Consider the situation of solute in all tration. let us denote by car, t), the tion of solute in a thin pipe of length l is transfer due to differences in concen- s denote by c(x, t), the concentration at x at time t and let (c. t) be the flux (mass per second) at r at time t. use the law of conservation to derive the diffusion equation for c, in the solute is pumped in the pipe at a rate of f (x, t).