Setting up and solving for the concentration profile in Maple
The starting point for this problem is with the equation of continuity. From there we go on to define the flux and then continue until we come up with a potential concentration profile.
The above result is the equation for constant flux that checks with the one in the book, eqn 18.5-5.
Now we must get the concentration profiles. There are two different ways of expressing them.
The first way is by equation 18.5-4. Here we are going to plug in 18.5-4 and see if this simplifies to zero, thus proving that it is a valid concentration profile.
This proves that eqn 18.5-4 is one of the concentration profiles.
The other check on the concentration profile and the flux equation comes from combining equation 18.5-4 with eqn 18.5-5 to give
So the equations for the concentration profile and the flux equation are both valid.
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