Based on constructal theory, the disc-shaped solid gas reactors combined heat and mass transfer are investigated in this paper. Radial- and branched-pattern of the discs are considered, and the two pattern discs are optimized based on entropy generation rate minimization. The results show that there exist a minimum value of the entropy generation rate and the corresponding optimal construct of the reactor. The minimum entropy generation rate increases with the increase in the radius of the first order disc; therefore, a proper radius of the first order disc should be adopted according to the practical demand of the reactor. The performance of the reactor can be improved by increasing the material amount of the integrated collector or reducing the number of elemental tributaries and the thermodynamic parameter eta. The design pattern of the disc depends on the relationship of the critical radius and disc radius. Moreover, the heat transfer or mass transfer models are special cases of the heat and mass transfer model in this paper. (C) 2015 Elsevier Ltd. All rights reserved.