Circular micro-channel

Acikalin T, Wait S, Garimella S, Raman A (2004) Experimental investigation of the thermal performance of piezoelectric fans. Heat Transfer Eng 25 4-14 Adams TM, Abdel-Khalik SI, Jeter SM, Qureshi ZH (1998) An experimental investigation of single-phase forced convection in micro-channels. Int J Heat Mass Transfer 41 851-857 Adams TM, Dowling ME, Abdel-Khalik SI, Jeter SM (1999) Applicability of traditional turbulent single phase forced convection correlations to non-circular micro-channels. Int J Heat Mass Transfer 42 4411 415... 

Table 3.5 Critical Reynolds number in circular micro-channels...

Table 4.2 Smooth circular micro-channels experimental conditions ...

Fig. 4.2a-c Circular micro-channels, (a) = 125.4—500 om. Test section used by Lelea et... 

Adams et al. (1998) investigated turbulent, single-phase forced convection of water in circular micro-channels with diameters of 0.76 and 1.09 mm. The Nusselt numbers determined experimentally were higher than those predicted by traditional Nusselt number correlations such as the Gnielinski correlation (1976). The data suggest that the extent of enhancement (deviation) increases as the channel diameter decreases. Owhaib and Palm (2004) investigated the heat transfer characteristics... 

Hetsroni et al. (2005) evaluated the effect of inlet temperature, channel size and fluid properties on energy dissipation in the flow of a viscous fluid. For fully developed laminar flow in circular micro-channels, they obtained an equation for the adiabatic increase of the fluid temperature due to viscous dissipation ... 

The objectives of the study by Kawahara et al. (2002) were to experimentally investigate the probability of appearance of different flow patterns in a circular micro-channel. The test section was a circular transparent channel made of fused silica with an internal diameter of 100 pm and length of 64.5 mm, providing an L/d ratio of 645. 

Sairson S, Wongwises S. The effects of channel diameter on flow pattern, void fraction and pressure drop of two-phase air-water flow in circular micro-channels. Exp. Thermal Fluid Sci. 2010 34(4) 454-462. 

Chapter 4 is devoted to single-phase heat transfer. Data on heat transfer in circular micro-tubes and in rectangular, trapezoidal and triangular ducts are presented. Attention is drawn to the effect of energy dissipation, axial conduction and wall roughness on the thermal characteristics of flow. Specific problems connected with electro-osmotic heat transfer in micro-channels, three-dimensional heat transfer in micro-channel heat sinks and optimization of micro-heat exchangers are also discussed. 

The CHF correlation (2.18) was developed by Qu and Mudawar (2004) for water in a rectangular micro-channel heat sink, as well as Bowers and Mudawar s CHF data (1994) for R-113 in a circular mini/micro-channel heat sink. 

Figure 2.48 compares the predictions of this correlation with the flow boiling CHF data for water both in the rectangular micro-channel heat sink (Qu and Mudawar 2004) and in the circular mini/micro-channel heat sinks (Bowers and Mudawar 1994). The overall mean absolute error of 4% demonstrates its predictive capability for different fluids, circumferential heating conditions, channel geometries, channel sizes, and length-to-diameter ratios. 

We consider the problem of liquid and gas flow in micro-channels under the conditions of small Knudsen and Mach numbers that correspond to the continuum model. Data from the literature on pressure drop in micro-channels of circular, rectangular, triangular and trapezoidal cross-sections are analyzed, whereas the hydraulic diameter ranges from 1.01 to 4,010 pm. The Reynolds number at the transition from laminar to turbulent flow is considered. Attention is paid to a comparison between predictions of the conventional theory and experimental data, obtained during the last decade, as well as to a discussion of possible sources of unexpected effects which were revealed by a number of previous investigations. 

We begin the comparison of experimental data with predictions of the conventional theory for results related to flow of incompressible fluids in smooth micro-channels. For liquid flow in the channels with the hydraulic diameter ranging from 10 m to 10 m the Knudsen number is much smaller than unity. Under these conditions, one might expect a fairly good agreement between the theoretical and experimental results. On the other hand, the existence of discrepancy between those results can be treated as a display of specific features of flow, which were not accounted for by the conventional theory. Bearing in mind these circumstances, we consider such experiments, which were performed under conditions close to those used for the theoretical description of flows in circular, rectangular, and trapezoidal micro-channels. 

The data on critical Reynolds numbers in micro-channels of circular and rectangular cross-section are presented in Tables 3.5 and 3.6, respectively. We also list geometrical characteristics of the micro-channels and the methods used for determination of the critical Reynolds number. 

For the most part of the experiments one can conclude that transition from laminar to turbulent flow in smooth and rough circular micro-tubes occurs at Reynolds numbers about RCcr = 2,000, corresponding to those in macro-channels. Note that other results were also reported. According to Yang et al. (2003) RCcr derived from the dependence of pressure drop on Reynolds number varied from RCcr = 1,200 to RCcr = 3,800. The lower value was obtained for the flow in a tube 4.01 mm in diameter, whereas the higher one was obtained for flow in a tube of 0.502mm diameter. These results look highly questionable since they contradict the data related to the flow in tubes of diameter d> mm. Actually, the 4.01 mm tube may be considered... 

