Page 26 - Modelling in Transport Phenomena A Conceptual Approach

1.3. MATHEMATICAL FORMULATION OF THE BASIC CONCEPTS 7

Figure 1.1 Flow between concentric spheres.

Substitution of the velocity distribution into Eq. (2) and integration gives

1.3.2 Rate of Generation Term

The generation rate per unit volume is denoted by % and it may be either constant
or dependent on position. Thus, the generation rate is expressed as

(%)(Volume) if % is constant

Generation rate = (1.3-2)
if % is position dependent
/I/ %dV
V
where V is the volume of the system in question. It is also possible to have the
depletion of a quantity. In that case, the plus sign in front of the generation term
must be replaced by the minus sign, i.e.,

Depletion rate = - Generation rate (1.3-3)