When an initially quiescent, fluid-saturated horizontal porous layer is heated by ramp-heating the bottom side of the layer at constant temporal rate, the critical condition of the onset of natural convection is analyzed by employing the propagation theory. For deep-pool systems the base temperature profile is approximated by using the integral method and a new stability equation is generated through the propagation theory which considers the variations of disturbance with time. Fior infinite Prandtl-number fluids saturated in a porous layer to satisfy Darcy's law, the critical condition is deduced to have the following relation:
τ_c = 6.55γ^4/3 Ra^-2/3
a _c = 0.41γ^-2/3 Ra^1/3
In comparison of the above prediction with the experimental data of Kaviany, it is seen that the initiated convection is amplified to observable magnitude at the time 4τ_c.