Three‐dimensional boundary layer dynamics of couple‐stress non‐Newtonian fluids: MHD effects and generalized flux analysis via OHAM

Abstract This paper presents an investigation of the three‐dimensional boundary layer dynamics of couple‐stress non‐Newtonian fluids under MHD effects. The generalized heat and mass flux models are formulated based on the non‐Fourier (Cattaneo‐Christov) and non‐Fick theories. With the application of the Optimal Homotopy Analysis Method (OHAM), the governing equations, developed from momentum, energy, and mass conservation laws, are solved to analyze the intricate interplay between thermal, solutal, and fluid dynamic parameters. The methodology takes into account factors such as rotation, magnetic fields, and others: chemical reactions, thermal radiation, and Brownian motion. The results are extremely insightful: rotational forces retard linear velocity due to increased friction, while magnetic fields reduce flow dynamics. Thermal radiation increases fluid temperature, and increased Prandtl number and relaxation parameters reduce the rates of thermal transmission. Concentration profiles respond dynamically to chemical reaction rates and Brownian motion, and higher reactions enhance delays in particle diffusion. Numerical findings supported by Mathematica reveal that Nusselt and Sherwood numbers increase with thermal and mass transport parameters, confirming enhanced heat and mass transfer under specific conditions.