  A solution is developed for a convection-diffusion equation describing
chemical transport with sorption, decay, and production. The problem is
formulated in a finite domain where the appropriate conservation law yields
Robin conditions at the ends. When the input concentration is arbitrary, the
problem is underdetermined because of an unknown exit concentration. We resolve
this by defining the exit concentration as a solution to a similar diffusion
equation which satisfies a Dirichlet condition at the left end of the half
line. This problem does not appear to have been solved in the literature, and
the resulting representation should be useful for problems of practical
interest. Authors of previous works on problems of this type have eliminated
the unknown exit concentration by assuming a continuous concentration at the
outflow boundary. This yields a well-posed problem by forcing a homogeneous
Neumann exit, widely known as the Danckwerts [1] condition. We provide a
solution to the Neumann problem and use it to produce an estimate which
demonstrates that the Danckwerts condition implies a zero concentration at the
outflow boundary, even for a long flow domain and a large time.
