In many natural and engineered fields, the mass transfer through micro size domains is essential and the study of physics of transfer is very challenging especially in medical fields. In this article we have explored a numerical study to enhance the blood transfer rate through a rectangular sized micro slit with sudden expansion where the characteristic height of the micro-channel is assumed to be 100µm. In these processes, the influence of red blood cell (RBC) accruement majorly occur due to the non-Newtonian flow behavior and thus memorizes the effects of surface tension and shear mechanism. The numerical estimation of blood flow velocity and pressure is executed by considering the blood flow viscosity following the power-law model. The obtained results are found satisfactory with the existing experimental results. The numerical estimation of flow enhancement due to wall shear is presented for moderate to strong shear rates determining the extent of aggregation present in the micro slit. The result shows a parabolic profile as large cell aggregates concentrate at the core of the channel due to higher flow resistance resulting in a nonlinear mechanism of pressure and surface tension. The summarized study can be considered as a powerful tool to observe the variations in viscosity and elasticity of types of blood.