Numerical study of nonlinear flow and mass transfer through a channel filled with a porous medium using a hybrid heuristic paradigm

Abstract

ABSTRACT The effects of mass transfer and chemical reactions on laminar viscous flow in a porous channel with moving or stationary walls are examined in this study. The mathematical model of the mass and flow transfer is in the form of a partial differential equation (PDE), a similarity transformation method used to convert the physical problem's governing partial differential equations (PDEs) into a group of nonlinear coupled ordinary differential equations (ODEs). The main accomplishment of the present study is the utilization of a precise and effective method based on artificial neural networks (ANNs) for the model of flow in a porous channel of a viscous fluid with a chemical reaction. To investigate the coupled nonlinear ordinary differential equations, a differential evolutionary (DE) is used for exploration to get optimal weights for the model, and then we use those optimal weights in interior point algorithms (IPA) for exploitation of the laminar viscous flow model in a porous channel with moving or stationary walls. Finally, the effects of Darcy number (Da), suction/injection parameter (α), Reynolds number (Re), and power-law index (m) influence are investigated in five different scenarios, each with four different cases. The outcomes of the hybrid of differential evolution and interior point algorithm (DE-IPA) are compared to the RK4 results. The statistical analysis (MAD, TIC, RMSE, and ENSE) is also performed to ensure that the proposed technique is stable and accurate.