Unsteady state diffusion in semiinfinite medium

1
Unsteady state diffusion in semi-infinite medium
C
t
C1
C0
x
Initial condition At t 0, for all x, C
C0 C(x,0) C0 Boundary conditions 1 At x 0,
for tgt0, C C1 C(0,t) C1 2 At x ?, for all
t, C C0 C(?,t) C0
Solution
2
Unsteady state diffusion in finite slab having
negligible surface resistance
C
2x1
C0
C1
C1
t
x
Initial condition At t 0, for all x, C
C0 C(x,0) C0 Boundary conditions 1 At x 0,
for tgt0, C C1 C(0,t) C1 2 At x 2x1, for
tgt0, C C1 C(2x1,t) C1
Solution
3
Unsteady state diffusion in spherical bead
?r
C0
R
r
C1
Initial condition At t 0, for all r, C
C0 C(r,0) C0 Boundary conditions 1 At r R,
for tgt0, C C1 C(R,t) C1 2 At r 0, for all
t, (?C/?r) 0
Solution