i have been struggling to compute a particular instance of cylindrical 3D heat equation.

Here is my code :

```
(*parameter*)
(Alpha) = 0.1;
eq = D(u(t, r, (Theta), z), t) ==
D(u(t, r, (Theta), z), r, r) + 1/r D(u(t, r, (Theta), z), r) +
1/(Alpha).b2r.b2 D(u(t, r, (Theta), z), (Theta), (Theta)) +
D(u(t, r, (Theta), z), z, z);
(*initial and boundary conditions*)
ic = {u(0, r, (Theta), z) == Exp(-r)};
bc = {u(t, 10^-6, (Theta), z) == 1,
u(t, 1, (Theta), z) == 0,
PeriodicBoundaryCondition(u(t, r, (Theta), z), (Theta) == 0,
TranslationTransform({2*Pi, 0})),
PeriodicBoundaryCondition(u(t, r, (Theta), z), (Theta) == 0,
TranslationTransform({2*Pi*(Alpha), 0})),
Derivative(0, 1, 0, 0)(u)(t, 1, (Theta), z) == 1,
Derivative(0, 1, 0, 0)(u)(t, 10^-6, (Theta), z) == 0};
(*solution*)
sol = NDSolve({eq, ic, bc},
u(t, r, (Theta), z), {t, 0, 1}, {r, 10^-6, 1}, {(Theta), 0,
2*Pi}, {z, 0, 1});
(*plot*)
Manipulate(
Plot3D(sol, {r, 0, 1}, {(Theta), 0, 2 Pi}), {t, 0, 10}, {z, 0, 1});
```

The problem is, i keep getting an error like this :

```
NDSolve::femcnmd: The PDE coefficient {{-1,0,0},{0,-(1/(Alpha).b2r.b2),0},{0,0,-1}} does not evaluate to a numeric matrix of dimensions {3,3} at the coordinate {0.500002,3.14159,0.5}; it evaluated to {{1.,0.,0.},{0.,1/(Alpha).b2r.b2,0.},{0.,0.,1.}} instead.
```

I am a relatively new mathematica user, so i do not see any issue that could arise from evaluating the coefficients at the point *{0.500002,3.14159,0.5}*.

Can you guys help me understand ? Thank you kindly.