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Microscale heat sinks based on channels or pipes are designed to restrict the temperatures of microelectromechanical systems, which have a wide range of applications in the modern engineering and mechanics. In this context, this work aims to study heat convection and entropy generation of a fully developed nanofluid flow in a circular micropipe in the presence of an electrical double layer. Buongiorno’s model is employed to exhibit the nanofluid behavior. The governing equations are reduced to a system of nonlinear ordinary differential equations through appropriate similarity transformations. Particularly, we rectify the pressure term as an unknown constant, which makes our flow model compatible with those well-known fluid flow models in macrosize. Highly accurate solutions are obtained and verified. Analysis for physical properties of electric field, velocity field, temperature, and nanoparticle distributions is discussed followed by an investigation of the entropy evolution in the flow. The results show that flow behavior and total entropy of the system depend on the electroosmosis, thermophoresis, and fluid viscosity. However, the influence of the electrical double layer on the flow and system entropy is negligible when the electroosmotic parameter exceeds a maximum value.