Reynolds number governing flow

Rarefied analyses of thermal coupling between the micro-nozzle with the surrounding substrate have also been reported [10]. In this work, steady low Reynolds number gas flows were again modeled by the DSMC approach, and the substrate transient thermal response was governed by the heat conduction equation. It was shown that propulsive efficiencies of the micronozzle decreased with higher nozzle wall temperatures and vice versa. These results are in agreement with the continuum-based heat transfer results previously discussed. 

The problems that arise when experiments are carried out in a greatly reduced scale can be overcome if the Reynolds number is high and the flow pattern is governed mainly by fully developed turbulence. It is possible to ignore the Reynolds number, the Schmidt number, and the Prandtl number because the structure of the turbulence and the flow pattern at a sufficiently high level of velocity will be similar at different supply velocities and therefore independent of the Reynolds number. The transport of thermal energy and mass by turbulent eddies will likewise dominate the molecular diffusion and will therefore also be independent of the Prandtl number and the Schmidt number. 

The drag coefficient also depends on shape and 0(, but in addition, because drag is partially due to friction, and frictional effects in a flow arc governed by a powerful dimensionless quantity called Reynolds number, then Cu is also a function of the Reynolds number. Re ... 

For an incompressible viscous fluid (such as the atmosphere) there are two types of flow behaviour 1) Laminar, in which the flow is uniform and regular, and 2) Turbulent, which is characterized by dynamic mixing with random subflows referred to as turbulent eddies. Which of these two flow types occurs depends on the ratio of the strengths of two types of forces governing the motion lossless inertial forces and dissipative viscous forces. The ratio is characterized by the dimensionless Reynolds number Re. 

Sy et al (S8, S9) and Morrison and Stewart (M12) analyzed the initial motion of fluid spheres with creeping flow in both phases. For bubbles (y = 0, k = 0), the condition that internal and external Reynolds numbers remain small is sufficient to ensure a spherical shape. However, for other k and y, the Weber number must also be small to prevent significant distortion (S9). For k = 0, the equation governing the particle velocity may be transformed to an ordinary differential equation (Kl), to give a result corresponding to Eq. (11-16), i.e.,... 

From equation (4.26), it is seen that the important dimensionless parameters driving momentum transport are the Reynolds number, the Froude number, the Euler number, and the length and velocity ratios in the flow field. The dimensionless variables all vary between zero and a value close to one, so they are not significant in determining which terms in the governing equation are important. 

Once the system of equations has been solved, the nondimensional temperature gradient can be easily evaluated at the surface, providing the Nusselt number. It should be expected that the heat transfer depends on the boundary-layer thickness, which in turn depends on the flow field, which is principally governed by the Reynolds number. Figure 6.9 shows a correlation between the Nusselt number and the Reynolds number that was obtained by solving the nondimensional system for several Reynolds numbers. 

Recall that in the semi-infinite stagnation flow, the Reynolds number does not appear in the governing flow equations. As a result the Nusselt number is simply a constant for... 

Summarizing this short discussion it has to be stated, that up to now experiments providing absolute numbers of kf during protein adsorption in fluidized beds are not available, the interpretations are based on correlations derived for small ions. As ion exchange with fluidized resins is performed at much higher Reynolds numbers and mostly is not limited by particle side transport, the validity of the correlations for proteins has to be proven. Nevertheless, the influence of bed expansion at increased linear flow rate cannot be neglected and fluid side mass transport should be considered as a system parameter governing the sorption process in a fluidized bed under certain conditions. 

The hydrodynamics of the falling film governs, as to be expected, the reaction behavior [322,323]. When increasing the flow rate, the reaction time was reduced and the film thickness was increased. For both reasons, the conversion decreased and exhibited in a linear dependence on log Re, Re being the Reynolds number. The hydrogenation conversion had only a weak dependence on hydrogen pressure. 

Because the Reynolds number Re has already been taken as a governing dimensionless number, 7t7 will be taken as U2/gD i.e., as the Froude number, Fr. In some ways the use of U in this dimensionless number contradicts the use of V as a prime variable. However, this is not really a problem because the gravitational acceleration can only affect the heat transfer if there is a flow, i.e., if U is nonzero. Hence ... 

It will be assumed that the Reynolds number is large enough for the boundary layer assumptions to be applicable. It will further be assumed that the flow is two-dimensional which means that the plate is assumed to be wide compared to its longitudinal dimension. As a result of these assumptions, the equations governing the problems are ... 

Solutions based on the use of the boundary layer approximations to the full governing equations have been discussed in the above sections. These boundary layer approximations qfe, however, often not applicable. For example, the boundary layer equations do not apply if there are significant areas of reversed flow or if the Reynolds number is low. Even with two-dimensional flow over a circular cylinder, the bound-... 

The boundary layer equations can, as previously discussed, only be applied to flows in which the Reynolds number is relatively large and in which there is no significant areas of reversed flow. This, in particular, severely limits the applicability of these equations in situations involving opposing flow. When these conditions are not satisfied, the solution must be obtained using the full governing equations. For example, if the flow can be assumed to be two-dimensional and if the Boussinesq approximations are applicable, the equations governing the flow are Eqs. (9.5) to (9.7). If the x-axis is vertical, these equations become ... 

Laminar flow to turbulent flow transition — When increasing the velocity of the flow, a transition from -> laminar flow to rippling and finally to turbulent flow will occur [i]. The transition from laminar to turbulent flow is governed by the dimensionless -> Reynolds number. Ref [i] Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs... 

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