Constructal optimizations of the first to fifth order line-to-line vascular channels (LVCs) with convective heat transfer are carried out in this paper by taking minimum entropy generation rate (EGR) and minimum entropy generation number (EGN) as the optimization objectives, respectively. The angles of the LVCs are taken as the optimization variables, and the fixed vascular channel areas and total volumes of LVCs are taken as the constraints. The optimal constructs corresponding to minimum EGR and minimum EGN are obtained, respectively. The influences of the mass flow rate (MFR) on the optimal results are analyzed. The results show that the EGR of the LVCs decreases when the angle freedom increases with the constant dimensionless MFR, which is more obvious when the order increases. When the order increases, the EGR increases but the EGN decreases. Both the EGR and-the EGN increase with the increase of the dimensionless MFR. The results obtained herein can provide some thermal design and management guidelines for the applications of LVCs. (C) 2018 Elsevier Ltd. All rights reserved.