The aim of this study is to obtain the non-similar solution of power law conducting fluid flow over a nonlinear moving permeable wedge utilizing the Levenberg–Marquardt scheme-artificial neural network. In this paper, a novel theoretical analysis that consists of the influence of a variable magnetic field on power law fluid flow past a stretchable porous wedge embedded in a Darcy-Forchheimer porous medium is performed. The second objective is to perform the local sensitivity analysis for fluid friction and heat transfer rate over the porous permeable wedge. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations via the local non-similarity method. The system of ordinary differential equations is numerically solved using a finite difference scheme implemented in MATLAB. To evaluate parameter sensitivity, response surface methodology based on central composite design, along with analysis of variance, is employed using MINITAB 21. The Levenberg–Marquardt scheme shows excellent agreement with the numerical results, with absolute errors consistently in the range of 10−4–10−5. The model achieved optimal validation performance with mean squared errors of 9.1185 × 10−10 for skin friction and 1.0251 × 10−11 for the heat transfer rate. Results indicate that the presence of a Darcy–Forchheimer porous medium leads to increased velocity and enhanced heat transfer, evidenced by reduced temperature profiles and elevated skin friction coefficients and the Nusselt numbers. Furthermore, the Forchheimer parameter is the most sensitive parameter for skin friction and Nusselt number as compared to other parameters.
Haq et al. (Fri,) studied this question.