High-order compact ETI-RK scheme for Eyring-Prandtl flow over a Riga plate

The work seeks to build an advanced computational technique to accurately simulate non-Newtonian fluid flow (unsteady Eyring-Prandtl, electrically operated Riga plate) with heat and mass transfer. The necessity of the work under consideration stems from the inability of classical numerical schemes to achieve high stability and reduced precision when modelling nonlinear convection-diffusion equations with electromagnetic forcing and nonlinear rheology. To address these, a three-step hybrid numerical scheme is suggested, where the first step applies the exponential time integrator, and the third and fourth steps apply the Strong Stability Preserving Runge-Kutta (SSP-RK) algorithm. A compact finite difference formulation is employed for spatial discretization, providing sixth-order accuracy at most grid points while ensuring numerical stability and rapid convergence. The novelty of the proposed framework lies in integrating exponential temporal integration with high-order compact spatial discretization, enabling precise resolution of transient nonlinear effects in Eyring-Prandtl fluids subjected to Lorentz forcing. Stability analysis confirms conditional stability based on von Neumann criteria, and convergence analysis demonstrates consistency for coupled nonlinear systems. Qualitative results show that velocity decreases with increasing Eyring number due to enhanced non-Newtonian resistance, while stronger electromagnetic parameters accelerate the flow near the plate. Increased velocity slip reduces wall shear, higher Eckert numbers elevate temperature due to viscous dissipation, larger Prandtl numbers suppress thermal diffusion, and stronger reaction rates reduce concentration through intensified chemical consumption. A comparison with the conventional third-order SSP Runge-Kutta scheme demonstrates reduced numerical error and improved computational efficiency of the proposed method. The practical significance of this work lies in its applications to electromagnetic flow control, polymer processing, MHD pumping, and thermal-mass transport in electrically actuated engineering devices. Therefore, the proposed hybrid scheme provides a robust and high-accuracy computational tool for addressing complex non-Newtonian transport phenomena in modern engineering systems. • A three-stage hybrid exponential–Runge–Kutta compact scheme is developed for solving unsteady nonlinear PDEs. • The method achieves third-order temporal and sixth-order spatial accuracy with excellent numerical stability. • The scheme is applied to Eyring–Prandtl non-Newtonian fluid flow over an electrically actuated Riga plate including heat and mass transfer. • Parametric analysis shows that velocity decreases with Eyring number but increases with electromagnetic parameter, while Eckert and reaction rate strongly affect temperature and concentration. • The proposed scheme demonstrates smaller numerical error and faster convergence compared to the existing third-order SSP Runge–Kutta method.