The curved geometry becomes an important tool in the rheological characterization and processing of polymer solutions as well as complex fluids, due to the longer channel length per unit area and its effect on fluid motions. The inertial force in curved channels provides a development of a secondary Dean flow in spite of the low Reynolds number, unlike flows in straight channels. The finite volume scheme with both SIMPLE (semi-implicit method for pressure-linked equations) and SIMPLER (revised SIMPLE) algorithms for the pressure-driven transport has been applied to examine the Dean flow of Newtonian fluids in curved rectangular channels. The framework is further extended to non-Newtonian fluids based on the theoretical model with coupled equations of Cauchy momentum with the constitutive model of electrolytic Carreau-Yasuda fluids, including electrokinetic field equations. The effects of non-Newtonian rheological properties on the flow pattern are explored with variations of zero-shear viscosity, power-law indices, and relaxation time constants. We set prototype channels having an aspect ratio (i.e., height/width) of 2/3 fabricated with polydimethylsiloxane materials and model polymer solution. The axial velocity profile shows the inward skewness with a secondary motion, according to very low Dean number. Regarding to a general trend of power-law index, axial and secondary velocity fields are found to be more affected by shear thinning fluids compared to the Newtonian fluid. The Dean flow becomes weaker with increasing fluid viscosity, providing that the vorticity in non-Newtonian fluids is weaker than that in the case of water. However, note that the behavior of Dean flow and relevant mixing effect should be carefully considered on the basis of the apparent viscosity of non-Newtonian fluid. Our computational results are expected to provide a useful insight into the fine manipulation and processing of electrolytic non-Newtonian fluids in curved channel devices.