Convective heat and mass transfer in a planar, trilayer, solid oxide fuel cell (SOFC) module is considered for a uniform supply of volatile species ( vapor) and oxidant to the electrolyte surface with a uniform electrochemical reaction rate. The coupled heat and mass transfer is modeled by steady incompressible fully developed laminar flow in the interconnect ducts of rectangular cross sections for both the anode-side fuel and cathode-side oxidant flows. The governing three-dimensional mass, momentum, energy, species transfer, and electrochemical kinetics equations are solved computationally. The homogeneous porous-layer flow, which is in thermal equilibrium with the solid matrix, is coupled with the electrochemical reaction rate to properly account for the flow-duct and anode/cathode interface heat/mass transfer. Parametric effects of the rectangular flow-duct cross-sectional aspect ratio and anode porous-layer thickness on the variations in temperature and mass/species distributions, flow friction factor, and convective heat transfer coefficient are presented. The thermal and hydrodynamic behavior is characterized for effective convective cooling performance, and interconnect channels of cross-sectional aspect ratio of along with relative anode porous-layer thickness of are seen to provide optimal thermal management and species mass transport benefits in the SOFC module.