Electromagnetohydrodynamic (EMHD) flow of Jeffrey fluid through a rough circular microchannel with surface charge–dependent slip

This research examines the electromagnetohydrodynamic (EMHD) flow of Jeffrey fluid in a rough circular microchannel while considering the effect of surface charge on slip. The channel wall corrugations are described as periodic sinusoidal waves with small amplitudes. The perturbation method is employed to derive solutions for velocity and volumetric flow rate, and a combination of three-dimensional (3D) and two-dimensional (2D) graphical representations is utilized to effectively illustrate the impacts of relevant parameters on them. The significance of the Reynolds number $Re$ in investigations of EMHD flow is particularly emphasized. Furthermore, the effect of wall roughness $\epsilon$ and wave number $k$ on velocity and the influence of wall roughness $\epsilon$ and surface charge density ${\sigma }_s$ on volumetric flow rate are primarily focused on, respectively, at various Reynolds numbers. The results suggest that increasing the wall roughness leads to a reduction in velocity at low Reynolds numbers ($Re=1$) and an increment at high Reynolds numbers ($Re=10$). For any Reynolds number, a roughness with an odd multiple of wave number ($k=6,10$) will result in a more stable velocity profile compared to one with an even multiple of wave number ($k=4,8$). Decreasing the relaxation time ${\overline{\lambda }}_1$ while increasing the retardation time ${\overline{\lambda }}_2$ and Hartmann number $Ha$ can diminish the impact of wall roughness $\epsilon$ and surface charge density ${\sigma }_s$ on volumetric flow rate, independent of the Reynolds number. Interestingly, in the existence of wall roughness, further consideration of the effect of surface charge on slip leads to a 15% drop in volumetric flow rate at $Re=1$ and a 32% slippage at $Re=10$. However, in the condition where the effect of surface charge on slip is considered, further examination of the presence of wall roughness only results in a 1.4% decline in volumetric flow rate at $Re=1$ and a 1.6% rise at $Re=10$. These findings are crucial for optimizing the EMHD flow models in microchannels.