14-41
P14-17
The presence of a minimum (run2) imply the presence of a radial temperature profile that
effects the reaction rate and determines the deviation from the concentration profile given
by Eq. (14.51).
The enthalpy balance allows the identification of the dimensionless thermal parameters:
Defining
&
)
( )
!
“
!
“
“
!
“
#=
$
$
#==
$
$
=1100 BiM
where
hR
Bi
!
=
ratio convection-radial conduction
14-42
P14-17 (a)
P14-17 (b)
P14-17 (c)
Overall heat transfer coefficient decreases:
P14-17 (d)
The coolant flow rate increases:
P14-17 (e)
The coolant flow rate decreases:
The external heat transfer coefficient increases, this implies an increase in the wall temperature
Below shows how to use FEMLAB for this problem.
Femlab Screenshots for the baseline case
(1) Domain
(2 ) Constants and scalar expressions
– Constants
14-43
– Scalar expressions
(3 ) Subdomain settings
– Physics
(Mass balance)
14-44
(Energy balance)
– Initial Values
(Mass balance) cA(t0) = cA0
(Energy balance) T(t0) = T0
14-45
P14-18
Vary the Peclet number and the reaction order in laminar flow (Example 14–3(c))
1
0
0
1
0
!! == n
A
n
AkC
U
L
kCDa
“
AB
DLUPe /
0
=
mL 36.6=
min/106.7 25 mDAB
“=
n
Pe
Conversion
Parameter
1.04×103
/
100* DAB
1.04×104
/
10 * DAB
1.04×105
/
DAB
1.04×106
/
0.1*DAB
0.1
Attempt to evaluate
non-integral power of
negative number!
1.04×107
/
0.01*DAB
14-46
1.04×107
/
0.01*DAB
1.04×103
0.721
100* DAB
1.04×104
0.717
10 * DAB
1.04×105
0.687
DAB
1.04×106
0.653
0.1*DAB
1
1.04×107
0.641
0.01*DAB
1.04×103
0.292
100* DAB
1.04×104
0.290
10 * DAB
1.04×105
0.281
DAB
1.04×106
0.270
0.1*DAB
2.5
1.04×107
0.265
0.01*DAB
14-47
0.8
0.9
1.0
Pe
n
0.8
1.0
1.5
2.0
(1) With the increase of the reaction order n, the conversion will decrease. The conversion
Below show FEMLAB screenshots useful for this problem.
Femlab Screenshots
(1) Domain
(4 ) Constants and scalar expressions
– Constants
14-48
– Scalar expressions
(5 ) Subdomain settings
– Physics
14-49
– Initial Values
(Mass balance) cA(t0) = cA0
– Boundary Conditions
P14-19 (a)
First order reaction
Input Parameters:
1=n
mR 05.0=
Conversion:
xA= 0.687 @ Open-vessel Boundary: –Ni·n =2 *U0*(1–(r/Ra)^2)*CA0
I. Variation of Da number
Conversion
Damköhler number/ Da
Closed-vessel
Open-vessel
Parameter
0.449
0.404
0.287
8*U0
II. Variation of Pe number
Conversion
Peclet number/Pe
Closed-vessel
Open-vessel
Parameter
1.04e3
0.781
0.781
100* DAB
III. Femlab Screen Shots
(1) Domain
(2) Constants and scalar expressions
– Constants
14-51
(3) Subdomain settings
– Physics
– Initial Values
(Mass balance) cA(t0) = cA0
– Boundary Conditions
@ r = 0, Axial symmetry
(4) Results
(Open-vessel Boundary)
(Close-vessel Boundary)
14-53
P14-19 (b)
Third order reaction with k *C2
A0= 0.7 min–1
Input Parameters:
3=n
mR 05.0=
I. Variation of Da number
Conversion
Damköhler number/ Da
Closed-vessel
Open-vessel
Parameter
0.255
0.381
0.253
8*U0
II. Variation of Pe number
Conversion
Peclet number/Pe
Closed-vessel
Open-vessel
Parameter
1.04e3
0.650
0.649
100* DAB
(c) Half order reaction with k= 0.495 (mol/dm3)1/2min–1
1
0
0
1
0
!! == n
A
n
AkC
U
L
kCDa
“
AB
DLUPe /
0
=
Input Parameters:
2/1=n