Two-dimensional convective flows in tall cavities with adiabatic or conducting horizontal boundaries and driven by differential heating of the two vertical sidewalls, are studied numerically over a range of Rayleigh numbers and Prandtl numbers. By using a Dufort-Frankel-Multigrid method, numerical results for the relevant end-zone problems in the limit of large aspect ratio are obtained for a range of Rayleigh numbers from A = 500 to 70000 and for different Prandtl numbers sigma. The flow patterns show that the parallel flow in the core region is destroyed at A(c) almost-equal-to 7880sigma, in good agreement with stability analysis. Nusselt number predictions are compared with those of previous numerical and experimental studies of the overall cavity flow.