We can define an overall heat transfer coefficient, U, that considers the conductive resistance through the pipe wall and the convective resistances near the pipe wall on both sides of the wall due to the flowing fluids. We learned that convective heat transport can be described by the equation:  =  Given that the fluid on the inside of the pipe has a heat transfer coefficient of hi and is at the bulk temperature Ti and the fluid on the outside of the pipe has a heat transfer coefficient of ho and bulk temperature To, you will derive the overall heat transfer coefficient, Ui, of this system based upon the inner surface area of the pipe. 

2 a. Draw and label a picture of the system in question. 

b. Starting with a defined control volume and a corresponding balance equation (material or energy balance), derive the expression for the overall heat transfer coefficient. Be sure to comment on each step in your derivation to demonstrate you understand its rationale.