Buoyancy effects in plane Poiseuille flow heated isothermally from below were analyzed. By employing the propagation theory we have developed the critical streamwise position to mark the onset of stationary longitudinal vortex rolls was predicted as a function of the Prandtl number. Combining the present stability criteria with the boundary-layer instability model, a new correlation of transport properties on mixed convection was derived. Even though the present modelling is rather simple, theoretical results compare well with experiments of both air and ionic mass transfer in aqueous CuSO4 solution systems.