Poisseulle flow

Let us consider laminar flow through a two-dimensional channel, the so-called Poisseulle flow. The geometry is shown in Figure 9. 

As in the classical Poisseulle flow, the channel is assumed to be two-dimensional (nothing varies in the z direction) and doubly infinite in the x direction. We will impose a constant temperature, T, on each wall and assume that T will not vary with x. An axial pressure gradient will have to exist in order for there to be an axial flow, and we recognize that it should be constant so that p will vary linearly with x. 

As in the classical Poisseulle flow, the y component of velocity will be zero, so that the overall mass continuity equation is identically satisfied. For a steady-state flow, we can write the simplified governing equations describing the velocity, temperature, and species conservation fields. 

This process is important during drainage of the liquid. As the radius is influencing the volume per time to the power of 4, flow is strongly reduced at small radii according to HAGEN-POISSEULLES-LAW. (fig. 8)... 

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