Based on constructal theory, a model of a "disc-point" flow system with various flow speeds is considered in this paper. The optimal constructs of the radial-pattern and first order branched-pattern discs are obtained by taking the minimum maximum flow time and minimum average flow time as optimization objectives, respectively. The results show that there exist an optimal aspect ratio of the elemental sector and an optimal elemental fraction of the high speed flow channel which lead to the minimizations of the maximum flow time and average flow time of the flow system, respectively. The optimal constructs based on these two objectives are different. When the first order fraction is 0.1 and the number of elemental tributaries is 2, the dimensionless critical radius, which determine whether the radial-pattern design or branched-pattern design for the high speed flow channels is adopted, is 3.02 for minimum maximum flow time objective and is 2.29 for minimum average flow time objective. There exists an optimal number of the elemental tributaries which leads to the double minimum dimensionless average flow time of the flow system. The constructal optimization of the flow system by taking minimum flow time as optimization objective is helpful to improve its transfer performance. (C) 2015 Elsevier Ltd. All rights reserved.