A New Look at Optimum Design for Convecting-Radiating Annular Fins of Trapezoidal Profile

This paper deals with a controversial problem in answering the question "Does the optimum fin design always exist? If not, what are the optimization ranges and limitations?" These authors employ a general example of convecting- radiating trapezoidal annular fin with heat transfer at the tip and wall resistance at the interface. The present results indicate that the answer to the above first question is negative. The ranges of fin optimum design under different thermal and physical conditions are proposed. The effects of Biot number, radiation number, the heat loss at the tip, fin profile and overall wall resistance on fin optimization range are further investigated and discussed.