Effects of variable viscosity, concentration and heat variation on MHD oscillatory flow for Bingham fluid through an inclined porous channel

<ns5:p>Background Magnetohydrodynamic oscillatory flows of non-Newtonian fluids in porous channels arise in many industrial and geophysical applications. Understanding the combined influence of variable viscosity, heat generation, and concentration is essential for accurate flow prediction. Methods A mathematical model for unsteady MHD oscillatory flow of a Bingham fluid through an inclined porous channel was formulated. The governing nonlinear partial differential equations for momentum, energy, and concentration were nondimensionalized and solved using the separation of variables technique. Numerical evaluation and graphical analysis were performed using Wolfram Mathematica. Results The results show that increasing heat generation and radiation parameters enhances fluid temperature and velocity, while higher magnetic and oscillation parameters suppress flow motion. Concentration was found to increase with higher oscillation frequency and Péclet number, whereas Schmidt and chemical reaction parameters reduced mass diffusion. Variable viscosity significantly amplified velocity compared to constant-viscosity cases. Conclusions The study demonstrates that temperature-dependent viscosity and yield-stress effects strongly control MHD oscillatory Bingham fluid flow in inclined porous channels. The results are relevant to engineering systems involving non-Newtonian transport with thermal and mass diffusion effects. The novelty of the present formulation lies in combining Bingham yield-stress behavior, temperature-dependent viscosity, porous-medium resistance, magnetic-field effects, heat generation, radiation, and concentration transport within a single analytical framework.</ns5:p>