## 3 Results and Discussion
### Effect of Filler Concentration and Combination of Nanofilers on the THERMAL Conductivity  
Generally, the thermal conductivity is a measure of the ability of a material to transfer heat. Thermal diffusivity (with the unit mm\({}^{2}\)/s) is a material-specific property for characterizing unsteady heat conduction. This value describes how quickly a material reacts to a change in temperature. Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of material from the hot side to the cold side. Thermal management is a crucial issue in the electronics industry as electronic devices are more integrated and miniaturized. If the heat is not dissipated promptly, the efficiency and the lifetime of the system could be reduced, or even damaged. Thus, a material with high thermal conductivity is needed to dissipate the heat [14]. Thermal conductivity through a polymer is a complex process, influenced by many parameters like temperature, crystallinity, orientation of the macromolecules, and so on [45; 46; 47]. Phonons are usually considered to be thermal carriers in polymers because there is a free electron [48]. In our study, GNP and MWCNTs are used as the fillers to enhance the thermal conductivity of PLA polymer materials. Figure 6a and Table 3 presents thermal conductivity vs. GNP and MWCNT filler content for mono-filler (PLA/GNP and PLA/MWCNT) and bi-filler (PLA/GNP/MWCNT) composites. The results show that the thermal conductivity or the ability of a material to transfer heat increases almost linearly with increasing of the filler content. This effect was more pronounced for the mono-filler composites based on PLA/GNP where the maximum value is 0.577 (W/ mK) at PLA/6 wt.% GNP compared with the 0.205 (W/ mK) for the pure PLA. The improvement of thermal conductivity for these systems is about 181% compared with the neat matrix. This can be attributed to the high thermal conductivity of the graphene when compared to the pristine polymeric matrix and the networks created by contact between the graphite layers with increasing of the filler content, thus forming a thermal conduction pathway. The improvement in thermal conductivity, can be related to the interfaces between fillers and matrix. A better adhesion between fillers and host material can suppress phonon scattering, leading to higher values of thermal conductivity. The effect of increasing of the filler content on the thermal conductivity of the mono-filler composites based on PLA/MWCNT was less pronounced and at a maximum MWCNT filler content of 6 wt.% the improvement was of about 48%, due to the shape of the carbon nanotubes and hence poor thermal conductive network of the filler. The thermal conductivity of graphene and carbon nanotubes is mainly accomplished by phonons and the thermal conduction through a polymer is a complicated process, which is influenced by many parameters like crystallinity, temperature, orientation of the macromolecules. On the other hand, carbon nanof fillers and polymers are usually considered to have lots of defects that contribute to numerous phonon scatting, leading to low thermal conductivity. MWCNT used in this study had a lower thermal conductivity, compared with GNP. In the mixed bi-filler systems, thermal conductivity depends mainly on the amount of GNP, which is a lower quantity of GNP, compared with the mono-filler GNP/PLA systems, at the same total filler content. This was the reason for no presence of synergetic effect with the combination of both fillers, in comparison with electrical conductivity, where both nanofillers showed high electrical conductivity. Figure 6b presents thermal diffusivity vs. GNP and MWCNT filler content for mono-filler (PLA/GNP and PLA/MWCNT) and bi-filler (PLA/GNP/MWCNT) composites.