In the present work, we numerically investigate the melting phenomena of carbon based nanocomposites in vertically oriented shell-tube latent heat thermal energy storage system. Organic alkane n-eicosane was considered as the phase change material and carbon allotropes as the nano fillers to enhance the thermal conductivity of n-alkane. The effect of different carbon allotropes like nanodiamond (spherical), single-walled carbon nanotubes (one-dimensional) and graphene nanoplatelets (two-dimensional) were considered. Thermal conductivity of nanocomposites was modeled using effective medium based formulation taking the interfacial thermal boundary resistance between nanomaterial and the surrounding host matrix into account. Numerical results show that spherical nano inclusions do not enhance the melting rate due to limited enhancement in the thermal conductivity of nanocomposites. However, the inclusion of one-dimensional and two-dimensional nanostructures shorten the melting time by similar to 15% and similar to 25% respectively at 1 vol% loading as a result of higher thermal conductivity enhancement. (C) 2017 Elsevier Ltd. All rights reserved.