Several fluid movement techniques in microchannel have been discussed in the past, the most recent technique is by applying an electric field to a fluid enclosed in a microchannel (viz electroosmotic flow). An immersed boundary method (IBM) is a methodology to deal with a body in the computational domain having complex or simple boundary which does not necessarily have to conform a Cartesian grid. The present study is an IBM based numerical investigation of two-dimensional transient electroosmotic flows in a microchannel populated with rectangular blocks to constrict the flow which eventually aims a short mixing channel. Electroosmotic potential, leads to the formation of Electrical Double Layer (EDL), is governed by Poisson-Boltzmann equation and is solved by PSOR method. The hyperbolic non-linearity associated with this equation is suitably tackled by the Taylor series expansion (neglecting the higher order terms). The electroosmotic flow is governed by the continuity equation impregnated with a mass source term and the Navier-Stokes equation along with electroosmotic forcing component and momentum forcing function. Both momentum forcing and mass source term are made active in the vicinity of the immersed body to satisfy the no-slip boundary condition on the same and also to satisfy the continuity for the cell containing the immersed boundary. Numerical solution of the governing equations are made possible by employing an ADI approximate factorization technique clubbed with powerful and accurate Tri-Diagonal Matrix Algorithm (TDMA). The results are generated in terms of α, the ionic energy parameter and β, which relates ionic energy parameter, characteristic length (microchannel height in the present study) and Debye-Huckel parameter.