Constructal optimization of cylindrical heat sources with forced convection based on entransy dissipation rate minimization

Based on constructal theory and entransy theory, the optimal designs of constant- and variable-cross-sectional cylindrical heat sources are carried out by taking dimensionless equivalent resistance minimization as optimization objective. The effects of the cylindrical height, the cylindrical shape and the ratio of thermal conductivity of the fin to that of the heat source are analyzed. The results show that when the volume of the heat source is fixed, there exists an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius which leads to the minimum dimensionless equivalent thermal resistance. With the increase in the height of the cylindrical heat source and the ratio of thermal conductivity, the minimum dimensionless equivalent thermal resistance decreases gradually. For the heat source model with inverted variable-cross-sectional cylinder, there exist an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius and an optimal radius ratio of the smaller and bigger circles of the cylindrical fin which lead to a double minimum dimensionless equivalent thermal resistance. Therefore, the heat transfer performance of the cylindrical heat source is improved by adopting the cylindrical model with variable-cross-section. The optimal constructs of the cylindrical heat source based on the minimizations of dimensionless maximum thermal resistance and dimensionless equivalent thermal resistance are different. When the thermal security is ensured, the optimal construct of the cylindrical heat source based on minimum equivalent thermal resistance can provide a new alternative scheme for the practical design of heat source. The results obtained herein enrich the work of constructal theory and entransy theory in the optimal design field of the heat sources, and they can provide some guidelines for the designs of practical heat source systems.