Heterogeneous bubble nucleation on heated surfaces, as the first stage of boiling, is a fundamental and prevalent process in industrial systems. A nucleation model based on chemical potential energy is revisited and a Gibbs free energy based model is developed. The nucleation models cover two types of bubble nucleation, i.e. nucleation with or without prefer nucleation site on heated surfaces which are denoted as type I bubble nucleation and type II bubble nucleation, respectively. The effect of surface wettability is also considered. Analytical solutions such as active nucleation size boundary, critical nucleation radius and heat flux at onset of bubble nucleation are obtained without the assumption that the temperature at the tip or center of nucleation bubbles is higher than saturated temperature which was commonly applied in previous studies. The high wall superheat usually found for type II bubble nucleation is illustrated. Bubble nucleation under flow condition is studied by analyzing the effects of heat transfer coefficient, fluid subcooling and pressure on bubble nucleation. For surfaces that cannot provide relative large initial bubbles, bubble nucleation transits from type Ito type II with the increase of heat transfer coefficient, fluid subcooling or pressure due to the decrease in the critical bubble radius. Comparisons with previous nucleation models and experiments indicate that the Gibbs free energy analysis is a very promising method in the prediction of bubble nucleation. (C) 2018 Elsevier Ltd. All rights reserved.