Constructal design of a disc-shaped heat exchanger (DSHE) is implemented in this paper. Maximum thermal efficiency and total tube volume are taken as the optimization objective and constraint, respectively. Optimal tube lengths of the DSHE are obtained, and the effect of mass flow rate on its optimal construct is analyzed. The results show that for the first order DSHE, its thermal efficiency has the maximum and the elemental tube angle has the corresponding optimal value. For the higher order DSHEs, the optimal constructs of the DSHEs are not varied when their mass flow rates are small and large enough, and the DSHE structure is simplified into the structure of the last order DSHE when the mass flow rate is large enough. For the same tube volume and area of the DSHEs with 4 central tubes and a large mass flow rate, the thermal efficiency of the third order DSHE is increased by 7.33% than that of the first order DSHE. Therefore, the performance of the DSHE is increased when its structure becomes complex in this case. The obtained results can offer some instructions for the optimal designs of various thermal systems, such as power, refrigeration and heat pump plants. (C) 2018 Elsevier Ltd. All rights reserved.