Melting in a finite slab with a second kind boundary condition is studied numerically in order to simulate the charging process of a thermal energy storage system. A dimensionless model is given, from which it is concluded that the main factors that influence the melting process are the dimensionless heating flux, the modified Stefan number, the relative thermal diffusivity and the relative thermal conductivity. The influence of preheating or solid subcooling is studied. It is found that though preheating does not have very important effects on the melting time, it does influence the interface marching velocity significantly. The melt fraction and the melting time are calculated extensively for various dimensionless numbers. The numerical results show that the ratio of the thermal conductivity of the solid to that of the liquid has little effect on the melting time, and the time for finishing melting can be expressed as a function of the dimensionless heating flux, the modified Stefan number and the relative thermal diffusivity, and the possible function form is suggested.