Generating constructal-conduction-networks for cooling discs at macro and micro scales

Heat-generating discs with point heat sinks on the rim are designed using the generating optimization method at both macroscale and microscale. The disc is constructed by elemental sectors with cooling channels extending inward from the rim. To formulate the initial structure for the generating optimization, an analytic analysis based on the constructal law and entransy theory is applied. It is the first time to analytically formulate the entransy dissipation rate on triangular element with variable but coupled lengths and widths. The analysis indicates that the initial structures for macro problems and micro problems are different. The macro disc should be divided into infinite elemental sectors, while the number of elemental sectors in the micro disc is limited owing to the size effect. Moreover, the difference between the macro problem and micro problem can also be observed in the final design. At the macroscale, tree-like constructal conduction networks are constructed using the generating optimization that exhibit better conduction performance than classic needle structures. At the microscale, the needle constructal conduction network is more capable of reducing thermal resistance. These findings are presented in numerical cases of generating optimization.