Page 338 - Modelling in Transport Phenomena A Conceptual Approach

318 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

8.5.3.1 Comment

The molar average velocity is given by Eq. (8.552) and since both NA, and c are
constants, vz remain constant for 0 5 z 5 6. On the other hand, from Q. (8.5-6)
the mas average velocity is
MANA, -t MBNB,
v, = (8.563)
P
Expressing NB, in terms of NA, by using Eq. (8.551) reduces Eq. (8.563) to
NA,(MA - 0.5M~)
v, = (8.564)
P
As a result of the dimerization reaction MA = 0.5M~ and we get
v, = 0 (8.565)
In this specific example, therefore, the mass average velocity can be determined
on the basis of a solution to a diffusion problem rather than a conservation of
momentum.

NOTATION

A area, m2
a, catalyst surface area per unit volume, 1/ m
& heat capacity at constant pressure, kJ/ kg. K
C total concentration, kmol/ m3
ci concentration of species i, kmol/ m3
D diameter, m
DAB diffusion coefficient for system A-L3, m2/ s
e total energy flux, W/ m2
FD drag force, N
H enthalpy, J; partition coefficient
h heat transfer coefficient, W/ m2. K
J* molecular molar flux, kmol/ m2. s
k thermal conductivity, W/ m. K
IC" surface reaction rate constant
L length, m
m mass flow rate, kg/s
M molecular weight, kg/ kmol
N total molar flux, kmol/ m2. s
n total molar flow rate, kmol/ s
ni molar flow rate of species i, kmol/ s