Analytical Treatment of Heat Transfer in Electrokinetic Flows

This paper investigates the effects of velocity slip in the presence of an electric double-layer on fluid flow and heat transfer in a parallel plate hydrophobic microchannel. The electric potential filed is determined through the Poisson-Boltzmann equation together with the Debye-Hu¨ckel (D-H) approximation, while the velocity field is obtained by solving the Navier-Stokes equations under fully developed conditions. In most previous studies, zeta-potential has been considered as an independent variable for the analysis of induced voltage. However, experimental findings show that in electrokinetic slip flows with constant wall potential, the zeta potential is related to the slip coefficient and the D-H parameter. Therefore, in the present study, the wall potential is considered as an independent variable and the zeta potential is determined from an available experimental correlation. The effects of velocity slip, the D-H parameter, the wall potential and the Brinkman number on the induced voltage and the velocity and temperature fields are examined in detail. Results indicate that the slip effects on the zeta potential dramatically affect the flow and temperature fields.