Radiation heat transfer for annular fins of trapezoidal profile

A numerical solution is obtained for the steady-state thermal behavior of annular fins of trapezoidal profile which transfer heat by conduction and radiation. The solution is obtained by utilizing a searching technique which is applicable only to problems in which the conduction may be treated as one-dimensional. An investigation is made of eight other methods for finding the temperature distribution in fins of this type. Any of these methods could be applied to problems in which the conductive heat flow is treated as two-dimensional. Only four of these methods produced any results and the results obtained tended to deviate from the actual solution as the number of finite radial increments was increased. The following idealizations were made in the formulation of the problem: 1. The conductive flow of heat is radial. 2. The heat flow and temperature distribution throughout the fin are independent of time. 3. There are no heat sources or sinks in the fin. 4. The temperature at the base of the fin is uniform. 5. The fin material is homogeneous, and the properties of the material are independent of the temperature. 6. The heat transfer from the tip of the fin is negligible. 7. There is no incident radiation on the surface of the fin. 8. The fin is a gray body.