The present paper discusses the electromagnetohydrodynamic (EMHD) electroosmotic flow (EOF) and entropy generation of incompressible third-grade fluids in a parallel microchannel. Numerical solutions of the non-homogeneous partial differential equations of velocity and temperature are obtained by the Chebyshev spectral collocation method. The effects of non-Newtonian parameter Λ, Hartman number Ha and Brinkman number Br on the velocity, temperature, Nusselt number and entropy generation are analyzed in detail and shown graphically. The main results show that both temperature and Nusselt number decrease with the non-Newtonian physical parameter, while the local and total entropy generation rates exhibit an adverse trend, which means that non-Newtonian parameter can provoke the local entropy generation rate. In addition, we also find that the increase of non-Newtonian parameter can lead to the increase of the critical Hartman number Hac.Numerous theoretical and experimental works in the literature are available on the analysis of the behaviors of EMHD flow. Jang and Lee [21] found low magnetic field could bring about impressive increments to the fluid velocity. A practical EMHD pump has been constructed by Lemoff and Lee [22], in which an electrolytic solution was propelled by the Lorentz force along a micro-channel. Jian and Chang [23] obtained approximate analytical solutions of the EMHD velocity distribution under the influence of a non-uniform magnetic field. Under the combined action of electroosmotic and electromagnetic forces, the heat transfer characteristics of EMHD flows in a narrow channel have been analyzed by Chakraborty et al. [24]. Sarkar et al. [25] carried out a study on streaming potential of EMHD flow combined with interfacial slip through a microparallel channel, and the effects of electrical double-layer (EDL) formation were also taken into account. The results show that the flow rate was greatly improved, even at lower values of surface potential.In recent years, it has been gradually realized that non-Newtonian fluids are more imperative than Newtonian fluids in a variety of industrial and engineering applications. For the non-Newtonian models, the relationship between shear stress and rate of strain is non-linear. Various non-Newtonian MHD flow models can be found in the existing literature [26][27][28][29] and hydrodynamic studies on non-Newtonian electroosmotic flows in reference [30,31]. Third-grade fluids model are able to discern normal stress differences and to describe shear thinning/thickening effect. Polymers, liquid metals, suspensions and so on belong to third-grade fluids. Wang and Jian [32] studied the EMHD third-grade fluids flow between two parallel microchannels and obtained the approximate analytical solutions of velocity and temperature by the perturbation method. Akgül et al. [33] discussed the analytical and numerical solutions of electroosmotical flow of third-grade fluid between parallel plates. Danish et al. [34] analyzed the flow characteristics of the Poiseuille and...