Page 170 - Modelling in Transport Phenomena A Conceptual Approach

150 CHAPTER 6. STEADY-STATE MACROSCOPIC BALANCES

6.1 CONSERVATION OF CHEMICAL
SPECIES

The inventory rate equation given by Eq. (1.1-1) holds for every conserved quantity
cp. Therefore, the conservation statement for the mass of the ith chemical species
under steady conditions is given by

( Rate of mass ) - ( Rate of mass ) + ( Rate of generation ) =O (6.1-1)
of i in
of mass i
of i out
The mass of i may enter or leave the system by two means: (i) by inlet or outlet
streams, (ii) by exchange of mass between the system and its surroundings through
the boundaries of the system, i.e., interphase mass transfer.

Figure 6.1 Steady-state flow system with fixed boundaries.

For a system with a single inlet and a single outlet stream as shown in Figure
6.1, Eq. (6.1-1) can be expressed as

(6.1-2)

in which the molar rate of generation of species i per unit volume, si, is expressed
by Eq. (5.3-27). The terms and (hi),ut represent the inlet and outlet mass
flow rates of species i, respectively, and Mi is the molecular weight of species i.
The interphase mass transfer rate, (hi)int, is expressed as

(hi)int = AM(^) (A~i)=h Mi (6.1-3)
where (Ac~),~ is the characteristic concentration difference. Note that (hi)int is
considered positive when mass is added to the system.
As stated in Section 2.4.1, the mass flow rate of species i, mi, is given by

h j = p,(v)A = pi& (6.1-4)