Velocity field-entrance region

Figure 4.5 Velocity field-entrance region of a T-shaped micromixer [4].

The entrance region of a microchannel corresponds to the part of the channel in which the velocity and/or the temperature fields are not completely developed. 

The development of the velocity and temperature fields has a marked effect on the friction factor and the heat transfer coefficient near the channel entrance region. Correlations for the calculation of the friction factor and of the convective heat transfer coefficients in the entrance region of a microchannel are given in entrance region. 

Estimation of Entrance Pressure-Pressure Losses from the Entrance Flow Field17 Consider the entrance flow pattern observed with polymer melts and solutions in Fig. 12.16(a). The flow can be modeled, for small values of a, as follows for 0 < a/2 the fluid is flowing in simple extensional flow and for a/2 < 0 < rc/2 the flow is that between two coaxial cylinders of which the inner is moving with axial velocity V. The flow in the outer region is a combined drag-pressure flow and, since it is circulatory, the net flow rate is equal to 0. The velocity V can be calculated at any upstream location knowing a and the capillary flow rate. Use this model for the entrance flow field to get an estimate for the entrance pressure drop. 

For simplicity, the transition regions in both temperature and flow fields near the channel entrance and at the junctions of un-thermostated and thermostated regions are assumed negligibly small and thus are not considered. This implies a discontinuity in the temperature and velocity at the above junctions. In each region itself, however, there are no axial variations. Given the fact that the radial profile of liquid temperature is essentially parabolic, one can obtain the cross-sectional average temperature Tj at each region of the capillary... 

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