Scale effects flow analysis

In our analysis, we discuss experimental results of heat transfer obtained by previous investigators and related to incompressible fluid flow in micro-channels of different geometry. The basic characteristics of experimental conditions are given in Table 4.1. The studies considered herein were selected to reveal the physical basis of scale effect on convective heat transfer and are confined mainly to consideration of laminar flows that are important for comparison with conventional theory. 

When considering scale effects, the implication of the foregoing analysis is that the hopper angle required for mass flow is principally dependent on the outlet size selected for the hopper under consideration. Note that the... 

The microanalytical methods of differential thermal analysis, differential scanning calorimetry, accelerating rate calorimetry, and thermomechanical analysis provide important information about chemical kinetics and thermodynamics but do not provide information about large-scale effects. Although a number of techniques are available for kinetics and heat-of-reaction analysis, a major advantage to heat flow calorimetry is that it better simulates the effects of real process conditions, such as degree of mixing or heat transfer coefficients. 

An important question in reactive flow analysis is whether or not the density changes due to non-ideal mixing and reaction have significant effects on the flow. In many reactor systems both chemistry and flow scales are important. The formulation of proper non-dimensional scales is thus a difficult task. Therefore, in our subsequent analysis the pressure changes in the flow are supposedly dominated by momentum effects as in non-reactive systems. 

Gale, B.K. Caldwell, K.D. Frazer, A.B. Geometric scaling effects in electrical field flow fractionation. 1 theoretical analysis. Anal. Chem. 2001, 73, 2345. 

The heat transfer in microchannels is expected to agree with conventional theory provided that the discussed continuum assumptions can be made. For example, under fully developed laminar flow conditions at low Re, Nu is constant. However, many experimental data show large deviations between each other and inconsistency with classical theory exists. There is an increase in Nu with increasing Re measured. According to Herwig and Hausner [37], a common theoretical basis on forced convection for macro- and microchannels can be used to describe forced convection of liquids in the laminar regime. However, there are effects which are more pronounced and which are of more importance on the microscale, such as surface tension, viscous forces and electrostatic forces [38]. These effects are called scaling effects with respect to standard macroscale analysis. 

Process Troubleshooting—instruction in the different types of troubleshooting techniques, methods, and models used to solve process problems. Topics include application of data collection and analysis, cause-effect relationships, and reasoning. Emphasizes application of troubleshooting methods to scale-up from laboratory bench to pilot unit. Describe unit operation concepts solve elementary chemical mass/energy balance problems interpret anal ical data and apply distillation and fluid flow principles. 

Most of the disagreement with the more exact solution appears in the low speed and heavy asp ty contact regions where asperity interaction is predominately the mechanism supporting the load. Compared to the universal treatment of the hydrodynamic pressure and asperity contact in the full-scale micro EHL model [4-5], the macro-micro approach superimposes the asperity contact pressure obtained fiom an off-line contact simulation to the hydrodynamic pressure from the average flow analysis, resulting in an under-estimation of asperity deformation but an over-estimation of the average asperity pressure. The next step in the macro-micro analysis partly compensates for this effect. 

A detailed and intricate scaling analysis for the Couette flow of nematics, similar in style to that contained in Section 5.5.5, has been carried out by Atkin and Leslie [6]. We do not pursue this aspect of the analysis in this text and refer the reader to Reference [6] for comments on possible experimentally determined quantities such as an apparent viscosity. As already mentioned, solutions for unequal elastic constants can also be found in [6]. A more extensive analysis of Couette flow incorporating the effects of an applied magnetic field has been provided by Currie [57], who also comments on other types of solutions which may be possible. 

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