1. The problem statement, all variables and given/known data The goal is to derive the heat equation with convection, ut=α2uxx-vux but for the case where u(x,t) instead models concentration changes by diffusion and convection. The idea is to use conservation of mass to do this. 2. Relevant equations We are given: Change of mass inside [x,x+Δx] = Change due to diffusion + Change due to material being carried across boundary 3. The attempt at a solution I can solve this problem for the case where we are using the actual heat equation, as it becomes a flux problem with Fourier's Law and some calc tricks, but I can't figure out how to set up this problem for material flow. I think that u(x,t) should be in units of mass/vol of some sort, making ut have units of mass/(vol*time), and for the heat equation, LHS = d/dt(∫cρAu(s,t)ds), so I'd expect it to look something like that. Perhaps without the thermal capacity constant c in the equation. For the RHS, I'm pretty lost, as I can't use Fourier's law for a concentration problem, or at least I don't think I can.