The present study is focused on experimental and numerical analysis of unconstrained melting of Paraffin wax-RT58 in a horizontally placed cylindrical container. After the validation of numerical model with experimental results, numerical analysis is extended to constrained melting to investigate the process. The experiments are carried out at constant wall temperature maintained on the lateral surface of the cylinder. The influence of initial sub-cooling and lateral surface temperature on the melting rate is investigated. The melting process is better analyzed by the melting phase front and temperature contours as time progresses. The results show that the melting rate decreases by increasing the initial sub-cooling, and increases with increasing lateral surface temperature of the cylinder. In unconstrained melting, heat transfer by conduction governs the melting process initially, but later it is restricted to only the bottom part of the cylinder as the solid PCM at a higher density sinks due to effects of gravity. Heat transfer in the upper half of the cylinder is dominated by natural convection set up in the liquid PCM. In constrained melting, pure conduction phenomenon exists only in the beginning, and later conjugate heat transfer occurs. When subjected to similar boundary conditions, PCM melt-time is lower in unconstrained melting than in constrained melting. A correlation between melt-time and Stefan number is also developed.