The critical condition of the onset of buoyancy-driven convective motion of uniformly heated horizontal fluid layer was analysed by the propagation theory which transforms the disturbance quantities similarly. The dimensionless critical time, $ au$$sub$c/, is obtained as a function of the Rayleigh number and the Prandtl number. Based on the stability criteria and the boundary-layer instability model, a new heat transfer correlation which can cover whole range of Rayleigh number was derived. Our theoretical results predict the experimental results quite reasonably.