Constructal design of multiple heat sources in a square-shaped fin

A new study area of constructal theory is presented by applying constructal design on multiple heat sources which connected to and cooled in a square-shaped fin. Analyzing the optimal location of the heat sources in the fin for several configurations is the primary goal of this study. According to the constructal theory, favorable distribution of the heat sources is achieved by minimizing the global thermal resistance of the fin body. Since the heat sources might be contemplated as heat-generating electronic bodies or hot-water pipes, two boundary conditions of uniform heat flux and uniform temperature are considered for the heat sources. The minimization of the thermal resistance in the uniform heat flux and uniform temperature cases leads to the minimization of the hot spot temperature and the maximization of the total heat removal, respectively. Temperature fields in the square-shaped fin are calculated using a finite element approach of MATLAB PDE Toolbox. The optimized configurations are numerically compared with each other. It is shown that the most commonly used configurations of the heat sources in a cooling industry are unfavorable and must be avoided. Favorable configurations such as triangular arrangement of heat sources are proposed to replace the unfavorable configurations.