polymath - cheric · 2005-11-10 · unsteady state mass transfer in a slab equation of continuity...

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%