Correlation for microchannels

The heat flux at this condition is referred to as the critical heat flux, or CHF. It depends on the flow conditions, channel geometry, local quality, fluid properties, channel material, and flow history. Bergles and Kandlikar [8] discuss the CHF in microchannels from a systems perspective. It is important to establish CHF condition as a function of the mass flux and quality for a given system to ensure its safe operation. Qu and Mudawar [9] presented CHF data with water in 21 parallel minichannels of 215 x 821 pm cross-section over a range of G = 86—268 kg/(m s) and q" = 264-542 kW/m r = 0.0-0.56, and Fi = 121.3—139.8 kPa. Kosar et al. [5] present low-pressure water data in microchannels enhanced with reentrant cavities. Also, the correlation by Katto [10] developed for large channels may be applied for approximate CHF estimation in the absence of an established CHF correlation for microchannels. 

Flow is typically laminar in microchannel devices, although not always rigorously so. Correlations for fully developed laminar flow in perfectly rectangular microchannels have been validated in the literature [33-35]. Transition and turbulent flows in a microchannel have no such consistent treatise, and are highly dependent upon channel shape, aspect ratio, and surface characteristics [36, 37]. 

A slightly different empirical correlation for square microchannels was recently proposed by van Male et al. [89] the correlation leads to an estimated Sherwood number that is about 20% lower than that estimated by Equation (28). 

The earliest studies related to thermophysieal property variation in tube flow conducted by Deissler [51] and Oskay and Kakac [52], who studied the variation of viscosity with temperature in a tube in macroscale flow. The concept seems to be well-understood for the macroscale heat transfer problem, but how it affects microscale heat transfer is an ongoing research area. Experimental and numerical studies point out to the non-negligible effects of the variation of especially viscosity with temperature. For example, Nusselt numbers may differ up to 30% as a result of thermophysieal property variation in microchannels [53]. Variable property effects have been analyzed with the traditional no-slip/no-temperature jump boundary conditions in microchannels for three-dimensional thermally-developing flow [22] and two-dimensional simultaneously developing flow [23, 26], where the effect of viscous dissipation was neglected. Another study includes the viscous dissipation effect and suggests a correlation for the Nusselt number and the variation of properties [24]. In contrast to the abovementioned studies, the slip velocity boundary condition was considered only recently, where variable viscosity and viscous dissipation effects on pressure drop and the friction factor were analyzed in microchannels [25]. 

The application of conventional pressure drop correlations for single and dual phase flow has been examined by Yue et al. [64], They reported that the single fluid behavior still obeys classical theory in microchannels with diameters of several hundred micrometers. For dual phase flow, they proposed a modified correlation, but recognized that further research would be necessary [64],... 

Heat Transfer Correlations for Flow Boiling in Minichannels and Microchannels... 

It is necessary to remark that a large number of comparisons between experimental and theoretical results for microchannels have revealed a deep mismatch in the thermal boundary and inlet conditions that can preclude the use of the conventional correlations. In addition, in experiments on flow and heat transfer in microchannels, some parameters, like the channel dimensions, the average roughness, the local convective heat transfer, the local value of the static pressure along a microchannel, and so on, are difficult to measure accurately. For this reason, a large number of inconsistencies in published data are very likely to be due to experimental inaccuracies. 

In order to provide some physical insight into the dynamics of microchannel heat sinks (MCHS), steady laminar water flow in a smooth single trapezoidal microchannel is discussed and compared with measured data sets. Then the effects of nanofluids on augmented MCHS heat transfer are introduced, employing very simple correlations for the enhanced thermal conductivities of the mixtures. The fluid flow and heat transfer simulations have been carried out with the commercial... 

Here, Ap is the pressure drop across a microchannel heat sink subject to an impinging jet and p, Vq, e, K, Ce, H, Re, Wc, and Ar are density, impinging velocity at the inlet of the microchannel heat sink, fluid dynamic viscosity, porosity, permeability, Ergun coefficient, channel height, Reynolds number, channel width, and aspect ratio, respectively. The correlations for the pressure drop and the thermal resistance were compared with experimental results, and both match with experimental results within 10 %. 

The fully developed turbulent friction factor seems to be in disagreement with the Blasius equation for smooth microcharmels and with the Colebrook correlation for rough microchannels. 

