Question

Tried to find in textbook but failed. I really need the analytical solution to the following PDE (diffusion from the infinite length cylinder, two-dimensional crosssection):

$\partial_t C(r,t)=D\frac{1}{r}\partial_{r}(r\partial_r C(r,t))$ with the following boundary conditions: $C(R,t)=C_0$ - the concentration of the cylinder is kept constant, $C(r,0)=C_{init}$, where $r>R$. Initial concentration in the domain is constant as well.

Need the analytical solution in the domain $r \geq R$.

Answer 1

I've got it answered on SolversMarket. The procedure was to introduce variable transformation $\ln\frac{r}{R}$ and then just do the same stuff as to derive the boundary layer as in the case of planar interfaces.