Mass transfer partial differential equations

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.