Numerical Investigation of Thermally Developing and Fully Developed Electro-Osmotic Flow in Channels with Rounded Corners

Nicola Suzzi,Marco Lorenzini

doi:10.3390/fluids6010022

Abstract

Electro-osmotic flow, that is, the motion of a polar fluid in microducts induced by an external electric field, is one micro-effect which allows fluid circulation without the use of mechanical pumping. This is of interest in the thermal management of electronic devices, as microchannels with cross sections of almost arbitrary shape can easily be integrated on the chips. It is therefore important to assess how the geometry of the channel influences the heat transfer performance. In this paper, the thermal entry region and the fully developed electro-osmotic flow in a microchannel of rectangular cross section with smoothed corners is investigated for uniform wall temperature. For the fully developed region, correlations for the Poiseuille and Nusselt numbers considering the aspect ratio and nondimensional smoothing radius are given, which can be used for practical design purposes. For thermally developing flow, it is highlighted how smoothing the corners increases the value of the local Nusselt number, with increases up to 18% over sharp corners, but that it also shortens the thermal entry length. It is also found that Joule heating in the fluid may cause a reversal of the heat flux, and that the thermal entry length has a linear dependence on the Reynolds number and the hydraulic diameter and on the logarithm of the nondimensional Joule heating.

Highlights

Fundamental research on microchannels has given rise to a vast body of studies ever since the seminal work by Tuckerman and Pease almost four decades ago [1]
It is highlighted how smoothing the corners increases the value of the local Nusselt number, with increases up to 18% over sharp corners, but that it shortens the thermal entry length
Knowledge acquired over the years allowed microchannels to establish themselves as the building blocks of so-called micro-flow devices (MFDs), as can be realized by comparing older reviews on the subject [2,3], to more recent ones [4,5,6], a fact recognized by the Tuckerman and Pease themselves in a retrospective article published in 2012 [7]

Summary

Introduction

Fundamental research on microchannels has given rise to a vast body of studies ever since the seminal work by Tuckerman and Pease almost four decades ago [1]. Microchannel heat sinks, a subset of MHXs, have great applicative potential where removal of high heat fluxes is in demand. This makes them interesting for the thermal management of electronic devices, which are steadily growing in compactness and, as a consequence, in power density. Pressure drop across such devices, may be significant, especially when liquids are employed as coolants, with the reduction in hydraulic diameter of the ducts quickly leading to viscous heating of the fluid circulated [23] which reverses the direction of the heat flow

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