I am trying to derive the differential equation along with boundary conditions for steady state operation of the following system. This is an extended surface (see picture) attached to a cooling tower to enhance heat transfer to the ambient. The tower to which it is attached is 200 C and the ambient temperature is 5 C.

I am very lost and am unable to begin this problem. Any tips or suggestions for these problems in general as well as a path to follow for solving this particular problem would be greatly appreciated. I am capable of doing the math, just not the equally important task of deriving the equation.

Derive differential equation and boundary conditions for heat transfer.-scan.jpg