Solving partial differential equation

I am new to mathematica and I want to solve the following pde. I have two boundary conditions and one initial condition.

I have tried the following code but the output is not the solution and it’s just a simplified version of the equation. This is the code that I’ve tried:

pde = D[T[r, t], t]/a == D[r^2 D[T[r, t], r], r]
ic = {T[r, 0] == 0, k*A*D[T[r, t], r] == Q*HeavisideTheta[tao - t] /. r -> 0.5 dp,T[Infinity, t] == 0}
DSolveValue[{pde, ic}, T[r, t], {r, t}]

I have used other functions like NDSolve, but nothing seems to work. I would appreciate it if you could tell me what is it that I am doing wrong.