Time-varying fluid mechanics of chemically reactive viscous fluid moving in a porous medium between two parallel plates

The present work provides a mathematical model for unsteady magnetohydrodynamic flow of Maxwell fluid with coupled heat and mass transfer between active parallel plates embedded in a porous medium. The model incorporates wall deformation, time-dependent plate separation, Brownian motion, thermophoresis, activation energy and endothermic-exothermic chemical reactions to describe complex non-Newtonian transfer phenomena. Similarity transformations reduce the governing partial differential equations to nonlinear ordinary differential equations, which are solved using the Meixner–Pollaczek polynomial-based collocation method. The Taguchi method is used to optimize the heat transfer rate, with a residual contribution of 0.04562%. The fitted model is statistically adequate, as confirmed by residual analysis. The regression model is a very good match for the numerical data, with a regression coefficient value of 99.95%. The effect of the Brownian motion parameter on the heat transfer rate is the greatest (71.1553%) and the least is the activation energy parameter (0.051513%). Furthermore, an artificial neural network is developed to accurately predict the temperature and concentration profiles for both endothermic and exothermic chemical reaction cases, showing its effectiveness as a surrogate predictive model. The suggested framework gives useful insights for thermal management, polymer processing, porous media transfer and chemical engineering applications.