In this article we discuss in detail the effective approaches to enhance the thermal conductivity in polymer composites. Numerical simulations show that maximizing interfacial area between filler and polymer enhances very significantly the effective thermal conductivity in composites. We show that among the different geometries thermal conductivity is high for those geometries for which the ratio of surface-area to volume is high. For fillers of a particular geometry, by maximizing its surface area without changing the volume fraction of the metallic filler, the effective thermal conductivity increases. Thus, the interfacial area between filler and polymer plays an important role in the enhancement of thermal conductivity. It is also observed that as this interfacial area increases, increase in effective thermal conductivity follows from linear to the logarithmic growth. It should be noted that to inherit the polymer properties there is a restriction on the upper bound of volume fraction of the fillers. The current study brings out an important step in this direction. Our results are technologically very important in designing composite polymers for better heat conduction and are very cost-effective. This study also provides a connection between the bulk and the surface area in effective determination of the thermal conductivity.