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

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

View Full Document Right Arrow Icon
(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, d c o () Dt Dt d c o 4 exp 2 2 2 1 π 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 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 = () = otherwise 0 0 0 , h x c x c o (b)
Background image of page 1

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

View Full DocumentRight Arrow Icon
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
Background image of page 2
Background image of page 3
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

This note was uploaded on 01/19/2010 for the course MAT SCI 503 taught by Professor Chen during the Spring '02 term at Penn State.

Page1 / 3

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online