AbstractReinforcing polymers with nanofillers is an advanced approach to improve and manage the thermal behaviors of polymeric nanocomposite materials. Among the proposed nanofillers, graphene and carbon nanotube (CNT) with superior thermal conductivity are two advanced nanofillers, which have extensively been utilized to enhance the heat transfer responses of host polymeric materials. In this work, the impacts of randomly oriented graphene and CNT to steady state and transient heat transfer behaviors of functionally graded (FG) nanocomposite cylinders have been investigated using an axisymmetric model. Nanocomposite cylinders have been assumed to be under heat fluxes, heat convections or temperatures as different types of thermal boundary conditions. The thermal properties of the resulted nanocomposite materials are estimated by micromechanical model. Moreover, the governing thermal equations of axisymmetric cylinders have been analyzed using a highly consistent and reliable developed mesh-free method. This numerical method predicts temperature fields via MLS shape functions and imposes essential boundary conditions with transformation approach. The effects of nanofiller content and distribution as well as thermal boundary conditions on the heat transfer responses of nanocomposite cylinders are studied. The results indicated that the use of nanofiller resulted in shorter stationary times and higher temperature gradients in FG nanocomposite cylinders. Moreover, the use of graphene in nanocomposites had stronger impact on thermal response than CNT.