
336 SECOND-ORDER PARABOLIC EQUATIONS WITH ONE SPACE VARIABLE
◮ Mass exchange between fluid film and gas.
The mass exchange between a fluid film and the gas above the free surface, provided that
the admixture concentration at the film surface is constant and there is no mass transfer
through the solid surface, meets the boundary conditions
w = 0 at x = 0 (0 < y < 1),
w = 1 at y = 0 (x > 0),
∂
y
w = 0 at y = 1 (x > 0).
The solution of the original equation subject to these boundary conditions is given by
w(x, y) = 1 −
∞
X
m=1
A
m
exp
−aλ
2
m
x
F
m
(y),
F
m
(y) = y exp
−
1
2
λ
m
y
2
Φ
3
4
−
1
4
λ
m
,
3
2
; λ
m
y
2
,
(1)
where the function F
m
and the coefficients A
m
and λ
m
are independent of the parameter ...