Mass transfer partial differential equations

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Hi,
I'm really struggling with the following problem. Do you have any pointers on how I would be able to go about solving it numerically? It is a partial differential equation.
dC/dt = A d2C/dz2 - B dC/dz
A and B are constants.
I am unsure how to go about solving it when there are three variables. The idea of the equation is to plot concentration against time in a packed bad adsorber.
Any help would be greatly appreaciated.

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