Heat transfer model for evaporation in microchannels. Part I: presentation of the model

https://doi.org/10.1016/j.ijheatmasstransfer.2004.01.006Get rights and content

Abstract

A three-zone flow boiling model is proposed to describe evaporation of elongated bubbles in microchannels. The heat transfer model describes the transient variation in local heat transfer coefficient during the sequential and cyclic passage of (i) a liquid slug, (ii) an evaporating elongated bubble and (iii) a vapor slug. A time-averaged local heat transfer coefficient is thus obtained. The new model illustrates the importance of the strong cyclic variation in the heat transfer coefficient and the strong dependency of heat transfer on the bubble frequency, the minimum liquid film thickness at dryout and the liquid film formation thickness.

Introduction

There is a growing number of experimental studies on two-phase flow and evaporation heat transfer in microchannels. A brief summary of research on evaporation in microchannels is presented here, a topic recently reviewed at length by Thome [1], Thome et al. [2], Kandlikar [3] and Bergles et al. [4]. These reviews addressed the topics of the threshold from macroscale to microscale heat transfer, two-phase flow regimes, flow boiling heat transfer results for microchannels, heat transfer mechanisms in microchannels and flow boiling prediction methods for microchannels. In contrast to macroscale evaporation, flow boiling heat transfer coefficients in microchannels have been shown experimentally to be nearly exclusively dependent on heat flux and saturation pressure while only slightly dependent on mass velocity and vapor quality. Applying macroscale ideas to the microscale, many experimental studies have concluded that nucleate boiling controls microchannel evaporation with a negligible convective evaporation contribution. Instead, a recent two-zone heat transfer model proposed by Jacobi and Thome [5] demonstrated that transient evaporation of the thin liquid films surrounding elongated bubbles is the dominant heat transfer mechanism, not nucleate boiling. Newer experimental studies have further shown that there is in fact some effect of mass velocity and vapor quality on heat transfer when covering a broader range of test conditions, including a sharp peak in the heat transfer coefficient at low vapor qualities in some cases, refer to [6], [7], [8]. Furthermore, it was concluded that macroscale models are not realistic for predicting flowing boiling coefficients in microchannels since they are based on the nucleate boiling and convective evaporation mechanisms rather than transient thin film evaporation, viz. just because an evaporation process is heat flux dependent does not mean it is nucleate boiling controlled.

As phase-change heat transfer phenomena in microscale show distinct differences from macroscale behavior, only part of the available knowledge about macroscale heat transfer can be transferred to the microscale. Several arbitrary classifications for the transition from macroscale to microscale heat transfer, based on the hydraulic diameter d for non-circular channels have been proposed. For example, Mehendale and Jacobi [9] recommend a size classification as follows: microchannels (1–100 μm), mesochannels (100 μm to 1 mm), macrochannels (1–mm) and conventional channels (d>6 mm) while Kandlikar [3] recommends the following classification and size ranges: microchannels (50–600 μm), minichannels (600 μm to 3 mm) and conventional channels (d>3 mm). Such transition criteria do not reflect the influence of channel size on the physical mechanisms. A more general definition should address the threshold where macroscale theory is no longer fully applicable with respect to the two-phase flow and heat transfer processes.

For now, this seems to suggest that the best threshold criterion is that to confined bubble flow, i.e. where bubble growth is confined by the channel such that bubbles grow in length rather than in diameter, which is referred to here as the elongated bubble regime. This is a likely condition below which macroscale heat transfer design methods become unreliable for predicting flow boiling heat transfer coefficients and two-phase flow pattern transitions; hence, this may provide a workable threshold for when to stop applying macroscale methods and to begin applying microscale design methods. Another important factor is the transition from laminar flow to turbulent flow. Essentially all macroscale prediction methods were developed from databases with turbulent flow occurring in the liquid phase, while many, but not all, microscale evaporation applications are at liquid Reynolds numbers below 2300.

