Heat Convection in Micro Ducts

The last decade of the twentieth century has witnessed an impressive progress in micromachining technology enabling the fabrication of micron-sized devices, which become more prevalent both in commercial applications and in scientific research. These microsystems have had a major impact on many disciplines, e.g. biology, chemistry, medicine, optics, aerospace, mechanical and electrical engineering. This emerging field not only provides miniature transducers for sensing and actuation in a domain that we could not examine in the past but also allows us to venture into a research area in which the surface effects dominate most of the physical phenomena [62]. Fundamental heat-transfer problems posed by the development and processing of advanced Integrated Circuits (ICs) and MicroElectroMechanical Systems (MEMS) are becoming a major consideration in the design and application of these microsystems. The demands on heat removal and temperature control in modern devices, with highly transient thermal loads, require new techniques for providing high cooling rates and uniform temperature distributions. Thus, thorough understanding of the physical mechanisms dominating microscale heat transfer is vital for continuous evolution and progress of microdevices and microsystems.

In the science of thermodynamics, which deals with energy in its various forms and with its transformation from one form to another, two particularly important transient forms are defined: work and heat. These energies are termed transient since, by definition, they exist only when there is an exchange of energy between two systems or between a system and its surrounding. When such an exchange takes place without the transfer of mass to/from the system and not by means of a temperature difference, the energy is said to be transferred through the performance of work. If the exchange of energy between the systems is the result of temperature difference, the exchange is said to be accomplished via the transfer of heat. The existence of a temperature difference is the distinguishing feature of the energy exchange form known as heat transfer. MicroChannel heat sinks or micro heat pipes are a class of devices that can be applied for the transfer of thermal energy from very small areas.

The continuity, momentum and energy differential equations derived based on the fundamental conservation laws provide a comprehensive description of convective heat transfer. These equations, however, are so complicated that they present insurmountable mathematical difficulties. Very few exact solutions to these equations have been found, which represent very simple flow systems. Hence, the development of convective heat transfer has depended heavily on experimental research, and solutions of real problems usually involve a combination of analytical and experimental information.

Fabrication of thermal microsystems involves techniques that were initially developed for the fabrication of integrated circuits (ICs) and later extended to the fabrication of microelctromechanical systems (MEMS). Analytical and experimental aspects of these techniques have been presented in great detail in many books and, therefore, will not be discussed here. However, the fabrication of thermal microsystem for either commercial applications or microscale heat transfer research imposes contradicting demands. This challenge can be met by utilizing standard microfabrication technologies in a unique and innovative approach. Therefore, only processes and techniques developed and used specifically for the fabrication of the two case studies, i.e. microchannel heat sinks and micro heat pipes, will be described hereafter.

Quantitative analysis of heat convection requires measurements of the relevant physical properties. Some integral properties, such as flow rate, can be measured by external means. However, local properties, such as temperature distribution, can be measured with adequate resolution and accuracy only by utilizing integrated sensors. A variety of microsensors have been developed for the study of heat transfer. In this chapter, two examples of microsensors will be described: thermoresistors for temperature distribution and capacitive sensors for void fraction measurements.

Flows completely bounded by solid surfaces are called internal flows, and they include flows through ducts, pipes, nozzles, diffusers, etc. External flows are flows over bodies in an unbounded fluid. Flows over a plate, a cylinder or a sphere are examples of external flows, and they are not within the scope of this chapter. Only internal flows, in either liquid or gas phase, in micro ducts will be discussed emphasizing size effects, which may potentially lead to a different behaviour in comparison with similar flows in macro ducts. For the practical application of single-phase heat convection in micro-ducts, e.g. heat exchangers, the friction factor and the heat transfer coefficient are the parameters of prime interest. As long as material properties, such as viscosity, are nearly constant over the temperature range of operation, the friction factor can be predicted analytically without invoking the energy equation. The extensive experimental and theoretical research has matured to a point where the size effects are well understood. Unfortunately, this is not the case with respect to the heat transfer coefficient, mainly due to lack of reliable experimental data needed to confirm or refute the numerous theoretical analyses and numerical simulations.

Convective boiling is defined as the addition of heat to a flowing liquid in such a way that generation of vapour occurs while, conversely, convective condensation is defined as the removal of heat from the fluid in such a way that vapour is converted into liquid. This definition, therefore, excludes the process of flashing where vapour generation occurs solely as the result of a reduction in flow pressure. However, in many systems, the two processes do occur simultaneously and, hence, cannot be clearly distinguished. This chapter will be concerned with only single-component microsystems, i.e. a pure liquid and its vapour. Furthermore, much of the information presented will be devoted to one such system, namely the water/steam system. Many other fluid systems of industrial importance, however, involve the use of multi-component systems such as refrigerants, organic liquids, cryogenic liquids and liquid metals. Very limited information is available on the processes of boiling and condensation with multi-component macrosystems and practically none with multi-component microsystems.

The classification between steady and unsteady convective boiling in internal flows refers only to the controlled parameters such as heat flux or mass flow rate. Single-phase heat convection flows under steady boundary conditions are expected to be steady, especially in microsystems as discussed in Chapter 6, in the sense that all flow properties are constant in time and may vary only in space. However, some properties of two-phase forced convection flow, under steady heating, may not be steady such as the oscillations of the liquid-vapour interface discussed in Chapter 7. Then, even if all boundary conditions are steady, some flow properties may vary in space and time due to flow instabilities that develop within the system. In this context, unsteady convective heat transfer to be discussed hereafter refers to controlled variations of certain parameters with respect to time. In particular, the response of the microsystem to a step or a periodic change of one of the input parameters is of interest as in control theory. Experimental and analytical studies of unsteady heat convection in microducts have just begun and some preliminary results are discussed [84,176].

The concept of combining phase-change heat transfer and microfabrication techniques to construct micro heat pipes for the dissipation of heat is due to Cotter [34]. Since the introduction of this idea, the proposed applications of micro heat pipes have expanded from the thermal control of localized heat generating devices such as laser diodes and infrared detectors to the removal of heat from the leading edges of stator vanes in turbines or the leading edges of hypersonic aircrafts. While not all the suggested applications have materialized, micro heat pipes have been fabricated, modelled and analysed. The larger of these systems have been implemented in commercially available products such as laptop computers or highprecision equipment. Indeed, most of the research work is still devoted to cooling of semiconductors chips. Micro heat pipes are used to eliminate hot spots, reduce temperature gradients, and improve chip reliability. The high power level currently possible, on the order of 100W/cm², together with the heat pipes being self-contained and self-starting make micro heat pipes an ideal heat transfer system. Furthermore, the introduction of newly developed CMOS-compatible techniques to integrate such thermal microsystems with microelectronic devices will surely enhance their range of applications.