Entrance effect

Entrance effects are usually not significant industrially if L/D > 60. Below this limit Nusselt recommended the conservative equation for 10 < L/D < 400 and properties evaluated at bulk temperature... 

For non-Newtonian fluids in slow flow, friclion loss across a square-woven or fuU-twill-woven screen can be estimated by considering the screen as a set of parallel tubes, each of diameter equal to the average minimal opening between achacent wires, and length twice the diameter, without entrance effects (Carley and Smith, Polym. Eng. Set., 18, 408-415 [1978]). For screen stacks, the losses of individual screens should be summed. 

It turns out that packed beds much less than a hundred particles thick behave as if they were weU-stirred due to the entrance effect. Although it may seem odd that a packed bed can behave as if weU-stirred, it typically takes at least a 100-particle bed depth in order for a phig-flow concentration wave to develop. 

New questions have arisen in micro-scale flow and heat transfer. The review by Gad-el-Hak (1999) focused on the physical aspect of the breakdown of the Navier-Stokes equations. Mehendale et al. (1999) concluded that since the heat transfer coefficients were based on the inlet and/or outlet fluid temperatures, rather than on the bulk temperatures in almost all studies, comparison of conventional correlations is problematic. Palm (2001) also suggested several possible explanations for the deviations of micro-scale single-phase heat transfer from convectional theory, including surface roughness and entrance effects. 

It was shown that data presented by other researchers can be carried over to entrance effects. The present results highlight the importance of accounting for com-... 

Several investigators obtained friction factors in micro-channels with rough walls that were greater than those in smooth wall channels. These observations should be considered taking into account the entrance effects, losses from change in channel size, etc. 

Because most applications for micro-channel heat sinks deal with liquids, most of the former studies were focused on micro-channel laminar flows. Several investigators obtained friction factors that were greater than those predicted by the standard theory for conventional size channels, and, as the diameter of the channels decreased, the deviation of the friction factor measurements from theory increased. The early transition to turbulence was also reported. These observations may have been due to the fact that the entrance effects were not appropriately accounted for. Losses from change in tube diameter, bends and tees must be determined and must be considered for any piping between the channel plenums and the pressure transducers. It is necessary to account for the loss coefficients associated with singlephase flow in micro-channels, which are comparable to those for large channels with the same area ratio. 

Gamart G, Favre-Marinet M, Asendrych D (2005) Conduction and entrance effects on laminar liquid flow and heat transfer in rectangular micro-channels. Int J Heat Mass Transfer 48 2943-2954... 

The flow regimes in the test sections were identified visually with the aid of a strobe and a digital camera. The camera was always targeted at the test section center. No systematic attempt was made to assess and eliminate the test section entrance effects on the flow regimes. However, the distance between the point pictured by the camera and the test section inlet was well over 100 channel diameters everywhere. Thus, although the possibility exists that the reported flow regimes are influenced by the test section entrance conditions, this influence may not be significant. 

These models are designed to define the complex entrance effects and convection phenomena that occur in a reactor and solve the complete equations of heat, mass balance, and momentum. They can be used to optimize the design parameters of a CVD reactor such as susceptor geometry, tilt angle, flow rates, and others. To obtain a complete and thorough analysis, these models should be complemented with experimental observations, such as the flow patterns mentioned above and in situ diagnostic, such as laser Raman spectroscopy. 

The terms represent, respectively, the effect of pressure gradient, acceleration, line friction, and potential energy (static head). The effect of fittings, bends, entrance effects, etc., is included in the term Ke correlated as a number of effective velocity heads. The inclination angle 0 is the angle to the horizontal from the elevation of the pipe connection to the vessel to the discharge point. The term bi is the two-phase multiplier that corrects the liquid-phase friction pressure loss to a two-phase pressure loss. Equation (23-39) is written in units of pressure/density. 

Jastrzebski, Z.D., Entrance effects and wall effects in an extrusion rheometer during the flow of concentrated suspensions, Industrial and Engineering Chemistry, 6, No. 3,pp. 445-54(1967). 

Moissis, R. and Griffith, P., Entrance effects in two-phase slug flow, Transactions of AS ME, Journal of Heat Transfer, Series C 84, pp. 29-38 (1962). 

The cordierite extruded monoliths, having 400 square cellsAn, were similar to those used in automobile catalytic converters. However, instead of using an alumina washcoat as in the catalytic converter, these catalyst supports were loaded directly with 12 to 14 wt.% Pt in the same manner as the foam monoliths. Because these extruded monoliths consist of several straight, parallel channels, the flow in these monoliths is laminar (with entrance effects) at the flow rates studied. 

Similarly, one must worry about exit pressure effects, or end corrections. Experimentally, it has been observed that there is a nonzero gange pressnre at the capillary exit, Pex (cnrve b of Fignre 7.70). It has been found that the ratio of exit to entrance effects, Pex tAPent, is between 0.15 and 0.20 and that althongh APgnt does not depend on L/Do, Pex decreases up to L/Dq = 10 and then remains constant. With these observations in mind, we can rewrite Eq. (7.68) to inclnde both entrance and exit effects ... 

A special advantage of this method is that the high shear rate range becomes available. It appears that one can measure nu — n33 up to the critical shear stress, at which extrusion defect (melt-fracture) occurs. On the other hand, entrance effects can also be studied, when the windows are located sufficiently close to the entrance. With the aid of the stress-optical coefficient, the corresponding normal stress difference can be... 

SiH2Cl2 + NH3- Si3N4 167 One-dimensional model of wafer space, onedimensional model of flow region, multiple component diffusion, gas phase and surface reactions, entrance effects, comparison with data, and numerical solution. 

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