The present study concerns the laminar mixed convection flow over a heated or cooled horizontal plate of finite length at a zero angle of attack and a small Richardson number. The plate is located either in a channel or in a semi-infinite space behind a flow straightener. In the limit of a small Prandtl number, these conditions correspond to the boundary-layer solutions of Müllner and Schneider (2010), and Schneider (2000), respectively. The hydrostatic pressure difference between the plate's lower and upper sides and the Kutta condition at the trailing edge induce a circulation with a global effect on the flow around the plate. In contrast to the classical aerodynamics problem of an isothermal flow around an inclined plate, the thermal wake also contributes to the circulation in the outer flow. This circulation can lead to flow separation at the bottom side of a heated plate (or an upper side of a cooled plate) when the Richardson number exceeds a certain threshold, depending on the Reynolds and Prandtl numbers. The steady two-dimensional solution of the governing equations under the Boussinesq approximation is computed with the Finite Element solver FEniCS. Goal-oriented adaptive mesh refinement is employed in order to resolve both the viscous and the thermal boundary layers. In the talk, the numerical solution will be compared to the boundary-layer solutions. The effect of the governing parameters on the flow will be investigated, also beyond the range of validity of the boundary-layer solutions. For a plate inside a channel, the flow separates close to the leading edge even for relatively low values of the Richardson number. The threshold Richardson number for separation decreases with increasing Reynolds number. For certain parameters, multiple steady two-dimensional solutions come into existence, differing by the size of the separation bubble. We show that the separation can be suppressed by bending a short leading section of the plate. Finally, we consider the effect of a heat source at the leading edge of a cooled plate. References M. Müllner and W. Schneider, Heat Mass Transf. 46, 1097-1110 (2010) W. Schneider, Proc. 3rd Eur. Therm. Sci. Conf., 195-198 (2000)