Page 30 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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w r— + w v — + w. — \dx.dy.dz.dT . (78)
& By oz )

In case of unsteady state diffusion, the following term

dC
dc.dy.dz
dr

has to be added to equation (78).
With this term from equations (65) and (66) to (68) it follows

2
2
2
Jd C 3 C B C\ 8C 8C dC 8C
D\—- + — - + — H = WT — + w v — + w 2 — + — (79)
2
I 8x 2 dy 2 dz ) * dx y dy ' dz dr
Equation (79) is the differential equation of diffusion (or mass transfer)
in a moving flow. In it, besides the concentration, the flow velocity is also
variable. That is why this equation must be considered together with the
equations of Navier-Stokes (20) to (22) and the equation of continuity (18).
Eq.(79) is the second Fick's low. Its structure is the same as that of the
differential equation of the convective heat transfer (in case of a steady state
process Eq. (56)). This gives the possibility, as shown later, to calculate the heat
transfer processes by means of experimental data or equations for mass fransfer.
The basic methods for these calculations are the similarity theory and the
dimensional analysis. That is why before considering the theory of mass
transfer processes, we present these important methods largely used in chemical
engineering and in particular in the area of packed columns.

1,3. Similarity theory and dimensional analysis

1.3.1, Similarity theory

Chemical technology uses different physical and chemical processes.
Applying the basic laws of the corresponding science areas it is possible to
describe these processes with differential equations like the equation of
continuity of the flow and the Navier-Stokes equations. These equations
describe a whole class of similar phenomena. To use them for a single concrete