Knowledge of heat transfer during melting and freezing in enclosures is important in the design of heat exchangers using phase change materials (PCMs) for thermal energy storage. While freezing heat transfer is governed mainly by conduction, melting of a PCM generally invokes free convective currents in the melt phase depending on the orientation and geometry of the heat transfer surfaces. In this paper, a Finite element simulation is carried out to predict the flow and temperature fields as well as the rate of heat storage during melting of a PCM in a horizontal cylindrical annulus heated from an isothermal inside surface. ri novel yet simple Method is suggested and validated numerically to enhance the heat storage rate in a PCM, The technique involves simply "flipping" the horizontal cylinder, i.e., turning it through 180 degrees about its own axis, at an optimum time during the melting process. It is found that up to 18% enhancement in the energy storage rate can be achieved with this simple technique.