Graetz problem for combined pressure-driven and electroosmotic flow in microchannels with distributed wall heat flux

Abstract

There has been a growing interest in the development of microchannel heat sinks deploying electrically modulated fluid flow in recent years. The efficient design of such devices requires heat transfer models that can account for complex distributions of heat generation in microelectronics. In this paper, expressions are obtained for temperature distribution and Nusselt number of thermally developing mixed electroosmotic and pressure-driven flow through circular/slit microchannels of axially non-uniform wall heat flux. The heating section is considered to be of a finite length in order to simulate a physically more realistic situation. Both the Joule heating and axial conduction effects are considered in the model. By comparing the results for linear, sinusoidal, and exponential distributions of the wall heat flux with the predictions of full numerical simulations, it is shown that the analytical solutions presented are accurate up to a Péclet number of 10. This threshold is demonstrated to be larger than the maximum Péclet number encountered in practical applications involving electroosmotic pumping mechanisms. After justification of the model, a parametric analysis is executed, revealing that the average Nusselt number is a decreasing function of the EDL thickness and pressure-driven velocity, irrespective of the wall heat flux distribution. Moreover, whereas a higher Joule heating rate is accompanied by a smaller value of the average Nusselt number for pure electroosmotic and pressure-assisted flows, the opposite is true in the presence of a significant back pressure.