Unsteady state heat transfer

Kalus

I'm hoping to start a simple heat transfer model. It's basically a cylinder filled with air at a temperature T=300K. The bottom wall of the cylinder, made of steel, is heated (and kept at the constant temperature of T=400K). The side walls and top for the moment are treated as adiabatic (since I assume it will make it easier to solve).

What equations can I use to describe the temperature distribution in the air with time and distance?

I'm really looking for a resource that explains a similar scenario or a fairly simple book on explaining how to solve heat transfer problems like these?

Thanks,

Kalus :)