While numerous types of flow patterns observations in microchannel flows are reported in the literature and several tentative flow pattern maps have been proposed, for example those by Triplett et al. [10], Serizawa and Kawara [11] and Tabatabai and Fahgri [12], additional research is required before a reliable prediction of flow pattern transition boundaries in microchannel flows is possible. For microchannel two-phase flows, since there is nearly no stratification effect and thus little orientation effect, the most important flow regimes are bubbly, elongated bubble, annular, mist and flows with partial dryout. For evaporating flows, the bubbly flow regime lifespan (that is, bubbles notably smaller than the channel size) is very short as bubbles grow to the channel size very quickly, typically within a few centimeters of tube length or less. The dominant flow regime is apparently the elongated bubble flow regime followed by the annular flow regime. As will be seen here, cyclical partial dryout is also possible in the elongated bubble regime in microchannels.

In the present study, a three-zone flow boiling model for evaporation of elongated bubbles in microchannels is presented that qualitatively and quantitatively attempts to describe all the observed heat transfer trends noted above (including the sharp peak in the heat transfer coefficient at low vapor qualities, which is shown by the present model to be caused by the local onset of dryout at the end of elongated bubbles). The turbulent versus laminar flow question is accounted for in the present model through heat transfer modeling in the liquid and vapor slugs, which is based on their local two-phase velocity and respective Reynolds numbers. An example of the microscale elongated bubble under consideration in this work is shown in Fig. 1.

Regarding applications, micro-heat exchangers, micro-cooling assemblies and thermal systems implementing such devices, referred to as micro-thermal-mechanical systems (MTMS) as opposed to micro-electronic-mechanical-systems (MEMS), are rapidly advancing to ever smaller sizes. These are used as micro-cooling elements for electronic components, portable computer chips, radar and aerospace avionics components, and micro-chemical reactors. In addition to single-phase cooling applications, numerous two-phase (evaporation) cooling applications are being identified, and current implementations are pursued without the benefit of thermal design methods. Such heuristic design methods are expensive, because they rely on extensive testing. In fact, what can now be fabricated, either by micro-machining of silicon wafers or micro-extrusion of aluminum elements, has vastly outpaced what can be thermally modeled. Moreover, while circular channels are the norm for macroscale evaporation processes, at the microscale non-circular channels are more common. For now, we limit our attention to channels with circular cross-sections. For general reviews on microchannel heat transfer for single-phase and two-phase flows, refer also to [9], [13].

Section snippets

Previous two-zone evaporation model

It is useful to review the previous two-zone heat transfer model of Jacobi and Thome [5]. They assumed a simplified physical description of the flow and proposed an analytical model to describe evaporation in microchannels in the elongated bubble flow regime, concentrating on the transient thin film evaporation mechanism in the liquid films trapped between the wall and passing bubbles. The frequency of the bubbles was obtained from the successive nucleation and growth of bubbles across the flow

Three-zone evaporation model

This model is formulated to predict the local dynamic heat transfer coefficient and the local time-averaged heat transfer coefficient at a fixed location along a microchannel during flow and evaporation of an elongated bubble at a constant, uniform heat flux boundary condition. The local vapor quality, heat flux, microchannel internal diameter, mass flow rate and fluid physical properties at the local saturation pressure are input parameters for the model. The objective of the present model is

Conclusions

A three-zone flow boiling model has been presented to describe evaporation of elongated bubbles in microchannels. The heat transfer model predicts the transient variation in local heat transfer coefficient during the cyclic passage of (i) a liquid slug, (ii) an evaporating elongated bubble and (iii) a vapor slug. The new model illustrates the importance of the strong cyclic variation in the heat transfer coefficient and the strong dependency of heat transfer on the bubble frequency, the minimum

Acknowledgements

A.M. Jacobi received partial support for this project as an ERCOFTAC Scientific Visitor to the Laboratory of Heat and Mass Transfer at the EPFL in Lausanne.

References (22)

  • A.M. Jacobi et al.

    Heat transfer model for evaporation of elongated bubble flows in microchannels

    J. Heat Transfer

    (2002)
  • Cited by (0)

    View full text