Numerical Simulation of Multiple Slip Effects on Unsteady MHD Stagnation-Point Flow of a Prandtl Fluid Using the Crank–Nicolson Scheme

This study presents a numerical investigation of multiple slip effects on an unsteady magnetohydrodynamic (MHD) stagnation-point flow of a Prandtl fluid over a flat plate. The model incorporates velocity, thermal, and concentration slip conditions at the fluid–solid interface, which significantly influence near-wall transport processes in non-Newtonian and micro-scale flow systems. The governing unsteady boundary-layer equations for momentum, energy, and species concentration are formulated as a coupled system of nonlinear partial differential equations under the influence of a transverse magnetic field and thermal radiation effects. The nonlinear governing equations are solved numerically using an implicit Crank–Nicolson finite difference scheme combined with Newton linearization. Grid and time-step independence studies are performed to ensure numerical stability and computational accuracy, and validation is carried out by comparison with previously published limiting-case results. The effects of important physical parameters, including the magnetic parameter, Reynolds number, radiation parameter, Prandtl fluid material parameter, and multiple slip coefficients, on the velocity, temperature, and concentration distributions are analyzed in detail. Engineering quantities of practical interest, namely the skin-friction coefficient, local Nusselt number, and Sherwood number, are also computed and discussed. The results indicate that the magnetic field and Prandtl fluid effects suppress the velocity distribution, while thermal radiation enhances the temperature field. Moreover, velocity, thermal, and concentration slip parameters significantly alter wall shear stress and heat and mass transfer rates. The present study provides useful insight into unsteady MHD transport behavior in Prandtl fluids and may assist in the design and optimization of advanced thermal and mass-transfer systems involving non-Newtonian fluids.