This investigation is about laminar natural convection through an open-ended vertical annulus with a rotating inner cylinder, one uniformly heated boundary, and one adiabatic boundary. The boundary-layer equations governing this case have been solved by means of a finite-difference scheme and results are presented for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5. These results clarify the characteristics of the induced flow due to a constant heat flux at one of the boundaries. The development of the tangential boundary-layer displacement thickness is also given, so that Astill's criterion for hydrodynamic instability can be utilized.