Joule Heating Effects In Electrokinetically Driven Flow Through Rectangular Microchannels: An Analytical Approach

Abstract

This is a theoretical study dealing with mixed electroosmotic and pressure-driven flow of a Newtonian liquid in a rectangular microchannel. Both and thermal boundary conditions are considered and the Debye-Hückel linearization is invoked. The governing equations are made dimensionless assuming fully developed conditions and then analytically solved using an infinite series solution. The governing factors are found to be the dimensionless Debye-Hückel parameter, velocity scale ratio, dimensionless Joule heating parameter, and channel aspect ratio. The results indicate that the Nusselt number is an increasing function of the channel aspect ratio, whereas the opposite is true for the velocity scale ratio. In addition, unless a sufficiently high opposed pressure is present, a higher Joule heating rate is generally accompanied by a lower Nusselt number. Moreover, increasing the dimensionless Debye-Hückel parameter gives rise to a higher Nusselt number, unless a high value of the channel aspect ratio with surface heating is considered.