Question: Modelling Conduction in a Short Cylinder

Hi

I have been using the pdesolve command to solve the heat conduction equation in an infinitely long cylinder, but now I need to incorporate the convection that occurs at the end surfaces, in the case of a short cylinder.

The following is the code I have been using:

>> PDE := diff(Theta(r, t), r, r)+(diff(Theta(r, t), r))/r = (diff(Theta(r, t), t))/alpha;

>> pdsolve(PDE);

I have tried to add the z direction to the PDE equation as follows:

>> PDE := diff(Theta(r, t), r, r)+(diff(Theta(r, t), r))/r + diff(Theta(z,t),z,z) = (diff(Theta(r, t), t))/alpha;

But when I try to solve it, I get the error:

Error, (in pdsolve/info) the name of the indeterminate function must be given

I am relatively new to Maple, but having looked at the user guide, I need to name the indeterminate function in the pdsolve(PDE, f) line.

Can anyone give me some advice on what the indeterminate function f should be?

Thank you for any help you can give :)