Analytical tools for calculating the maximum heat transfer of annular stepped fins with internal heat generation and radiation effects

ASFs (Annular stepped fins) require less material than ADFs (annular disc fins) while retaining the ability to produce the same cooling rate in a convection environment. A simple analysis was developed for ASFs that considered radiative heat transfer and heat generated by a nuclear reactor through linearization of the radiation terms. The linearized equations were solved by exact and approximate analytical methods. Without any linearization, a new closed-form analysis was established for the temperature profile with the help of the differential transform method. An integral differential transform method was introduced to determine the actual heat-transfer rate when heat was generated inside an ASF under nonlinear radiation surface conditions. The temperature results obtained using this analytical approach were compared with those obtained from a finite-difference analysis, and were in excellent agreement. The fin performance was defined as a function of the heat generated for a given set of design conditions. An optimization study with varying heat generation was carried out to compare the performance of ADFs and ASFs, which highlighted the superior aspects of an annular fin design.