A heat and mass transfer process for solid-gas reactors in a disc-shaped body is investigated in this paper. Radial- and branched-pattern integrated collectors are embedded in the body to enhance heat and mass transfers. The distributions of the integrated collectors in the two pattern discs are optimized using constructal theory and entransy theory. The results indicate that the optimal elemental volume fractions obtained by the minimizations of entransy dissipation rate and entropy generation rate are evidently different. There exists a critical radius, which decides whether the radial- or branched-pattern design is used. The decrease in the thermal conductivity ratio and increase in the first order volume fraction of the integrated collector lead to a better performance of the solid-gas reactor. The model with pure heat conduction or mass transfer is special case of the model in this paper. The results obtained in this paper can provide some design guidelines for the solid-gas reactors. (C) 2015 Elsevier Ltd. All rights reserved.