Optimal Positioning of Tubes in Arbitrary Two-Dimensional Regions Using a Special Boundary Integral Method

Two-dimensional steady conduction heat transfer from a set of parallel tubes located in a finite two-dimensional region enclosed by an arbitrarily shaped boundary is considered. A special boundary integral method is used in an optimization scheme where the tube sizes, positions, and surface temperatures can be determined in an iterative procedure with the objective of minimizing the variation of temperature over a specified segment of the boundary. Previous studies of this type were limited not only to rectangular regions but also to uniform heat flux results on the surface of each tube. However, the optimization scheme developed in this study is applicable to any arbitrarily shaped two-dimensional region and considers angular variation of heat flux on the surface of each tube. Results for three sample geometries are presented and discussed.