细管内的传热和压降

Appendix A. Heat Transfer and Pressure Drop in Small Scale Channels 223 Appendix A Literature – Heat Transfer and Pressure Drop in Small-Scale Channels Table of Contents A.1. Introduction ..........................................................................................223 A.2. Some Published Papers ......................................................................224 A.2.1. Appearing in 1992...........................................................................224 A.2.2. Appearing in 1994...........................................................................224 A.2.3. Appearing in 1995...........................................................................224 A.2.4. Appearing in 1996...........................................................................225 A.2.5. Appearing in 1997...........................................................................225 A.2.6. Appearing in 1999...........................................................................226 A.2.7. Appearing in 2000...........................................................................227 A.2.8. Appearing in 2001...........................................................................227 A.3. Tabular Summary of Literature Cited .................................................232 A.4. Discussion of Literature ......................................................................235 A.5. Conclusion............................................................................................235 A.6. References............................................................................................236 A.1. Introduction Research in the heat transfer, pressure drop, and flow characteristics in small scale channels and tubes have become increasingly important for the continuation of technological advances in a wide variety of scientific and engineering fields. These fields include amongst many others, biotechnology, aerospace, mechatronics and micro devices, miniaturisation of systems, compact fission reactor cores, medical applications, and thermal control of electronic devices. Small-scale tubes and channels, being smaller than conventional tubes and pipes are defined in terms of the hydraulic diameter. Conventional sized channels and tubes have a hydraulic diameter greater than 3 mm. Minichannels have hydraulic diameters of between 200 �m and 3 mm while microchannels range between 10 �m and 200 �m [1]. A large proportion of current research involving small-scale tubes is done with the electronics industries in mind. Increased integration and miniaturisation of electronic components and Appendix A. Heat Transfer and Pressure Drop in Small Scale Channels 224 devices has made it necessary to improve heat extraction from, and thermal management methods applied to these devices and components. In the early 1980’s Tuckermann and Pease [2] introduced the concept of microchannel heat sinks. It was demonstrated that laminar flow in micro rectangular channels has higher heat extraction abilities than turbulent flow in conventional sized flow channels. This discovery opened up an entire new research field and it was followed by many more studies conducted by various authors. The following section gives a description of some research done in the field of heat transfer and pressure drop characteristics at small scales. A.2. Some Published Papers A.2.1. Appearing in 1992 A paper by Weisberg and Bau [3] was published which report was given on the optimisation of the thermal performance of a microchannel heat sink. The objective of the study was to check the validity of the various approximations employed by previous researchers, to obtain relevant heat transfer correlations and devise an algorithm for the design of compact heat exchangers. Focus was places on flat plate heat exchangers. By solving conjugate heat transfer problems numerically, the approximations used by previous researchers were eliminated. In the model that was used by Weisberg and Bau, the axial conduction in both the wall and fluid was neglected. The temperature distribution in the liquid and the solid was computed for 9 channel geometries. A.2.2. Appearing in 1994 Bowers and Mudawar [4] published a paper concerned with high flux boiling in low flow rate, low pressure drop minichannel and microchannel heat sinks. An experimental study of pressure drop and convective heat flux in minichannel and microchannel heat sinks of 1 cm heated length was performed on R-113. The diameters of the minichannels and microchannels were 2.54 mm and 510 �m. It was found that overall, the minichannel’s performance proved to be superior to the microchannel due to lower pressure drops and the reduced likelihood of clogging and the relative ease in fabrication. A.2.3. Appearing in 1995 A paper by Harley et al. [5] appeared in which report was given of an experimental and theoretical investigation of low Reynolds number, high subsonic Mach number, compressible gas flow in microchannels. It was found that the measured friction factor was in good agreement with theoretical predictions assuming isothermal, locally fully developed first-order, slip flow. A numerical simulations indicated that the pressure may be assumed to be uniform in the conduit cross-sections perpendicular to the direction of the flow and that the traverse velocity can be neglected. In all the experiments, the Knudsen number was less than 0.38 and the data were within 8% of theoretical predictions of the friction. A paper by Peng et al. [6] appeared reporting on an experimental study which was conducted in order to determine the heat transfer characteristics of single-phase forced convection, and nucleate boiling of methanol in parallel rectangular shaped microgrooves. Six different groove configurations with different aspect ratios and a variety of centre-to-centre spacing were evaluated. It was found that the liquid velocity, liquid subcooling, liquid properties and geometry of the microchannels all have significant influence on the heat transfer performance, Appendix A. Heat Transfer and Pressure Drop in Small Scale Channels 225 cooling characteristics and liquid flow mode transition. The heat transfer characteristics performance and cooling characteristics were enhanced as the channel number increased and the size of the microchannel approached some optimal geometry. Peng and Peterson [7] published a paper concerned with the effect of thermo fluid and geometrical parameters