Buoyancy effect in an internally heated horizontal fluid layer is considered under the linear stability analysis. The horizontal fluid layer is confined between a rigid adiabatic lower boundary and a rigid isothermal upper boundary. The onset of thermal convection is analyzed by using the propagation theory which transforms partial disturbance equations into ordinary ones similarly under the principle of exchanges of stabilities. The eigenvalue problem is solved by the method of rapidly converging power series. In addition, the convection of stability condition to the fully developed heat transport is investigated. Results show that the critical time to mark cellular convection has increased with a decrease in the Prandtl number. Based on the present stability criteria, a new correlation of the Nusselt number is produced as a function of both the Rayleigh number and the Prandtl number. It is shown that the present correlation on thermal convection compares reasonably with existing experimental data of wa-ter.