The behavior of non-Newtonian fluids is considered as an important subject in micro scale and microfluidic flow researches. Because of the complexity and cost in the numerical works and the experimental set-ups in some instances, the analytical approach can be taken into account as a robust alternative tool to solve the non-Newtonian microfluidic flows in some special cases benefiting from a few simplified assumptions. In this work, we analyze the flow of two non-Newtonian fluids including the power-law and grade-fluid models in microchannels. For the grade-fluid, the stress tensors are defined considering the Rivlin-Ericksen tensor definitions. To avoid the complexities in the entrance region, the flow is assumed to be hydrodynamically developed. The flow is steady and laminar and the fluid has constant properties independent of its temperature. We treat three different relations between slip velocity and wall shear stress as the slip boundary condition in our analysis. The Homotopy perturbation method is applied to solve the Navier-Stokes equations in case of grade fluid. To achieve the best slip coefficient, our power-law model solution is compared with available experimental data. Moreover, we compare the results of our Homotopy perturbation method with the numerical solutions. The current results show that the best slip relation is the one with a square of wall shear stress dependency.

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