This thesis deals with the onset of Rayleigh-Benard convection in an initially quiescent and isothermal fluid layer confined between two horizontal and rigid planes due to time-dependent heating from below. The lower surface is heated with various prescribed temperature in time or with a suddenly applied constant heat flux, while the upper surface is held at the constant initial temperature. In the time-dependent stability analysis, effects of random fluctuations are included. Initial conditions and random forcing of the velocity fields during the heating procedure are specified by random fluctuations. By expanding the flow and the temperature fields in terms of the eigenfunctions of the stationary Rayleigh-Benard convection, the problem is reduced to a random initial value problem, which is solved by a Monte Carlo technique. The onset time of convection is defined as the ensemble average of the time at which the time-dependent Nusselt number starts to grow for the first time. The dependency of the onset time on the Rayleigh number, Prandtl number, Nusselt number and time-dependent heating methods is investigated. Numerical results are in good agreement with available experimental data.
