Abstract The streamfunction-vorticity formulation is used to analyze unsteady laminar-convection problems in two-dimensional incompressible flows. The Bubnov-Galerkin finite-element method and a sequential procedure are employed to discretize and solve the governing differential equations. Very accurate results are obtained by employing “advective derivative conditions” at the outflow for all the variables involved. The boundary conditions for the streamfUnction at internal walls are imposed during the assembly process, and the vorticity at inflow and wall boundaries is evaluated in the framework of the stream/unction equation. The accuracy of the approach is demonstrated by the solution of two well-known benchmark problems concerning forced convection over a circular cylinder in cross flow and mixed convection in a plane channel heated from below.