Nonlinear squeezing flow of stratified fluids: A comprehensive study on convective conditions and probable errors

A thorough understanding of magnetohydrodynamic (MHD) squeezing fluid flow in non-Darcian media is essential for advancing a wide range of engineering applications, including cooling systems, polymer processing, and biomedical devices. This study investigates the dynamics of MHD squeezing flow over a stretching permeable plate, focusing on the combined effects of convection and nonlinear stratification on mass and heat transfer processes. The influence of thermal radiation is also considered to provide a comprehensive analysis of heat transfer mechanisms. The fourth-order Runge–Kutta method (RK-4), coupled with a shooting technique, is employed to numerically solve the system of nonlinear governing equations. The contribution of key variables to the flow field is studied and visualized through graphical representations. In addition, Sherwood number, Nusselt number, and skin friction coefficient are determined for various parameter values, with their statistical significance examined using correlation coefficients and probable error analysis. The results reveal that increasing solutal and thermal stratification parameters diminishes concentration and temperature fields, whereas higher Biot numbers enhance fluid concentration and temperature. Notably, all values are statistically significant except for length variable δ in the local Nusselt number.