Reynolds number model predictions comparison

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. 

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. 

The heat transfer coefficient h was calculated according to Hand-ley and Heggs (24) with the Reynolds number based upon an equivalent diameter, namely that of a sphere with the same volume as the actual particle. The overall heat transfer coefficient U was calculated from the heat transfer parameters of the two dimensional pseudohomogeneous model (since the interfacial At was found to be negligible), to allow for a consistent comparison with two dimensional predictions and to try to predict as closely as possible radially averaged temperatures in the bed (25). Therefore ... 

More tests are needed comparing measured conversions and temperature profiles with model predictions for tubular reactors. Comparisons will be easier for reactions with simple kinetics than for complex reactions such as partial oxidations. Tests should be made over a wide range of Reynolds numbers, which may require high velocities and long reactors. If kinetic data are uncertain or unavailable, the overall heat transfer coefficient for the 1-D model can be obtained from the axial temperature profile and the total heat removal [41] ... 

In order to validate this result, the experimental data of Celata et al. [4] are used. Celata et al. measured the temperature difference between inlet and outlet of a smooth capillary mbes (fRe = 16) of fused silica with hydraulic diameters equal to 100, 70, and 50 pm through which water is circulated at different Reynolds numbers in the laminar regime. The comparison between the prediction of Eq. 22 and the experimental data is shown in Fig. 4, and the agreement between the model and the measurements is good. The agreement improves for larger Reynolds numbers and smaller diameters this fact is due to the smaller temperature rise at lower Reynolds number and larger diameters. 

A semi-emperical turbulent one-equation model is developed for rectangular open channel flows of water and viscoelastic fluids. The model is used to predict friction factor vs. Reynolds number relations, velocity profiles, eddy viscosity distributions and turbulent energy budgets. Comparisons are made between the model and the measured results using a Laser Doppler Anemometer. 

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