# Boundary condition problem for diffusion equation

1. Oct 24, 2012

### brambram

1. The problem statement, all variables and given/known data
BOUNDARY CONDITION PROBLEM
I have came up with matrix for numerical solution for a problem where chemical is introduced to channel domain, concentration equation:

δc/δt=D*((δ^2c)/(δx^2))-kc

assuming boundary conditions for c(x,t) as : c(0,t)=1, c(a,t)=0. Where a is channel's length.

What if domain is not-infinite (as it is above) and we cannot assume that the chemical is not dispersed at the end of the channel- so the boundary condition c(a,t)=0 is no longer valid?

2. Relevant equations

What boundary condition can we use when we cannot assume that the chemical is not dispersed at the outlet of the channel?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 24, 2012

### haruspex

Perhaps it is asking you to set c(a, t) = f(t) for some unknown function f and obtain a solution in terms of f. But I'm only guessing.

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