufour and power law stretching index values cause the Sherwood number to increase, but lower Prandtl and curvature parameter values cause it to drop.