Variation of parameters method for optimizing annular fins with variable thermal properties

The aim of this study is to offer useful correlation equations to the designer for the optimum design of annular fins with thermal properties varying with temperature. in order to obtain the optimum size of the fins, the heat transfer from the fin must be calculated with the least assumptions possible. therefore, the variation of the heat transfer coefficient and thermal conductivity with the temperature are considered in this study and a nonlinear fin equation is solved with the variation of parameters method, which is quite new in the solution of nonlinear heat transfer problems. heat transfer rate from the fin to the environment is calculated in terms of dimensionless problem parameters with the help of the obtained temperature distribution. fin geometries maximizing the heat transfer rate are determined for the given problem parameters. these results, which can be used for nucleate boiling, natural convection and forced convection heat transfer modes, are offered to the designer with two identical correlation equations.