The Numerical Optimization of a Neumann-Type Boundary for the Graetz Problem

Abstract

The main goal of this study is to numerically determine a converged optimal heating pattern for the Graetz problem in a two-dimension channel subjected to a discrete heating profile. The heat input is provided by multiple independent heaters, while considering the following conditions: symmetric and asymmetric heating without a conductive wall and symmetric heating with a conductive wall. The optimization process, which was based on the genetic algorithm, shows a strong dependence of the cooling performance on the heating profile which is especially affected at relatively low flow speeds if the wall conduction is not present. If conduction through the wall is considered, the importance of the heating pattern is reduced for relatively thick walls. Results also indicate that asymmetric heating conditions are not recommended when compared with symmetric patterns.

Acknowledgments

Gosselin's work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).