An environmentally toxic radioactive chemical is continuallyreleased at a constant rate of 1 (mg per vol per time) at themidpoint of a canal of length L with still water. As it diffusesthrough the canal with diffusion constant D = 1, it decays at rate? (per unit time) The ends of the canal are connected to largebodies of toxic-free water. Set up the model equations and theboundary conditions. Find the steady-state concentration and sketchits spatial profile for different values of L and ?.
[Hint: Break the problem up into two parts, on each sideof the source. At the source the concentration must be continuous,and in a small interval about the source, the ‘flux in’ minus the‘flux out’ equals one.]
