Electromagnetic electro-osmotic flow of the Jeffrey fluid in rectangular microchannel

Following a thorough analysis of the existing research on periodic electro-osmotic flow in rectangular microchannels, this paper offers a comprehensive investigation of the distinctive characteristics of electromagnetic electro-osmotic flow in Jeffery fluids, emphasising particularly on the combined impact of the intricate interplay between the electric field and electromagnetic forces. A precise analytical expression for the velocity has been successfully derived by employing the technique of variable separation. Moreover, a comprehensive analysis has been conducted utilising intricate calculations and image evaluation to delve into the implications of Hartmann number (Ha), Reynolds number (Re), relaxation time, electrokinetic width and retardation time on the distribution of flow velocity. The findings indicate that as Ha rises, the flow velocity initially gains momentum, but subsequently exhibits a gradual decline. When Re is 0.5, the speed increases by about 29% and then decreases by about 61%. When Re is 4.5, the speed increases by about 20% and then decreases by about 42%. The increase in electrokinetic width and relaxation time results in an increase in speed. When Ha is 0.5, the velocity rises about 29% by the effect of the electrokinetic width and about 730% by the effect of the relaxation time. When Ha is 6, the velocity rises by about 71% by the effect of the electrokinetic width and the velocity rises by about 100% by the effect of the relaxation time. However, an increase in the retardation time and Re will result in a decrease in the flow rate. When Ha is 0.5, the velocity decreases by 83% under the effect of retardation time and 80% under the effect of Re. When Ha is 6, the velocity decreases by 40% under the effect of retardation time and 25% under the effect of Re. It should be emphasised that the velocity distribution of Jeffrey fluid is mainly concentrated near the channel wall, especially when Ha increases, resulting in the fluid velocity tending to be relatively slow. It is particularly interesting that when Ha reaches a high level, the fluid velocity is almost no longer affected by changes in Re. In order to validate the accuracy of this study, the resulting findings were cross-checked with previous findings and these comparisons support that the conclusions of this paper are plausible.