{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture5

# lecture5 - where A and B are constants to be determined...

This preview shows pages 1–3. Sign up to view the full content.

(2) Extended initial distributions, e.g., for the initial condition, ( ) > < = 0 for 0 0 for 0 , x x c x c o c o c x ξ x = 0 Consider a line source of strength, ξ d c o ( ) Dt Dt d c o 4 exp 2 2 2 1 ξ π ξ ξ d Superposition of the profiles from all elements, ( ) ( ) = = x o o Dt x erfc c d Dt Dt c t x c 2 2 4 exp 2 , 2 2 1 ξ ξ π Derive the short-time non-steady state concentration profiles for the following two cases c o c x =0 x h (a) initial x x =0 c initial ( ) 2 0 , x e Q x c = π ( ) = otherwise 0 0 0 , h x c x c o (b)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Error Function Solution ( ) 2 2 0 2 , 0 0 0 c Dt x erfc c t x c = = = = c c o /2 x = 0 x The concentration profile in a semi-infinite system with initial concentration zero and a constant surface concentration, c o /2, is given by the same expression Error Function Solution ( ) + = Dt x Berf A t x c 2 , In general, for infinite and semi-infinite systems with constant surface concentration, the general solution is given by
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: where A and B are constants to be determined from the boundary conditions. ( ) Dt x erfc c s 2 c s c o c o c s ( ) Dt x erf c o 2 c o c s ( ) ( ) Dt x erf s c o c s c 2 − + Surface Flux ( ) = Dt x erfc c t x c s 2 , Example, an infinite system with zero initial concentration and with its surface concentration maintained at c s , the solution is given by Surface flux, t D c Dt e Dc x c D J s x Dt x s x x π = − − = ∂ ∂ − = = − = = 4 2 1 2 2 Total Amount of Diffusion Dt Dt c dt t D c dt J Q s t s t x ∝ = = = ∫ ∫ = 2...
View Full Document

{[ snackBarMessage ]}