An analysis has been provided for the entropy generation in thermally fully developed electro-osmotically generated flow in a parallel plate microchannel in terms of Brinkman number, Peclet number, dimensionless joule heating parameter, dimensionless viscous heating parameter as well as physical properties of the fluid under imposed constant wall heat flux boundary condition. Such a flow is established not by an imposed pressure gradient, but by a voltage potential gradient along the length of the tube. The solution for momentum and energy equations is used to get the exact solution for the dimensionless entropy generation number. This analysis assumes no pressure-driven component to the velocity field and constant fluid properties. Different variables namely, dimensionless joule heating parameter, viscous heating parameter, Peclet number and Brinkman number have been identified from the dimensionless entropy generation number equation. Various results for dimensionless entropy generation number, Bejan number, Irreversibility ratio, entropy generation due to fluid friction etc. are presented.