In each of these problems, begin by deriving the governing equation using energy balances (even if we already derived the governing equation in class). This is important to practice.
1) Consider one-dimensional, steady state conduction through the wall of a pipe. The pipe has inner diameter Di and outer diameter Do. If the outside of the pipe is fixed at temperature To, and inside the pipe there is a convective boundary condition with T = T∞ and convective heat transfer coefficient h, find the temperature profile in the pipe.
2) Solve for the temperature profile in an extended fin of length L, with the prescribed temperature boundary condition, that is, T(L) = TL. What is the fin efficiency for this fin?
3) Consider one-dimensional transient conduction in a slab of thickness L. Initially, the entire slab is at temperature Ti and both surfaces are at temperature Ti. At time t = 0, the left surface (x = 0) temperature is increased to Ts. Find the temperature profile in the slab as a function of time. (Note the solution to this problem involves eigenfunctions).