# Boundary condition problem for diffusion equation

## Main Question or Discussion Point

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we cannot assume that the chemical is not dispersed at the end of the channel- so the boundary condition c(a,t)=0 is no longer valid?

What boundary condition can we use when we cannot assume that the chemical is not dispersed at the outlet of the channel? Can you state it or not? How about computational fluid dynamics boundary conditions options?

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mfb
Mentor
##\lim_{a\to\infty} c(a,t)=0##?

Chestermiller
Mentor
At the two ends of the sample, you can have a wide variety of different combinations of boundary conditions:

Specified concentration c = C(t)
Zero flux: δc/δx = 0
Specified flux: -D ∂c/∂x = $\phi$(t)
Convective mass transfer: -D ∂c/∂x = k (c - c)

There are an infinite number of others also, but these are the ones you run into most often in practice.

AlephZero