Page 137 - Process Modelling and Simulation With Finite Element Methods

124 Process Modelling and Simulation with Finite Element Methods

convenience, but this is not a realistic assumption which can be relaxed in
FEMLAB without any difficulty. This problem has a long history in the
chemical engineering literature, and the equal Peclet numbers are a legacy of an
analytic approximation by Amundson [ 81 which provides validation for the
solution.

Table 3.2 Parameters for Case 1.
I-- VL I 30 (-AH kC,, L2
)

I r2=5=Pe 1 1.2X1O8
VL

IE

Table 3.3 Parameters for Case 2.
VL 30 (-M)~c,,L~ 8.47~10~
y =-
I Bl =
a PCJO 3

kL2
VL
y =-=Pe 30 B, =- 1 .2X1O1O
23 3
a 1 E 23
- QQ=-
- 3 RTO

Amundson’s technique combines the mass and energy equations by linear
transforms:
n=O

This, in turn, leads to equations (3.7) and (3.8), along with the BCs, being
described identically, if and only if, the ratio of diffusivities is unity, 5 = 1 :
3
a2n an
-- Pe-+B2(n,, -n)exp(-QQln)=O (3.9)
ax2 ax