on convection of liquids through rectangular microchannels. Test were conducted on 4 test sections, using both water and methanol as working fluids. They came to the conclusion that the experimental results indicated that the liquid convection characteristics are quite different from those observed in conventionally sized channels. It was found that the range of the transition zone, and the heat transfer characteristics of both the transition and the laminar flow regimes, were strongly affected by the liquid temperature, liquid velocity and microchannel size, and hence were not only determined by the Reynolds number. Evidence was presented to support the existence of an optimum channel size in terms of the forced convection flow heat transfer in a single-phase liquid flowing in a rectangular microchannel. A.2.4. Appearing in 1996 Peng and Peterson [8] published a paper concerning an experimental investigation which done on single-phase forced convective heat transfer and flow characteristics of water in microchannel structures/plates with small rectangular channels having hydraulic diameters of 0.133-0.343 mm. The aim of the work was to determine the effects of the geometric configuration on the flow and heat transfer and to further develop heat transfer and flow friction correlations. Twelve different microchannel structure configurations were evaluated. Heat was applied from the sides and bottom of the channels. It was observed that for channels as small as those evaluated in the investigation, the shape of the channel played a negligible role on friction for both the laminar and turbulent flow conditions. It was however found that laminar heat transfer was dependent on the aspect ratio and the ratio of the hydraulic diameter to the centre-to-centre distance in the microchannels. The turbulent heat transfer was found to be a further function of a new dimensionless variable. The optimum configuration for turbulent heat transfer, regardless of the groove aspect ratio, was found to exist at particular value of the new dimensionless variable. When compared with predictions of classical relationships, it was found that the measured turbulent flow resistance was usually smaller, and the Reynolds number for the transition to fully developed turbulent flow became much smaller than with ordinary channel flow. It was observed that for a given plate with the same size and number of channels, the convection heat transfer from the two sides of the channel in the centre section of the plate decreases as the centre-to- centre distance is decreased. Correlations for the prediction of Nusselt and friction factor for single phase liquid laminar and turbulent flow were proposed. Deviations of predicted Nusselt numbers from experimental values were reported to have been ±30% and ±25 for laminar and turbulent flow respectively. A.2.5. Appearing in 1997 Adams et al. [9] reported on an experimental study of single-phase forced convection in microchannels. Turbulent flow of water in circular channels with diameters of 0.76 mm and 1.09 mm were investigated. It was noted that most of previous studies by various authors involved rectangular channels and that the effects of aspect ratio was not isolated. It was also Appendix A. Heat Transfer and Pressure Drop in Small Scale Channels 226 noted that even though gap sizes in these studies were often small fractions of a millimetre, the width of the passages were much larger. The opinion was raised that at that in general at that stage there seemed to be a lack of reliable data on turbulent single-phase convection in circular microchannels. The data which was obtained from their experiments showed that the Nusselt numbers for the microchannels are higher than those predicted by traditional large channel correlations. Based on the data, along with previously obtained data for smaller diameter channels, a generalised correlation for the Nusselt number for turbulent, single-phase, forced convection in circular microchannels was developed. Accommodation was given for this enhancement caused by the small microchannel diameters and the correlation was in the format of a modified Gnielinski correlation. Resulting predictions had a confidence level of 95% while, differences between experimental and predicted Nusselt numbers values were les than ±18.6%. A.2.6. Appearing in 1999 A paper by Adams et al. [10] appeared in which the role of the release of dissolved noncondensibles might have been playing in the enhancement of liquid forced convection heat transfer in microchannels. It was noted that dissolved condensables usually undergo little release in large channels. In microchannels, however, due to the typically large axial pressure gradients, significant desorption of dissolved noncondensables may take place, leading to the development of a gas-liquid two-phase flow with enhanced velocity and convection heat transfer characteristics. An experimental investigation was conducted on a long heated microchannel subject to subcooled liquid forced convection. The convection heat transfer coefficients near the exit of the copper microchannel with 0.76 mm inner diameter and 16 cm heated length, subject to forced-flow cooling by subcooled water were measured. It was found that the convection heat transfer coefficients obtained with degassed water were systematically under predicted by the widely-used Dittus Boelter correlation for turbulent pipe flow. It was observed that the presence of dissolved air in water could increase the heat transfer coefficients by as much as 17%, despite the fact that the maximum increase in the coolant velocity due to the noncondensable gas release was only a few percent. A paper by Harms et al. [11] appeared reporting experimental results for single phase forced convection of water in deep rectangular microchannels. Two configurations were tested, a single channel system with a hydraulic diameter of 1.923 mm, and a multiple channel system with 68 channels and hydraulic diameters of 0.404 mm. It was found that the experimentally obtained Nusselt numbers agreed reasonable well with classically developed channel flow theory. Furthermore, it was observed that in terms of flow and heat transfer characteristics, the microchannel system designed and used for developing flow, outperformed the comparable single channel system designed for turbulent flow. Mala and Li [12] published on flow characteristics of water flow through. Experimental investigations