Page 508 - Modelling in Transport Phenomena A Conceptual Approach

488 CHAPTER 11. UNSTEADY MCROSCOPIC BALANCES WITH GEN.

Solution

Diferentiation of Eq. (11.3-14) with respect to t by using Leibnitz's rule gives
6C
- = Ic~$(t,x) e-kt - kc$(t,x) e-kt + -
a4 e- kt
at at
-_
e- kt
-at
Differentiation of Eq. (11.3-14) twice with respect to x yields

The use of Eq. (11.2-15) in Eq. (2) leads to

Substitution of Eq. (1) into Eq. (3) yields

or,

which is identical with Eq. (11.3-lf?).

NOTATION

A area, m2
CP heat capacity at constant pressure, kJ/ kg. K
ci concentration of species i, kmol/ m3
DAB diffusion coefficient for system AB, m2/ s
e total energy flux, W/ m2
J* molecular molar flux, kmol/ m2. s
L length, m
m mass flow rate, kg/ s
M molecular weight, kg/ kmol
N total molar flux, kmol/ m2. s