ESG-1 Efficiency of Extended Surfaces
A review is given of the concept of the efficiency of extended surfaces. An analytical derivation of the fin efficiency for straight longitudinal fins is first used to illustrate the usefulness of this concept. A discussion is then presented of the various methods used to calculate the fin efficiency of extended surfaces of different shape and form. Simple analytical expressions are given for calculating the fin efficiency of round cross fins and rectangular cross fins. These expressions can be readily incorporated in a computer program, thus eliminating the necessity of using fin efficiency graphs. The inadequacy of the fin efficiency concept in light of the simplifying assumptions used in its derivation are outlined. The assumption of uniformity of heat transfer coefficient on the surface of the fins is shown to be the most unrealistic of the assumptions used for the fin efficiency. The nonuniformity in the heat transfer coefficient reduces the fin efficiency below its theoretical value. Nevertheless, the theoretical fin efficiency can be still used with a correction factor formula given in the report. Special aspects of the fin efficiency as fin bond, the experimental electrical analogy technique and heat transfer under different modes than forced convection are all reviewed.