The functioning of the solid-gas reactors is governed by several combined phenomena: heat and mass transfer and solid-gas chemical reaction. Heat and mass transfer phenomena have an antagonistic behavior in the reactive material used in the solid-gas reactors. This behavior of the material influences strongly both their power and energy performance and their design. In this paper, an optimal tree-shaped network for heat and mass transfer is constructed by using the constructal approach and the entropy generation minimisation method. The results of these optimisation show that, for a given heat and gas diffuser and a fixed porosity, we can find an optimal diffusers network design for any material. These optimal designs have the same minimum of entropy generation or "entropy generation number". (C) 2004 Elsevier Ltd. All rights reserved.