Constructal design for “+” shaped high conductivity pathways over a square body

A heat generating model with “+” shaped high conductivity pathway over a square body is built in this paper. For the specified areas of the high conductivity pathway and square body, the constructal optimizations of the square body with single and multilevel “+” shaped high conductivity pathways are carried out by taking minimum dimensionless peak temperature as optimization objective. The optimal constructs of the “+” shaped high conductivity pathways and triple minimum dimensionless peak temperature of the square body are obtained. The results show that the minimum dimensionless peak temperature of the square body with multilevel “+” shaped high conductivity pathway is reduced by 75.79% compared with that with X shaped one. The heat transfer performance of the square body is obviously improved by adopting the multilevel “+” shaped high conductivity pathway, and it can be further improved by increasing the dimensionless thermal conductivity and area fraction of the high conductivity material. Thermal stress performance should be also considered in the constructal design of a heat generating body. The results obtained in this paper can provide some guidelines for the designs of electronic devices.