It is consensus among researchers that the mathematical formulation of non-Newtonian fluid models results in nonlinear differential equations. Therefore, the solution to such equations remains a challenging task for the investigators affiliated with fluid science. Owning to such difficulty, the present chapter contains a numerical solution for non-Newtonian fluid flow toward an inclined cylindrical surface. The flow field is carried with various physical effects. The shooting method is used to solve flow equations. The surface quantity, namely skin friction coefficient (SFC), is evaluated by using the prediction application of artificial intelligence. A total of 160 sample values of SFC are collected toward mixed convection, magnetic field, Casson fluid, and velocities ratio parameters. 70% data is used for training of artificial neural networking (ANN) model, while 15% data is used for each validation and testing. Levenberg-Marquardt is considered a training technique, while both Tan-Sig and Purelin are used as transfer functions. The mean square error and determination coefficient admit the prediction accuracy of the ANN model. Considering such accuracy, we observed that the SFC shows a higher magnitude at the porous cylindrical surface as compared to the nonporous surface.