PolymathPolymath
for Partial for Partial Differential Differential EquationsEquations
Partial Differnetial Equations (PDEs)
One dimensional problem : t and x
Two dimensional problem : t , x, and y
t
x y z
t
x
x
t
t
x y
yt
x
ty
z
x
Unsteady state mass transfer in a slab
0 0
Diffusion and Reaction in Falling Liquid Film
0
Diffusion Equations as PDEs
Unsteady state mass transfer in a slab
Equation of continuity of A for constant ρ and DAB
0 0
No mass transfer
Distribution coefficient, K
kc for external mass transfer
Questions
1. Concentration vs. Distance after 2500s ( interval=0.0005)
2. Concentration vs. time to 25000s at x=0.001, 0.002, 0.003 and 0.004
3. Concentration vs. Distance after 2500s ( Interval=0.00025)
1 2 3 4 5 6 7 8 9
CA1 CA2
CA3 CA9CA4
CA5CA8
CA7CA6
Boundary Condition for case (1)
for case (2)X=0.0
X=0.004
0.004m
Initial Condition : linear concentration profile
0.001kg-mol/m3
0.002kg-mol/m3
Final time=30000
Final time=50000
K=300
Final time=50000
K=0.01
Final time=2500
kc=0.000001
Final time=40000
kc=0.000001
Diffusion and Reaction in Falling Liquid Film
CA1
CA2
CA3 CA11
CA4
CA5
CA8
CA7
CA6
CA9
CA10
1 2 3 4 5 6 7 8 9 10 11
V max
CO2
x
z
0
CAn = 0 at Z=0
CA1=0.03 for z≥0
CA11=(4CA10-CA9)/3
Questions
1. Concentration of dissolved A within the solution at z=1m, no reaction
2. Average flux of A
3. Concentration vs z
4. Compare adsorbed A with exiting A value
5. Reaction constant, k=1s-1
6. Compare 1 with 5
9.438×10-7
MA1=Navg*H*W=9.438×10-7
MA2=H∫vzCAdx=1.108×10-6
(MA2/MA1)= 117.4%, error=17.4%