were done on 13 microchannels with diameters ranging from 50 �m to 254 �m. Pressure drops and flow rates were measured to analyse the flow characteristics. It was found that the experimental results indicated significant departure of flow characteristics from the predictions of conventional theory. For microtubes with large diameters, the experimental results were found to be in rough agreement with the conventional theory. The friction factor was Appendix A. Heat Transfer and Pressure Drop in Small Scale Channels 227 observed to be higher than that given in conventional theory. A roughness viscosity model was proposed to interpret the experimental data. A.2.7. Appearing in 2000 Qu et al. [13] published a paper concerned with heat transfer in trapezoidal microchannels. Experiments were conducted on water flowing through trapezoidal silicon microchannels with a hydraulic diameters which ranged from 62 �m to 169 �m. A numerical analysis was carried out by solving the conjugate heat transfer problem of the temperature field in both the solid and the fluid regions. The results obtained indicated that the experimental determined Nusselt number is much lower than that given by the numerical analysis. It was suspected that the lower measured Nusselt numbers might have been due to the effects of surface roughness of the microchannel walls. Based on the a roughness-viscosity model established in previous work, a modified relation which accounts for the roughness-viscosity effects was proposed to interpret the experimental results. Good agreement between the experimental data and the predictions from the modified relationships was found to exist. Rahman [14] published on measurements of heat transfer in microchannel heat sinks. Two different channel patterns were studies, parallel and series. The parallel pattern distributed the fluid through several parallel passages between the inlet and outlet headers located at the two ends of standard silicon wafers. The series pattern carries the fluid through a longer winding channel between the inlet and the outlet headers. Channels of different depths (or aspect ratios) were studied. Tests were carried out using water as the working fluid. The flow rate, pressure and temperature of the fluid at the inlets and the outlets and the temperature at several locations in the wafer were measured. These measurements were used to calculate local and average Nusselt number and coefficient of friction in the device for different flow rate, channel size, and channel configuration. It was concluded that the results showed that the measured values of average Nusselt number are usually larger than those predicted by correlations for larger sized channels. The larger heat transfer is believes to be caused by the breakage of velocity boundary layer by surface roughness associated with etched channel structure. The transition from laminar to turbulent was somewhat gradual because of small channel dimensions. A.2.8. Appearing in 2001 Ghiaasiaan and Laker [15] published a paper in which the opposing trends in published data dealing with turbulent flow friction and heat transfer coefficients in microchannels, and their disagreement with macroscale correlations were discussed. The authors came to the conclusion that experimental data that were available in literature dealing with turbulent flow in microchannels were inconsistent, some indicated higher friction factors and heat transfer coefficients than what is predicted by macroscale theory correlations, while others indicated an opposite trend. The origin of these disagreements was unknown, and it was suspected that it might have been the result of a multiple of mechanisms. It was suggested that suspended microscopic particles might be a major contributor to the disagreement in published data. Jiang et al. [16] reported on an experimental investigation conducted involving fluid flow and forced convection heat transfer in micro-heat-exchangers with either micro-channels or porous Appendix A. Heat Transfer and Pressure Drop in Small Scale Channels 228 media. Water was used as fluid. The influence of the dimensions of the microchannels on the heat transfer performance was first analysed numerically. Six different channel depths were analyses while maintaining a constant channel width and offset. Heat flux was applied to both the top and bottom of channels. Based on these computations, deep microchannels were used for the experimental investigation due to its higher ratio of volumetric heat transfer coefficient and the pressure drop. It was found that over the range of test conditions, the maximum volumetric heat transfer coefficient of the micro-heat-exchanger with porous media was more than twice the maximum volumetric heat transfer coefficient when microchannels were used. Although when considering both the heat transfer and pressure drop characteristics of the heat exchangers, it was found that the deep microchannel-design offers better overall performance than either the porous media or the shallow microchannel alternatives. Appearing in 2002 A paper by Brutin et al. [17] appeared reporting on an experimental study performed on two- phase flow and heat transfer in capillaries. It was observed that convective boiling in confined geometries such as capillaries may under specific conditions display unsteady behaviour. The aim of their study was to understand the different types of two-phase flow behaviour through experiments and physical models. A rectangular channel configuration with a hydraulic diameter of 889 �m were investigated. It was shown that when instabilities develop, wall temperatures increased and average heat transfer coefficients decreased. A relationship that defines the transition between the steady and unsteady zones in a non-dimensional diagram was proposed. Wen et al. [18] reported on flow boiling of water in a narrow vertical channel, with the focus on local phenomena at low mass flux. A channel that had dimensions of 1 mm by 2 mm was used. Measurements of pressure, temperature, heat flux and heat transfer coefficient fluctuations and simultaneous video recordings are compared with previous observations at higher mass fluxes. Gao et al. [19] published a paper which was devoted to the experimental investigation of the flow of water and the associated heat transfer and hydrodynamics in a two-dimensional small scale channel. The width of the channel was 25 mm while the height was varied to be bet