I'm writing a simple FDM algorithm for solving the well known 3D heat equation
$$ \frac{\partial u}{\partial t} = \alpha \nabla^2 u + \frac{q}{c_p \rho} $$
where $q(x,y,z,t)$ represents the internal heat generation and $\alpha$, $\rho$ and $c_p$ are constants. Now, in order to test my numerical solution, it would be great to have some (even easy) initial conditions and boundary conditions for which an analytical solution is known so I can evaluate my algorithm and different finite difference schema. Can someone point me out in the right direction?