Constructal entransy dissipation rate minimization for helm-shaped fin with inner heat sources

A model of three-dimensional helm-shaped body composed of a helm-shaped fin and inner heat sources is built in this paper. For the specified volumes of the body, fin and heat source, the constructal optimizations of the body with single and multiple inner heat sources are implemented. The entransy-dissipation-rate-based equivalent thermal resistance(ETR) is minimized in the optimizations. It shows that for the helm-shaped body with multiple inner heat sources, there exist an optimal ratio of the heat source distance to the radius of the extended fin and a twice optimal radius ratio of the centre fin to the extended fin which lead to the double minimum dimensionless ETR. Comparing the optimal result of the body with helm-shaped fin with that with annular fin, the radius of the centre fin and the distance between the heat source and the center of the body are decreased, and the ETR is decreased by 9.57%. Essentially, the temperature gradient field of the helm-shaped body is more homogenous, and its global heat transfer performance is improved.