Entrance length

As a rough guide for plate heat exchangers, the rate of the hydrodynamic entrance length to the corresponding thermal entrance length is given by... 

To maintain a laminar flow profile over a long distance the entrance length (Lg) of the flow channel has to be small compared to the total length. The entrance length is given by... 

Depending on the aspect ratio of the channel, values between 0.01 and 0.1 are found for the non-dimensional entrance length [100]. From Eq. (71) it can be deduced, vrith Ljjy being Re independent, that increases linearly with the hydraulic diameter and the Reynolds number. 

Reference slip length Thermal entrance length... 

This expression has been used to correlate results obtained in a rectangular channel, Eq. (14) in Table VII, the hydrodynamic entrance length of the channel (Le = 0.0575 d Red) being too short to assure a fully developed flow. The results were still 24/ high, compared with Eq. (31) modified by a relaxation assumption ... 

Equation (31) has also been used to correlate results obtained in annular channels with insufficient hydrodynamic entrance length (B2, B3). Some of the data fit Eq. (31) with a slightly smaller coefficient. A similar expression, including terms for the hydrodynamic entrance length, was used by Pickett and Ong (P3a). 

The plot of growth rate in Figure 8a shows that even without buoyancy-driven secondary flows, a considerable variation in the growth rate in the transverse direction exists. The decrease in the axial velocity near the side walls leads to both a shorter thermal entrance length and a greater depletion near the walls compared with the behavior in the middle of the reactor. These perturbations from two-dimensional behavior induced by the side walls extend away from the side walls to a distance about equal to the reactor height. Thus, two-dimensional models may not be sufficient to predict CVD reactor performance even in the absence of buoyancy-driven rolls. 

Solution. The computer program discussed above has been run for Reynolds numbers between 104 and 3 x 105 for a Prandtl number of 0.7. The calculated variation of Num with Z was then considered. The final value of Num was multiplied by 1.01 and the results scanned to find the value of Z at which Num was 1.01 times the final value. This value of Z was taken as z m/W, Zent being the assumed entrance length, i.e., the distance from the inlet at which Num is within 1% of its final value. 

Hartnett, J. P. Experimental Determination of the Thermal Entrance Length for the Flow of Water and of Oil in Circular Pipes, Trans. ASME, vol. 77, p. 1211, 1955. 

When the upstream pressure is increased, the number of fringes oscillates throughout the field of observation in a similar way to that described above, and the period of the phenomenon decreases. Simultaneously, the entrance length increases until it occupies the entire length of the capillary. 

Kavehpour et al. [20] solved the compressible two-dimensional fluid flow and heat transfer characteristics of a gas flowing between two parallel plates under both uniform temperature and uniform heat flux boundary conditions. They compared their results with the experimental results of Arkilic [3] for Helium in a 52.25x1.33x7500 mm channel. They observed an increase in the entrance length and a decrease in the Nusselt number... 

For parallel plates, Shah and London [14] propose the following law for the PoiseuiUe number which takes the entrance length into account ... 

The initial region extends over an entrance length Xo and consists of boundary layer 2 over the wall with width d0(x), internal boundary layer 3 with depth dx x), and initial region core 1 between them. External boundary layer 4 with width d2(x) transports perturbations caused by the EPR far away over it. 

---