Thus, the available data related to transition in circular micro-tubes testify to the fact that the critical Reynolds number, which corresponds to the onset of such transition, is about 2,000. The evaluation of critical Reynolds number in irregular micro-channels will entail great difficulty since this problem contains a number of characteristic length scales. This fact leads to some vagueness in definition of critical Reynolds number that is not a single criterion, which determines flow characteristics. 

Estimation of adiabatic increase in the liquid temperature in circular micro-tubes with diameter ranging from 15 to 150 pm, under the experimental conditions reported by Judy et al. (2002), are presented in Table 3.7. The calculations were carried out for water, isopropanol and methanol flows, respectively, at initial temperature Tin = 298 K and v = 8.7 x 10" m /s, 2.5 x 10 m /s, 1.63 x 10 m /s, and Cp = 4,178 J/kgK, 2,606J/kgK, 2,531 J/kgK, respectively. The lower and higher values of AT/Tm correspond to limiting values of micro-channel length and Reynolds numbers. Table 3.7 shows adiabatic heating of liquid in micro-tubes can reach ten degrees the increase in mean fluid temperature (Tin -F Tout)/2 is about 9 °C, 121 °C, 38 °C for the water d = 20 pm), isopropanol d = 20 pm) and methanol d = 30 pm) flows, respectively. 

The analysis of the behavior of the fluid temperature and the Nusselt number performed for a circular tube at the thermal wall boundary condition 7(v = const, also reflects general features of heat transfer in micro-channels of other geometries. 

Heat transfer in micro-channels occurs under superposition of hydrodynamic and thermal effects, determining the main characteristics of this process. Experimental study of the heat transfer in micro-channels is problematic because of their small size, which makes a direct diagnostics of temperature field in the fluid and the wall difficult. Certain information on mechanisms of this phenomenon can be obtained by analysis of the experimental data, in particular, by comparison of measurements with predictions that are based on several models of heat transfer in circular, rectangular and trapezoidal micro-channels. This approach makes it possible to estimate the applicability of the conventional theory, and the correctness of several hypotheses related to the mechanism of heat transfer. It is possible to reveal the effects of the Reynolds number, axial conduction, energy dissipation, heat losses to the environment, etc., on the heat transfer. 

A variety of studies can be found in the literature for the solution of the convection heat transfer problem in micro-channels. Some of the analytical methods are very powerful, computationally very fast, and provide highly accurate results. Usually, their application is shown only for those channels and thermal boundary conditions for which solutions already exist, such as circular tube and parallel plates for constant heat flux or constant temperature thermal boundary conditions. The majority of experimental investigations are carried out under other thermal boundary conditions (e.g., experiments in rectangular and trapezoidal channels were conducted with heating only the bottom and/or the top of the channel). These experiments should be compared to solutions obtained for a given channel geometry at the same thermal boundary conditions. Results obtained in devices that are built up from a number of parallel micro-channels should account for heat flux and temperature distribution not only due to heat conduction in the streamwise direction but also conduction across the experimental set-up, and new computational models should be elaborated to compare the measurements with theory. 

Kroeker CJ, Soliman HM, Ormiston SJ (2004) Three-dimensional thermal analysis of heat sinks with circular cooling micro-channels. Int J Heat Mass Transfer 47 4733 744 Lee PS, Garimella SV, Liu D (2005) Investigation of heat transfer in rectangular micro-channels. Int J Heat Mass Transfer 48 1688-1704... 

Me et al. (2006) addressed the differences in gas-liquid two-phase flow characteristics that occur in conventional size channels and micro-channels by examining the two-phase flow pattern, interfacial wave, void fraction and friction pressure drop data obtained in circular and rectangular channels with a hydraulic diameter ranging from 50 pm to 6.0 mm. 

Parameters 7c,onb, s.onb, and 74,onb change in the range of 0 < 7 < 1. They account for a specific temperature field in heated micro-channels and are criteria for the relative micro-channel length. Note, if 7 < 1 the value of parameter 7 is significantly less than unity. The paper by Celata et al. (1997) reports the results of experimental research of the onset of subcooled water boiling in the circular... 

Hwan and Kim (2006) investigated the pressure drop in circular stainless steel tubes with inner diameter of 244, 430, and 792 pm. These data show that mass flux strongly affects two-phase pressure drop in micro-channels of different diameters. 

The convective and nucleate boiling heat transfer coefficient was the subject of experiments by Grohmann (2005). The measurements were performed in microtubes of 250 and 500 pm in diameter. The nucleate boiling metastable flow regimes were observed. Heat transfer characteristics at the nucleate and convective boiling in micro-channels with different cross-sections were studied by Yen et al. (2006). Two types of micro-channels were tested a circular micro-tube with a 210 pm diameter, and a square micro-channel with a 214 pm hydraulic diameter. The heat transfer coefficient was higher for the square micro-channel because the corners acted as effective nucleation sites. 

Effectively, Eqs. (86) and (87) describe two interpenetrating continua which are thermally coupled. The value of the heat transfer coefficient a depends on the specific shape of the channels considered suitable correlations have been determined for circular or for rectangular channels [100]. In general, the temperature fields obtained from Eqs. (86) and (87) for the solid and the fluid phases are different, in contrast to the assumptions made in most other models for heat transfer in porous media [117]. Kim et al. [118] have used a model similar to that described here to compute the temperature distribution in a micro channel heat sink. They considered various values of the channel width (expressed in dimensionless form as the Darcy number) and various ratios of the solid and fluid thermal conductivity and determined the regimes where major deviations of the fluid temperature from the solid temperature are found. 

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