Page 133 - Separation process principles 2

98 Chapter 3 Mass Transfer and Diffusion

Table 3.13 Some Useful Dimensionless Groups
Name Formula Meaning Analogy

Fluid Mechanics
Drag force
Drag Coefficient
Projected area x Velocity head
Pipe wall shear stress
Fanning Friction Factor
Velocity head
Inertial force
Froude Number
Gravitational force
Liip Lii LG Inertial force
Reynolds Number NRe=-=-=-
P U P Viscous force
Inertial force
Weber Number
Surface-tension force

Heat Transfer
- -
j-Factor for Heat Transfer j~ = N~~~(NR)~'~ j~
h L Convective heat transfer
Nusselt Number NNu = - Ns~
k Conductive heat transfer
Bulk transfer of heat
Peclet Number for Heat Transfer
Conductive heat transfer
Momentum diffusivity
Prandtl Number
Thermal diffusivity
Heat transfer
Stanton Number for Heat Transfer
Thermal capacity
Mass Transfer

j-Factor for Mass Transfer JM = NS~M(NSC)~'~ j~
NSC k a Thermal diffusivity
Lewis Number NLe=-=--- -
NR PCPDAB DAB Mass diffusivity
LU Bulk transfer of mass
Peclet Number for Mass Transfer NpeM = NR~NSC = - NpeH
DAB Molecular diffusion
P
v
Schmidt Number Nsc = - - Momentum diffusivity
-
-
PDAB DAB Mass diffusivity NP~
kc L Convective mass transfer
Shenvood Number NSh = - NNU
DAB Molecular diffusion
Nsh kc Mass transfer
-
-
Stanton Number for Mass Transfer NstM = - Mass capacity N~tH
-
NR~NSC CP
L = characteristic length G = mass velocity = iip
Subscripts: M = mass transfer H = heat transfer
mean fluid velocity in the direction of flow and on position By analogy, the same mixing length is valid for turbulent-
in the fluid with respect to the solid boundaries. flow heat transfer and mass transfer. To use this analogy,
In 1925, in an attempt to quantify turbulent transport, (3-151) to (3-153) are rewritten in diffusivity form:
Prandtl [52] developed an expression for p,, in terms of an
7zx dux
eddy mixing length, I, which is a function of position. The - = -(v + eM) - (3- 154)
P
eddy mixing length is a measure of the average distance that * dz
an eddy travels before it loses its identity and mingles with = dT (3-155)
other eddies. The mixing length is analogous to the mean CPP d z
free path of gas molecules, which is the average distance a ~CA
NA, = -(DAB + ED)- (3-156)
molecule travels before it collides with another molecule. dz