Saddle and nodal point aspects on stagnation point MHD Casson nanofluid flow over Howarth’s wavy circular cylinder with pollutant concentration with stochastic intelligence approach

Recent years have seen an increase in the need for enhanced thermal transmission and management of the transport of contaminants in intricate systems. A complete understanding of the concentrations of waste discharge over a circular sinusoidal cylinder is essential for ensuring environmental stability and developing efficient techniques in disciplines including materials production and environmental engineering, with strong mathematical techniques such as artificial neural networks. The objective of the present study is to examine the heat and mass transfer of three-dimensional steady incompressible Casson hybrid nanofluid flow via a circular sinusoidal cylinder with the consequences of pollutant concentration, magnetic field, chemical reaction, and heat generation/absorption. The ordinary differential equations (ODEs) are gotten from the nonlinear partial differential equations (PDEs). To solve the modified ODEs, the Runge–Kutta–Fehlberg 4th 5th order (RKF-45) and shooting methods are employed. Many useful and related characteristics for connected profiles are demonstrated graphically. Additionally, the engineering coefficients are also studied. The major conclusions of this examination are that enhancing the value of the external pollutant source variation and local pollutant external source constraints improves the concentration profiles. Sherwood number is decreased by raising the value of the solid volume fraction and the local pollutant external source constraint. To determine estimated parameter solutions for physical system variations and to demonstrate the correctness of the suggested Levenberg–Marquardt technique, the training, testing, and validation procedures are carried out using baseline information. To successfully solve parameters, the accuracy of the Levenberg–Marquardt technique is examined using regression analysis, mean square error, and histogram.