Thermal behavior of electro-osmotically driven flows through rectangular microchannels

The understanding of electro-osmotic flows is essential to design and optimize electro-osmotic pumps, which are commonly used to generate flows inside channels whose characteristic length is in the micro or nano-scale. The velocity distribution that arise from such devices is quite different from the classical Poiseuille parabolic profile because the flow is driven by an electrical force, which acts chiefly in the region adjacent to the wall. Even though in the literature there are several analytical, numerical and experimental works that deal with electro-osmotic flows, only recently some parametrical studies of their dynamical and thermal behaviour through channels with simple but realistic geometries, i.e., rectangular and trapezoidal cross-sections have been published. However, up to now, no analytical solutions have been presented for combined electro-osmotic and pressure-driven flows through rectangular microchannels. In this work an analytical solution for microchannels with a rectangular cross-section is presented for the electric potential generated by the charge distribution at the wall, the velocity field and the temperature field under H boundary conditions (H1 and H2). The solution is obtained by means of the integral transform technique for a steady state, laminar, hydro-dynamically and thermally fully developed flow.