Particle concentration and thermal profiling of Bingham fluid in oscillating channel under perfect slip

Abstract This study investigates molecular transfer within Bingham fluids, with an emphasis on optimizing thermal transfer processes via an exhaustive analytical and numerical approach. A slip boundary model is developed to effectively evaluate slip conditions at the interface between fluid and solid. In order to simplify the analysis, the governing equations are modeled assuming long wavelengths and smaller Reynolds numbers for convection. Utilizing the perturbation method, an analytical answer is derived. Mathematica numerical simulations cast light on the underlying mechanisms of mass transfer. The research highlights the significant influence of slide conditions on flow dynamics, heat and mass transfer rates, and concentration distribution near the interface. Various physical effects and viscous dissipation‐related parameters are utilized to conduct a comprehensive heat transfer analysis. The research indicates that slip circumstances, magnetic field intensity, and the Bingham number significantly influence velocity, temperature, and concentration profiles, with heightened slip augmenting velocity and diminishing the volume of trapped boluses. Moreover, heat transmission is enhanced by viscous dissipation and buoyant forces, while concentration profiles diminish with increasing Schmidt, Soret, and Brinkmann numbers. The results of this study have practical implications for the optimization of processes involving Bingham fluids and contribute to a greater understanding of mass transfer in this context.