## 3 Results and Discussion
### Thermal Conductivity Measurements  
Polymers are usually characterized by very low thermal conductivity (0.1-0.5 W/m.K), which is strongly affected by the complex polymer morphology, crystallinity, molecular orientation, etc. [35]. Enhancing the thermal conductivity of polymers is important for many applications, and it has recently become a strategic research topic. The graphene-based polymer composites are expected to provide superior thermal conductivity due to the exceptional thermal properties of graphene, which are among the highest of any known material [36]. As anticipated, the addition of GNPs and MWCNTs significantly increased the polymer matrix's thermal conductivity at all set temperatures. It can be seen that the highest thermal conductivity in the nanocomposite range was shown by the compound 4 wt%MWCNT/HDPE, and the lowest was exhibited by the hybrid-polymer-based sample 2 wt%GNP2 wt%MWCNT/HDPE (see Figure 5).  
Generally, the thermal conductivity of a composite material is influenced by several factors, including the intrinsic thermal conductivity of the components, their volume fraction, and the dispersion and alignment of the fillers within the polymer die. These studies state that carbon fillers with a platelet shape are superior to those with other morphologies because of their huge contact area, which allows for considerably tighter contact between neighboring platelets and hence less phonon dispersion [37], but as mentioned above, in this case, the MWCNTs-containing composite has better thermal conductivity than the one reinforced with GNPs. A possible explanation for this phenomenon could be the more uniform dispersion of MWCNTs in the HDPE matrix compared to that of the GNPs, which own the tendency to stack in aggregates. This alleged better dispersion not only enhances the thermal conduction path in the composite, leading to higher thermal conductivity, but also supports the already-discussed superior nanomechanical properties of the sample 4 wt%MWCNT/HDPE. Along with the dispersion, the alignment of GNPs and MWCNTs within the polymer matrix, the physical interactions at the interface polymer chain-carbon nanoparticles, and the presence of defects or functional groups in the carbon nanofillers' structure would altogether affect the thermal conductivity. Furthermore, [PERSON] et al. [38] discovered that the electrical conductivity of PLA-based composites reinforced with MWCNTs is greater than these ones loaded with GNPs, which under definite conditions, may increase the thermal conductivity of polymer composites via electron transfer, notwithstanding its minor contribution compared to the phonon scattering.  
Figure 5: Thermal conductivity of the composite materials as a function of the testing temperatures.  
It was also found that over the investigated temperature range, the thermal conductivity of the composites did not undergo any significant change, except for 4 wt%GNP/HDPE that displayed a slight lowering trend in thermal conductivity upon increasing temperature. This distinct behavior is probably related to the thermal expansion of the composites leading to variations in the capacity for thermal conductivity. When the temperature goes up, materials typically expand, which can disrupt the conductive pathways and reduce the thermal conductivity. However, the thermal expansion of the samples is small within the temperature range of 25-75 degrees Celsius, so the effect on thermal conductivity is negligible. Moreover, the thermal vibrations of atoms and molecules in these materials are not strong enough to modify their structures keeping a stable phonon scattering mechanisms in the nanocomposite architecture.