Page 17 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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2
The expressions V w x, V w and V w zare the second derivatives of
the velocities on the corresponding coordinate axis. So for example, for the z
axis the corresponding term is:

2
8 w.
23
dx 2 By 1 dz 2 ( )

The product of these sums (the Laplace operator) and the viscosity ju is
the friction force per unit of fluid volume.

n ..... . 80 90 J 80 _, ,_ t
The partial derivatives — , — and — denote the change of the
dx dy dz
velocity on the corresponding axis connected with the contraction and tension in
the fluid because of its movement. 8 is expressed by

dx dy dz

This sum marked as div w is the divergence of the velocity vector in
direction of the coordinate axes. Its product with the viscosity /J is the force for
unit of fluid volume because of contraction and tension of the fluid.
As already mentioned by solving the equations of Navier-Stokes
together with the equation of continuity for each of the phases of a multi-phase
flow system at the corresponding boundary condition theoretically, it is
possible to describe the hydrodynamic processes in all technical and nature
systems. Practically, it is possible to solve these equations only in some simple
cases which usually are not of great practical importance. A possibility to solve
these equations for practical purpose is given by the similarity theory and the
dimensional analysis considered in part 1.3 of this chapter.

1.2.1.2. Heat transport equations
There are three mechanisms of heat transfer: heat conduction, heat
radiation and heat convection. Usually they take place together but for better
understanding they are considered separately. Because the heat radiation is of
importance at temperatures much higher than those in the packed bed column,
this phenomenon is not considered in this book.