Numerical simulation of laminar natural convection in a Vertical cylinder is proposed. The cylinder is insulated at the bottom, laterally heated at a uniform heat flux density and cooled at the same flux at the top surface. The influence of the characteristic parameters of the problem on the steady-state solution is analysed (10(2) less than or equal to Ra less than or equal to 10(6); 0.7 less than or equal to Pr less than or equal to 92.5; 1/5 less than or equal to Al less than or equal to 2). The fluid transient behaviour is also investigated. It is found that the stationary convective heat transfer is more important at the top surface for 1/5 less than or equal to Al less than or equal to 1/2 and is explicitly independent of the Prandtl number. The steady-state Bow presents a single roil pattern in all cases. On the other hand, in the transient phase a time-limited two-roll flow is predicted when Al less than or equal to 1/3.