Entropy generation at the onset of natural convection

The entropy generation due to heat transfer and friction has been determined in transient state for laminar natural convection by solving numerically the mass, momentum and energy balance equations, using a control volume finite-element method. The variations of the total entropy generation as function of time for Rayleigh number and irreversibility distribution ratio set at 10³?Ra?10⁵ and 10⁻⁴???10⁻¹ were investigated. The evolution of the maximum of entropy generation with the Rayleigh number is studied. The effect of the irreversibility distribution ratio on the maximum entropy generation and the entropy generation in steady state are analyzed. The irreversibility maps for Rayleigh number set at 10³?Ra?10⁵ and irreversibility distribution ratio ?=10⁻⁴ are plotted.