For turbulent flows, the friction factor is a function of both the Reynolds number and the relative roughness, where s is the root-mean-square roughness of the pipe or channel walls. For turbulent flows, the friction factor is found experimentally. The experimentally measured values for friction factor as a function of Re and are compiled in the Moody chart [1]. Whether the macroscale correlations for friction factor compiled in the Moody chart apply to microchannel flows has also been a point of contention, as numerous researchers have suggested that the behavior of flows in microchannels may deviate from these well-established results. However, a close reexamination of previous experimental studies as well as the results of recent experimental investigations suggests that microchannel flows do, indeed, exhibit frictional behavior similar to that observed at the macroscale. This assertion will be addressed in greater detail later in this chapter. 

In summary, even though the characteristic length scales of turbulent flows in microchannels are several orders of magnitudes smaller than their counterparts in macroscale pipes and channels, experimental evidence suggests the flows are statistically and structurally similar. As such, long established correlations for pressure drop in pipes and channels and computational tools available for the study of turbulent pipe and chaimel flows should be equally applicable to turbulent microchannel flows. 

Qu and Mudawar [34], based on the Katto and Ohno [97] correlation (which was based on data for diameters down to 1 mm) and using their own saturated data for water in a rectangular microchannel heat sink, and also data for R-113 in a circular multi-microchannel heat sink from a previous study by Bowers and Mudawar [37], obtained the following correlation for saturated CHF ... 

Higher heat transfer rates in turbulent microchannels than predicted by traditional large-scale correlations were observed by Adams et al. [23]. Based on the work of Gnielinski, a generalized correlation for turbulent single-phase flow in microchannels is derived ... 

Figure 9.3 clearly shows that different applications measure different heat transfer coefficients and no general correlation for single-phase heat transfer in microchannels can be derived so far. 

In this chapter, heat transfer from or to a fluid in microchannels with diameters of less than 1 mm was discussed. It was seen from the literature that correlations for Nusselt numbers in microcharmels show little agreement whether heat transfer is enhanced or decreased at the microscale. The findings were often restricted to the individual setup used in a particular study. This leads to the conclusion that so far, no general correlation for heat transfer coefficients in microchannels can be suggested. The comparison with heat transfer analysis in macroscopic systems... 

Vandu et al. [88] investigated the absorption of oxygen from an oxygen-nitrogen mixture in water in microchannels of square and circular cross sections (diameter 1, 2, or 3 mm). These authors su ested an empirical correlation for kpa as a function of the gas and liquid superficial velocities, the unit cell length, and the difiusivity in the liquid phase D ) ... 

More recently, Yue et al. [81] measured the rate of pure CO2 absorption into a COs VHCOs solution in a 1 mm x 0.5 mm microchannel. They proposed a correlation for kpa as follows ... 

They obtained an empirical correlation for the estimation of kpa in this microchannel ... 

Design rules for microreactors have already been formulated and many aspects are generally well understood. Heat and mass transfer in single-phase fluid flow in microchannels has been extensively studied during the last 15 years, and it was demonstrated that classical engineering correlations for calculation of heat and mass transfer coefficients can be used. For example, for fully developed laminar flow, the Nusselt number is a constant... 

The Uquid fihn thickness surrounding the Taylor bubble in a microchannel can be precisely predicted with a number of correlations derived from Bretherton s theory. In the closed micro-channels, the pressure drop in Taylor flow can be correctly estimated by the Wamier model and in the annular regime by the Lockhart-Martinelli model. A number of correlations for the C-factor are available for the Lockhart-MartinelU model... 

Shin and Kim [8] obtained pressure drop measurements for condensation flow of R134a in a microtube having a hydraulic diameter of 691 xm. Figure 8 shows a comparison of their pressure drop measurements with available correlation equations for macrochannels. Figure 8a shows that the pressure drop in condensation flow at low mass flux (G < 200 kg/m s) in a microchannel is lower than that predicted by Friedel s correlation for macrotubes [9]. At higher mass fluxes (G = 400kg/m s, for example), however, their pressure drop measurements for condensation flow in a microchannel can be predicted well by Friedel s correlation, as shown in Fig. 8b. 

The development of the velocity and temperature fields has a marked effect on the friction factor and the heat transfer coefficient near the channel entrance region. Correlations for the calculation of the friction factor and of the convective heat transfer coefficients in the entrance region of a microchannel are given in entrance region. 

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