SCHMIDT,ERNST APPROACH TO FIN OPTIMIZATION - AN EXTENSION TO FINS WITH VARIABLE CONDUCTIVITY AND THE DESIGN OF DUCTS FOR FLUID-FLOW

In the first part of the paper, Ernst Schmidt's intuitive argument for choosing the optimum fin shape for least material is translated into analysis using the method of variational calculus. In the second part of the paper the analytical generalization of Schmidt's argument is applied to the design of ducts for fluid flow. It is shown that the shape of a duct the flow pattern or temperature of which varies with the longitudinal position can be selected optimally such that the overall flow resistance of the duct is minimized. The optimization of the duct shapes illustrated in this paper is conducted subject to one of two constraints, constant total duct volume or constant total duct wall surface.