Page 259 - Modelling in Transport Phenomena A Conceptual Approach

8.1. MOMENTUM TRANSPORT 239

xL* +v

Figure 8.1 Couette flow between two parallel plates.

The first step in the translation of Eq. (8.1-1) into mathematical terms is to
postulate the functional forms of the non-zero velocity components. This can be
done by making reasonable assumptions and examining the boundary conditions.
For the problem at hand, the simplification of the velocity components is shown in
Figure 8.2.

One-dimensional flow
vx=vy=o vz = VZ (x, y, z, f)

Large aspect ratio
W/B >>I
I

Fully developed flow
avz/az = 0 vz = vz (4

Figure 8.2 Simplification of the velocity components for Couette flow between
two parallel plates.

Since v, = v,(z) and vz = vy = 0, Table C.l in Appendix C indicates that the
only non-zero shear-stress component is T~,. Therefore, the components of the