This paper investigates two-dimensional, time-independent elecroosmotic pressure-driven flow generated by a direct current electric potential with asymmetrical and symmetrical zeta potential distributions along the microchannel walls. Fluid flow through the horizontal microchannel is simulated using a numerical method. Two different cases are proposed to study the effect of electric potential on the flow field. First, negative electric potential is applied on the microchannel walls. In this case, large segments with negative electric potential are initially placed on the first half of the microchannel walls with two different arrangements. Afterward, smaller segments with negative electric potential are placed on the microchannel walls. Next, negative electric potential is replaced by positive electric potential on the microchannel walls in the similar manner. It is shown that applying positive potential on the walls contributes to the localized circular flows within the microchannel. The size of these vortices is also proved to considerably vary with the applied zeta potential magnitude. Finally, the effect of wall zeta potential on heat transfer was studied for all the four types of microchannels by imposing a constant uniform heat flux on the walls. The Nusselt number plots indicate how heat transfer varies along the microchannel walls. The Nusselt number fluctuation can be observed where the positive and negative electric potentials are located.