Packed bed mean field model

Hi,

I am trying to solve the time-dependent concentration profile in a packed bed using the mean field theory rather than the whole CFD definition of the problem. The mass giving rise to the concentration in the bed comes from a source (diffusive flux coming out of spheres in the bed).

I have tried the convection-diffusion equation in the Mathematics library. My problem though is that I am not quite sure how to couple the diffusion out the spheres to the external flow.

Any help is greatly appreciated