Heat pipes are well known as simple and effective heat transport devices, utilizing two-phase flow and the capillary phenomenon to remove heat. However, the generation of capillary pressure requires a wicking structure and the overall heat transport capacity of the heat pipe is generally limited by the amount of capillary pressure generation that the wicking structure can achieve. Therefore, to increase the heat transport capacity, the capillary phenomenon must be either augmented or replaced by some other pumping technique. Electrohydrodynamic (EHD) conduction pumping can be readily used to pump a thin film of a dielectric liquid along a surface, using electrodes that are embedded into the surface. In this study, two two-phase heat transport devices are created. The first device transports the heat in a linear direction. The second device transports the heat in a radial direction from a central heat source. The radial pumping configuration provides several advantages. Most notably, the heat source is wetted with fresh liquid from all directions, thereby reducing the amount of distance that must be travelled by the working fluid. The power required to operate the EHD conduction pumps is a trivial amount relative to the heat that is transported.