A semi-analytical solution is presented using method of Laplace transform for the transient pulse electroosmotic flow (EOF) of Maxwell fluid in a circular micro-channel. The driving mode of pulse EOF here is considered as an ideal rectangle pulse. The solution involves solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. The results show that the profiles of pulse EOF velocity vary rapidly and gradually stabilize as the increase of time？？within a half period. The velocity profiles at the center of the micro-channel increase significantly with relaxation time , especially for the smaller pulse width a. However, as the pulse width a increases, this change will be less obvious. At the same time, the different change frequency of velocity profiles will slow down, which means a long cycle time. Additionally, the time needed to attain the steady status becomes longer with the increase of relaxation time？ and pulse width a.
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![\"\"](\"Edit_440fb0f5-5539-4a78-8311-93b2664c8117.png\")
？within a half period. The velocity profiles at the center of the micro-channel increase significantly with relaxation time ![\"\"](\"Edit_ffb813ed-0046-40bc-95e6-76057f46ce32.png\")
, especially for the smaller pulse width a. However, as the pulse width a increases, this change will be less obvious. At the same time, the different change frequency of velocity profiles will slow down, which means a long cycle time. Additionally, the time needed to attain the steady status becomes longer with the increase of relaxation time？![\"\"](\"Edit_d1b31535-84c1-417e-b987-6ca53ab1616b.png\")
and pulse width a.
