Page 73 - Modelling in Transport Phenomena A Conceptual Approach

54 CHAPTER 3. INTERPHASE TRANSPORT

3.4 DIMENSIONLESS NUMBERS

Rearrangement of Eqs. (3.1-4), (3.2-4) and (3.3-4) gives

(3.41)

(3.42)

(3.43)

Note that E@. (3.41)-(3.43) has the general form

Interphase ) = ( Transfer ) ( Difference in (3.44)
coefficient Quantity/Volume

and the terms f42, h/pep, and IC, all have the same units, m/s. Thus, the
ratio of these quantities must yield dimensionless numbers:
Heat transfer Stanton number = StH = - (3.45)
h
p CPVch

Mass transfer Stanton number = StM = - (3.46)
kC
Vch
Since the term f/2 is dimensionless itself, it is omitted in Eqs. (3.45) and (3.46).
Dimensionless numbers can also be obtained by taking the ratio of the fluxes.
For example, when the concentration gradient is expressed in the form

Difference in Quantity/Volume
Gradient of Quantity/Volume = (3.47)
Characteristic length
the expression for the molecular flux, l3q. (2.2-5), becomes

(Diffusivity) (Difference in Quantity/Volume)
Molecular flux = (3.48)
Characteristic length

Therefore, the ratio of the total interphase flux, Eq. (3.44), to the molecular flux,
Eq. (3.48), is

Interphase flux - (Transfer coefficient) (Characteristic length)
-
Molecular flux Diffusivity (3.49)
The quantities in Eq. (3.49) for various transport processes are given in Table 3.1.