This is a simple (*yet not simple to solve!*) transient heat transfer problem using cylindrical coordinates. There are solutions available in handbooks if you do not want to go through the math. Its been a while since I have done it, but I found this myself. 


**The boundary condition is the tricky part. If you are using convective boundary condition with known $h$, then you can use these charts provided by Cengel. With radiative heat tranfer, its a bit tricky. You would need to use Stephan-Boltzmann law and somehow estimate the emmisivity of your surface, as well as the view factor.**

![enter image description here][1]


  [1]: https://i.sstatic.net/L3Q7x.jpg