A numerical study was carried out to examine the development of duct flows being affected by combined buoyancy force-driven secondary flow and mass transfer. The developing flow and heat transfer have been simulated numerically for a horizontal fuel cell duct with rectangular and trapezoidal cross section. Constant heat flux and mass transfer rate are prescribed on the bottom wall, while thermal insulation is implemented on the other three impermeable walls. The buoyancy-generated secondary flow and mass transfer can disrupt the hydrodynamic and thermal boundary layers, and thus affect the friction factor and Nusselt number. Calculations have been performed to determine the effects of various Grashof number, mass transfer rate, and Reynolds number. Comparisons of these numerical results with available data are presented.