Theoretical analysis of transient natural convection flow in a vertical microchannel with electrokinetic effect

Abstract

In this article, a theoretical analysis is carried out to understand the role of electrokinetic effect on transient natural convection flow in a vertical microchannel. By incorporating the electrokinetic body force and the natural convection term in the classical Navier–Stokes equations, the governing momentum equation for the current investigation is developed and solved analytically using the classical Laplace transform technique. Due to the complexity of solutions obtained in Laplace domain, the Riemann-sum approximation (RSA) technique is used to transform the solutions from Laplace domain to time domain. For accuracy check, the steady-state solution is also computed and compared with the implicit finite difference method and RSA at large time. Results show that skin-friction at the walls as well as the mass-flux can be optimized by careful selection of flow controlling parameters. In addition, it is found that the time required to attain steady-state skin-friction and mass-flux is weakly dependent on EDL size while strongly dependent on Knudsen number.

Keywords

• electrokinetic effect
• transient state
• streaming potential
• microchannel
• natural convection