An Analytical Modeling on Flow and Heat Transfer for a Pressure-Driven Electroosmotic Flow in Microchannel Considering First Order Slip Model

Abstract

An analytical solution to study fundamental behaviors of a pressure-driven electroosmotic flow in a parallel plate microchannel is presented in the present work. A thermally fully developed flow of a Newtonian liquid is considered. The fluid motion is assumed to be caused with a pressure gradient applied externally and an electrostatic potential field. The electrical potential field is determined by solving the Poisson–Boltzmann equation. The Debye–Huckel approximation is not considered for higher accuracy of results. A modified form of the Navier–Stokes equation with slip boundary conditions is considered to evaluate velocity field and skin friction coefficient, whereas the energy equation is simplified to obtain temperature profile as well as Nusselt number. Homotopy perturbation method (HPM) is applied to solve the Poisson–Boltzmann equation, whereas the momentum and the energy equations has been solved analytically to achieve the velocity and temperature profiles, respectively. The predicted results are compared with existing work and show a good harmony. Results obtained for electric potential, velocity and temperature fields have been shown graphically varying wall zeta potential, slip coefficient and pressure gradient. Subsequently, a parametric study is presented for skin friction coefficient and the Nusselt number. Finally, an effort is made to determine local volumetric entropy generation and global entropy generation. The proposed results exhibit both the influence of the Brinkman number and pressure gradient on the entropy generation.