Transient natural convection phenomena in an annulus between horizontal concentric cylinders were atudied numerically for the axisymmetric cases using the finite difference schemes. boussinewq approximation was applied to the equations of motion describing the buoyant circulation of air, and the vorticity-stream function approach was adopted for the solution of the problems. the simulations of temperature distribution, streamline and vorticity variations were perfourmed under the prescribed conditions such that the outside cylin der was maintained at a variable temperature of vertical stratification condition and the inner cylinder was either thermally insulated to be adiabatic or its surface temperature was kept constant.