The effect of the geometry of the soil in electrokinetic application has been studied by using capillary models of annular geometry. The Joule heating generation has been included as a primary effect of temperature development leading to buoyancy flows. The heat transfer model has been formulated for conduction-dominated regime. The results of this model have been coupled with the motion equation to obtain the analytical hydrodynamic velocity profile. Numerical illustrations, demonstrating the effect of the cross-sectional area of the annular region on the velocity field, have been included. It is observed that a substantial effect on the magnitude of such velocity field for different parameters of the system. The results are useful to obtain better understanding of the role of the soil geometry in potential soil cleaning field operations.