The onset of buoyancy-driven convection in a horizontal fluid layer heated suddenly from below

► New approaches were applied to study the onset of transient Rayleigh-Bénard convection. ► Most dangerous initial disturbance was identified through the initial growth rate analysis. ► The neutral stability conditions were obtained under the relative stability criterion. ► Excellent agreement between the analytical analysis and the numerical simulation is obtained. ► Nonlinear numerical simulation results explained the previous experimental work quite well.