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• Carbon nanotubes are considered. • Flow is assumed in channel. • Heat transfer is considered. The current study aims to examine the peristaltic movement of carbon nanotubes (CNTs) flow in an electro-osmotic curved channel with variable viscosity. No-slip conditions near the channel walls are used. Poisson and Nernst–Planck equations are used to model the electro-osmotic phenomena. Using a curvilinear coordinate system, the equations for nanofluid flow along a curved pipe are formed. Firstly the problem is formulated and then un-dimensionalized. The approximation of long-wavelength along with a lesser Reynolds number has been applied to estimate the equations. The resulting mathematical relations are numerically solved by using the shooting method. To analyze the behavior graphically, we use MATLAB software. Graphical findings show the influence of parameters that affect the flow characteristics. It is noted that the velocity and temperature of the flow decrease by increasing the viscosity parameter. It is also observe that the heat absorption parameter helps to raise the temperature profile for CNTs. [ABSTRACT FROM AUTHOR]