Two dimensional effects and design criteria with Biot and transfer number for circular (annular) fins having internal heat generation density

An analysis of the thermal performance as well as the usefulness criteria of extended constant cross section circular fins having internal heat generation density is presented. The solution of the optimal problem is given, when either the desired heat dissipation rate or the volume of the fin is specified. After having specified the criteria of effectiveness, usefulness, and optimization of the fin, based on these criteria the conditions that allow the optimal fin to be manufactured and used will be extracted. Thus the possibility of such a simplification of a complex problem will be proved. The Transfer (removal) number is numerically determined as a function of Biot number and the plots extracted are particularly useful for computerized calculations. Also the application of the theoretical results to practical problems is demonstrated. © 2013 praise worthy prize S.r.l.-All rights reserved