Shell and tube type latent heat thermal energy storage (STLHTES) device is numerically evaluated by applying fully implicit finite volume method. A 2-D axisymmetric numerical model is developed in order to analyse the dynamic behaviour of charging and discharging of elementary unit of STLHTES. The STLHTESconsists of a pipe of finite thickness carrying heat transfer fluid (HTF). It issurrounded by latent heat storage medium or the phase change material (PCM). In the 2-D axisymmetric PCM domain, diffusion dominated heat transfer mechanism is considered while the flow of HTF in 1-D is considered to be dominatedby convection. Coupling has beendone between the two domains through energy balance at the pipe wall taking half control volume at the boundary. The present work proposes a novel scheme, liquid-fraction updating scheme, for solving the energy conservation equation in PCM domain. Comparison has been done between the base case (no thermal conductivity enhancement in the PCM by graphite incorporation) and other cases (where thermal conductivity enhancement of PCM is done by incorporation of graphite) with parametric analysis based on variable pipe sizes of HTF pipe. During graphite incorporation, anisotropic effects are also taken into account. Simulations are also performed to obtain the evolution of temperature in PCM and HTF domain along with extent of melting/solidification in the PCM domain for different values of fraction of graphite. The analysis shows significant reduction in cycle time for charging and discharging due to incorporation of graphite in the PCM composite and increase in heat transfer rate caused by increase in Reynolds number following smaller pipe sizes of HTF pipe (central pipe through which HTF flows). Key Words:LHTES, shell and tube LHTES, Liquidfraction update technique, Solidification, Melting, Charging, Discharging, anisotropy, graphite.