What do you know about tensor formulation? If you don't know about tensor formulation you need to learn it to answer these kinds of questions.
This is what I have, thought?. ρcp (δT/δt) = k (δ2T/δr2) + (k/r2)(δ2T/δθ2) + k(δ2T/δz2) Note all the 2s are squares.
Do you know the tensor formulation for the statement in co-ordinate free representation?
I ask this because if you don't, then learning it will make these problems very easy to not only understand how to solve, but also conceptually.
If i know it I don't know it by that name. Thanks for the help.