I am looking for the analytical solution of 1-dimensional advection-diffusion equation with Neumann boundary condition at both the inlet and outlet of a cylinder through which the fluid flow occurs. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2}-v\frac{\partial C}{\partial x}$$ with initial condition $$c(x,0) = C_i$$ and with Neumann boundary condition $$\frac{\partial C}{\partial x}=0\text{ at }t>0.$$
Could someone suggest a reference?
I had a chance to look at the answer posted here. Out of the solutions listed, I couldn't find the analytical solution for the transport equation with Neumann boundary condition at both the ends.