Electro-osmotic flow (EOF) in microchannels with and without porous media has been analysed in this work. The effect of the charge of solid particles on EOF has been taken into account by introducing an equivalent reference length into the equation that governs the static potential distribution. External electric field and internal potential have been determined by solving the Laplace and Poisson-Boltzmann equations, respectively. Their effect has been introduced into the Navier-Stokes equations to simulate fluid flow and heat transfer due to electro-osmosis. The set of equations that describes the problem has been solved using the finite element method combined with the characteristic-based split algorithm.