A cylindrical cooling fin is installed on a wall. The fin is immersed in an air flow and, far from the fin, the ambient air temperature is To, and the heat transfer coefficient between the air and fin is given by h. The heat flux at the wall (x=0) is a constant qo. Assume that T within the fin is a function of only x, that no heat is lost from the end of the fin at x=L, and that heat conductivity k is constant. 

4a: Derive the governing differential equation for T(x) within the fin (x=0) 9x=9. 

4b: Identify the boundary conditions 4c: Make 4a dimensionless using O=(T-T.)/Ta, (=x/L, and N'=2hL'/kR 

4d: Given that qozakT.N/L, make 4b dimensionless using 

4c (a: dimensionless coefficient) Ta (X=L) q,=0 

4e: Solve 4c using 4d to get O(4)