Modulating flow and heat transfer through the competition of electroosmotic and electromagnetic driving forces

This study systematically investigates the velocity and temperature fields under various parameter conditions using the perturbation method and finite difference method. The effects of the Hartmann number Ha, wavenumber kappa, slip coefficient d, nonlinear coefficient Gamma, source term S, and Brinkman number Br on flow and heat transfer characteristics are analyzed. Fig2 validates the accuracy of the perturbation method, showing excellent agreement between the perturbation solutions and numerical solutions at multiple time points, while also revealing the boundary layer characteristics of velocity profiles under different kappa values. Figs3 and 4 compare the velocity evolution under low and high Ha conditions, demonstrating that both Ha and S suppress the velocity peak, with S having a more pronounced effect. Fig5 illustrates the role of the wavenumber kappa in regulating the velocity profile, where larger kappa causes the velocity peak to shift toward the wall, forming a typical boundary layer structure. Fig6 investigates the coupled effects of the slip coefficient d and Ha, showing that increasing d elevates the velocity distribution, while increasing Ha reduces the velocity peak, indicating a competitive relationship between the two parameters. Fig7 analyzes the influence of the nonlinear coefficient Gamma on velocity evolution, revealing that larger Gamma values decrease the velocity peak, and the velocity profile tends to a steady state after sufficient time development. Fig8 presents the temperature distribution characteristics, where an increase in the source term S significantly raises the temperature amplitude. Figs9 and 10 focus on the variation of the Nusselt number Nu with the Brinkman number Br, showing that Nu decreases monotonically with increasing Br, while larger S reduces Nu, and the slip boundary condition (d=0.02) slightly enhances heat transfer. The comprehensive dataset covers key physical quantities including velocity, temperature, and Nusselt number, providing systematic numerical support for understanding nonlinear flow and heat transfer mechanisms.