Constrained Optimization of Heat Transfer from an Extended Surface

Abstract

Two different zero-order optimization techniques are used to maximize the rates of heat transfer from a fin assembly of a specified cost and in the shape of several annular fins that are mounted on a central stem. The problem is formulated to account for two-dimensional steady-state heat transfer that is limited by several inequality constraints. The dimensionless governing equations are used to identify the relevant decision variables. The number of fins making up the assembly is treated as an input parameter. A digital computer is used to determine the required temperature distributions and to implement the optimization search algorithms. Three different fin materials are assessed-aluminum, copper and carbon steel. Design optimizations of the extended surface assembly were made over a range of operating conditions, encompassing several different convection heat transfer coefficients that are representative of free and forced convection in air, and several different overall temperature differences between the substrate surface and air. A few recommendations based on trends in the predicted results are given.