A numerical study has been conducted on natural convection in a vertical slot with a narrow upper section. The fluid (air) in the slot is initially at a uniform temperature and is motionless. The top and bottom are insulated. The left walls are subjected to a step change in temperature, while the right walls are kept at the initial temperature. The resulting flow patterns and heat transfer for different Rayleigh numbers are numerically studied by a projection method involving a Godunov-type discretization for connective terms.