Investigation of heat transfer in rectangular microchannels

Abstract

An experimental investigation was conducted to explore the validity of classical correlations based on conventional-sized channels for predicting the thermal behavior in single-phase flow through rectangular microchannels. The microchannels considered ranged in width from 194 μm to 534 μm, with the channel depth being nominally five times the width in each case. Each test piece was made of copper and contained ten microchannels in parallel. The experiments were conducted with deionized water, with the Reynolds number ranging from approximately 300 to 3500. Numerical predictions obtained based on a classical, continuum approach were found to be in good agreement with the experimental data (showing an average deviation of 5%), suggesting that a conventional analysis approach can be employed in predicting heat transfer behavior in microchannels of the dimensions considered in this study. However, the entrance and boundary conditions imposed in the experiment need to be carefully matched in the predictive approaches.

Introduction

Heat transfer in microchannels has been studied in a number of investigations, and has been compared and contrasted with the behavior at “conventional” (i.e., larger-sized) length scales. However, there have been wide discrepancies between different sets of published results. Measured heat transfer coefficients have either well exceeded [1], or fallen far below [2], [3], those predicted for conventional channels. The Reynolds number at which the thermal behavior indicates a transition from laminar to turbulent flow has also differed widely in these studies. Possible reasons advanced to account for the deviation from classical theory have included surface roughness [4], electrical double layer [5] and aspect ratio [6] effects. The capability of Navier–Stokes equations to adequately represent the flow and heat transfer behavior in microchannels has been called into question in some of these studies.

Tuckerman and Pease [7] first suggested the use of microchannels for high heat flux removal; this heat sink is simply a substrate with numerous small channels and fins arranged in parallel, such that heat is efficiently carried from the substrate into the coolant. Their study was conducted for water flowing under laminar conditions through microchannels machined in a silicon wafer. Heat fluxes as high as 790 W/cm² were achieved with the chip temperature maintained below 110 °C. Peng et al. [2], [8] experimentally investigated the flow and heat transfer characteristics of water flowing through rectangular stainless steel microchannels with hydraulic diameters of 133–367 μm at channel aspect ratios of 0.33–1. Their fluid flow results were found to deviate from the values predicted by classical correlations and the onset of transition was observed to occur at Reynolds numbers from 200 to 700. These results were contradicted by the experiments of Xu et al. [9] who considered liquid flow in 30–344 μm (hydraulic diameter) channels at Reynolds numbers of 20–4000. Their results showed that characteristics of flow in microchannels agree with conventional behavior predicted by Navier–Stokes equations. They suggested that deviations from classical behavior reported in earlier studies may have resulted from errors in the measurement of microchannel dimensions, rather than any microscale effects.

More recent studies have confirmed that the behavior of microchannels is quite similar to that of conventional channels. Liu and Garimella [10] showed that conventional correlations offer reliable predictions for the laminar flow characteristics in rectangular microchannels over a hydraulic diameter range of 244–974 μm. Judy et al. [11] made extensive frictional pressure drop measurements for Reynolds numbers of 8–2300 in 15–150 μm diameter microtubes. They used three different fluids, two tube materials, and two different tube cross-section geometries. No significant deviation from macroscale flow theory was revealed from their measurements. They concluded that if any non-Navier–Stokes flow phenomena existed, their influence was masked by experimental uncertainty.

Popescu et al. [12] conducted heat transfer experiments under laminar flow conditions at Reynolds numbers of 300–900 using very shallow channels, which were 10 mm wide and 128–521 μm deep. Their results showed small to non-existent departure from macroscale predictions. Although deviations were observed for the smallest channel size studied, the paucity of data under these conditions precluded firm conclusions from being drawn. Harms et al. [13] studied convective heat transfer of water in rectangular microchannels of 251 μm width and 1000 μm depth. In the laminar regime of Reynolds number investigated, the measured local Nusselt numbers agreed well with classical developing-flow theory. Qu and Mudawar [14] performed experimental and numerical investigations of pressure drop and heat transfer characteristics of single-phase laminar flow in 231 μm by 713 μm channels. Good agreement was found between the measurements and numerical predictions, validating the use of conventional Navier–Stokes equations for microchannels.

Other studies have considered the turbulent regime. Adams et al. [15] investigated single-phase forced convection of water in circular microchannels of diameter 0.76 and 1.09 mm. Their experimental Nusselt numbers were significantly higher than those predicted by traditional large-channel correlations, such as the Gnielinski [16] correlation. Adams et al. [17] extended this work to non-circular microchannels of larger hydraulic diameters, greater than 1.13 mm. All their data for the larger diameters were well predicted by the Gnielinski [16] correlation, leading them to suggest a hydraulic diameter of approximately 1.2 mm as a lower limit for the applicability of standard turbulent single-phase Nusselt-type correlations to non-circular channels.

Recent reviews of the state of the art [18], [19] indicate that before predictions of flow and heat transfer rates in microchannels can be made with confidence, careful experiments are needed to resolve the discrepancies in the literature and to provide practical information on the design of microchannel heat sinks.

The present work complements the detailed flow field and pressure drop measurements of Liu and Garimella [10]. A systematic investigation is conducted of single-phase heat transfer in microchannels of hydraulic diameters ranging from 318 to 903 μm, at flow Reynolds numbers of 300–3500. An important focus of this work is to examine the validity of conventional correlations and numerical analysis approaches in predicting the heat transfer behavior in microchannels, for correctly matched inlet and boundary conditions.