The onset of natural convection in a fluid layer suddenly heated from below (Q1073686)

The onset of convection in a fluid layer in which the temperature profile is developing in time is considered with inclusion of random fluctuations when a constant heat flux is suddenly applied to the bottom surface. Using the expansion in terms of the eigenfunctions of the linear instability, the governing equations are reduced to a set of ordinary random differential equations, which are solved by a Monte Carlo simulation. The dependency of the onset time of convection on the Rayleigh number and the Prandtl number is investigated. Numerical results are in good agreement with available experimental data.