Evaporative Modeling In A Thin-Film Region of Micro-Channel

A mathematical model which can be predicted the flow and heat transfer characteristics for evaporating thin film region in micro channel is presented and an analytical investigation is performed by using the presented model. For the formulation of modeling, the flow of the vapor phase and the shear stress at the liquid-vapor interface are considered. In addition, the disjoining pressure and the capillary force which drive the liquid flow at the liquid-vapor interface in thin film region are adopted. Comparing the magnitude of capillary and disjoining pressures, the length of thin film region can be calculated. Results show that the influence of variation of vapor pressure on the liquid film flow is not negligible. It is also found that as the heat flux increases, the length of thin film region and the film thickness decrease and the local evaporative mass flux increases linearly. NOMENCLATURE In text INTRODUCTION For the reliability, high performance, and compactness of electronic devices, the technologies for dissipating the generated heat in electronic devices have been proposed and developed. Among them, the use of phase-change technique to enhance the heat transfer has been paid attention in chemical processing equipment and nuclear reactor as well as electronic cooling. The capillary heat pumps such as capillary pumped loop (CPL) system and heat pipes have been used successfully for this application. Recently, the advancement of packaging technology has led to the miniaturization (i.e. the hydraulic diameter of these devices is on the order of 100-300μm) and the increasing in density of electronics component. Therefore, it becomes more important to remove the generated heat in micro-scale devices. The micro-CPL system consists of the evaporator, condenser, vapor and liquid lines and can be applicable to the small-scale device that uses phase change to transfer thermal energy and it belongs to the application of MEMS (micro-electro-mechanical systems). When a liquid contacts a solid surface, the extended meniscus is divided into three parts; (1) the intrinsic meniscus region which is dominated by the capillary forces, (2) the evaporating thin film region which is governed by the combined effects of both capillary and disjoining pressure, and (3) the adsorbed region where the evaporation doses not occur. Among these three parts, the thin film region where the majority of heat is transferred may be the most important region. Many efforts have been devoted to establishing the analytical models and conducting the experiments for the performance of the extended meniscus on a flat plate for last two decades. Derjaguin et. al. (1965) established first the analysis of the thermo-fluid characteristics in the evaporating thin film region and showed that the effect of the solid-liquid molecular interactions on the liquid in the thin film was a pressure reduction relative to the vapor pressure in equilibrium with the thin film. Potash and Wayner (1972) studied the transport processes occurring in an evaporating extended meniscus in view of the physicochemical phenomena. They said that the liquid flows by both disjoining pressure and a change in the meniscus curvature provided the necessary pressure gradient. Mirzamoghadam and Catton (1988) investigated analytically the transport phenomena to obtain the shape of an evaporating meniscus attached to an inclined heated plate. They derived the meniscus profile by using an appropriate liquid film velocity and temperature distribution in an integral approach method. Xu and Carey (1990) conducted a combined analytical and experimental investigation of the liquid flow behavior in V-shaped microgrooves. They suggested an analytical model that predicted the heat transfer characteristics of film evaporation and found that the disjoining pressure differences may play a central role in evaporation processes. Swanson and Herdt (1992) formulated the evaporating meniscus in a capillary tube by considering the Young-Laplace equation, Marangoni convection, London-van der Waals dispersion forces, and non-equilibrium interface conditions. They found that the effect of the dispersion number (A) on the meniscus profile was very large and the liquid pressure difference increased with increasing dispersion number. Schonberg and Wayner (1992) developed an analytical model that introduced the concept of an integral heat sink. They showed that the thin film curvature approached a constant asymptotic value of the thin film joined the meniscus. Ha and Peterson (1996) developed a theoretical model for the heat transfer characteristics of the evaporating thin liquid films in V-shaped microgrooves with non-uniform input heat fluxes. The result showed that when the dispersion number and the superheat are constant, the main factor affecting the length of the evaporating interline region is the heat flux supplied to the bottom of the plate. Kobayashi et. al. (1996) investigated the evaporative heat and mass transfer phenomena in the vicinity of the liquid meniscus edge in the evaporator of a groove heat pipe theoretically and experimentally. The result showed that a large heat flux is transported in the narrow micro-region. As stated above, a number of investigations have been conducted on this region because the high heat transport rates are occurred in the process of evaporating thin film. However, most of these works neglected the effect of vapor flow (i.e. the vapor pressure was assumed to be constant) and some of them ignored the disjoining pressure effect also. The objectives of this work are to obtain the new mathematical modeling of thin film region of evaporator and to investigate the effect of the applied heat on the flow and heat transfer characteristics. The results of this work can be used as a fundamental data in design of the micro scale evaporator. MATHEMATICAL MODELING The geometrical configuration and the coordinate system for the evaporating thin film flow in a micro parallel plate are shown in Fig. 1. As the majority of the heat transfer is occurred at the thin film region due to the very thin thickness, we focus on this region for the predicting of flow and thermal characteristics. As shown in Fig. 1, we only consider the one-half of parallel plate for calculation because of the geometric symmetry. The following assumptions are employed in the derivation of the governing equations. • Steady-state, two-dimensional laminar flow δ (H/2)-δ Vapor