We're currently studying steady state one dimensional conduction heat transfer. We've touched on some surface convection, resistances in layers and fins.
I don't think I'll have much issue with this problem once I find this out:
What is a thermal driving force?
You know what, based on the information given, I would let velocity drop out as well. In a basic thermo class most prevalent place you're going to see velocity -not- being negligible is in nozzle and diffuser problems, or where it is expressively given to you in the problem statement.
I would treat this as a steady state problem. Meaning your mass flow rate in is going to equal your mass flow rate out. and de/dt is zero.
Since we're not given any sorts of elevation, the potential energy will be drop out. No work is happening, so W will also drop out.
You will be...
Closed system, control mass.
What you're going to want to do is model both objects as incompressible.
ca=specific heat aluminum
ci=specific heat iron
Imcompressible 1st Law
U=Q-W Q=0, W=0