Temporal Stability Analysis of Unsteady Slip Flow of Magnetic Nanofluid Past a Heated Permeable Stretching/Shrinking Sheet in a Non-Darcian Porous Medium

The study of boundary layer flow has attracted significant interest due to its diverse engineering applications. This numerical study develops a mathematical model and analyzes the stability of time-dependent, reactive, and radiative magnetic nanofluid flow past a convectively heated, permeable stretching/shrinking sheet embedded in a non-Darcian porous medium. Using similarity transformations, the governing partial differential equations are reduced to a system of nonlinear ordinary differential equations and solved numerically via the shooting method with a fourth-fifth order Runge-Kutta-Fehlberg (RKF45) integration scheme in MAPLE. Dual solutions are obtained, and their characteristics are examined in detail. The effects of key parameters on velocity, temperature, and concentration profiles are investigated, along with their influence on the skin friction coefficient, Nusselt number, and Sherwood number, presented graphically and in tabular form. Stability analysis confirms that the upper branch solution is stable and physically realizable, while the second solution is unstable, supported by the presence of a positive smallest eigenvalue in the upper branch.