In the present research work, solid-liquid phase change heat transfer was studied experimentally as well as numerically for paraffin wax encapsulated in the annulus of two coaxial circular cylinders with variable heat flux. Two-dimensional mathematical model (Navier-Stokes equation) in terms of primitive variables has been formulated to study the melting characteristics of the phase change material (PCM). The finite volume method (FVM) and semi-implicit, that is, SIMPLE scheme are applied to discretize the governing equations and track the solid-liquid moving front. From the comparison of experimental data and numerical simulation, it is evident that the convective heat transfer is dominant in melting phase. From the computational results it is also observed that both eccentricity and the variation in the angle of inclination of the eccentricity plays an important role for the net circulation of the molten phase as well as the thermal flux at the inner surface of the annulus.