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Unformatted text preview: nce equation for a boundary cell. Let’s consider the approximate balance
equation for the first cell. ( ) The problem is that we don’t have an unknown outside the mesh to compute , i.e., we don’t have a .
To deal with this difficulty, we must just recognize that whatever we do, the boundary condition must
play a role. Let’s assume a vacuum boundary condition. Analytically, we know that
()
Equivalently, () The only problem here is that we don’t have a
equation for , so let’s add one to the first cell. Now, we need an . How about using continuity of the current to define ? The boundary condition gives us And Fick’s law using and gives us
( ) If we equate the two, we can solve for
( ( Now, we can solve for Thus, our equation in the first cell becomes ) ) ( ) By analogy in the last cell, we get
( )...
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This note was uploaded on 10/06/2013 for the course NEUN 430 taught by Professor Morel during the Fall '10 term at Texas A&M.
 Fall '10
 Morel

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