2) ( 50 p) Air at the temperature of T1 is being heated with the help of a cylindrical cooling fin shown in the figure below. A hot fluid at temperature To passes through the pipe with radius Rc. a) (35p) Derive the mathematical model that gives the variation of the temperature inside the fin at the dynamic conditions. b) (15p) Determine the initial and boundary conditions to solve the equation derived in (a). Assumptions: 1. Temperature is a function of only r direction 2. There is no heat loss from the surface of A 3. Convective heat transfer coefficient is constant