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A finite-difference scheme is developed for solving the boundary layer equations governing the laminar free convection flow in open ended vertical concentric annuli with rotating inner walls. Numerical results are presented for a fluid of Pr = 0.7 in an annulus of radius ratio 0.5 under the thermal boundary conditions of one wall being isothermal and the opposite wall adiabatic. Comparing the present results for the development of δθ (tangential boundary layer displacement thickness) with those corresponding results of forced flows shows that heating the inner cylinder has always stabilizing effects while heating the outer cylinder has either destabilizing or stabilizing effects.