This article is aimed to present an analytic study of electro-osmotic (EO) pumping of a micro-duct with inserted fin vanes. Finned structures are known to be an efficient and very important tool in conducting heat generated in fluid transport system, such as Joule's heating in micro-fluidic devices. The present semi-analytical analysis is performed under the Debye-Huckel approximation (DHA), enabling us to explicitly investigate the combined effects of various parameters for optimizing the EO pumping rate while retaining substantial fin vanes for heat removal. A mathematical model based on the solutions of two fundamental EO flows is introduced to explain how the choice of the fin vane width may optimize the EO pumping rate in the general case. Moreover, we present the optimized EO flow rates in diagrams plotted on the plane of zeta potentials, which may serve as an easily used reference for engineering design and applications. (C) 2016 Elsevier Ltd. All rights reserved.