# Thermal Conductivity Calculations for Nanoparticles Embedded in a Base Fluid
## 1 Introduction  
Traditional thermal fluids, such as ethylene glycol (EG), oil and water, play an important role in many engineering sectors, such as power generation and heating and cooling processes. However, their heat transfer capability is limited by their very low thermal conductivity. Nanofluids (NFs) are fluids produced by the dispersion of metallic or nonmetallic nanoparticlesfor nanofibers in a liquid. The addition of these dispersed particles in traditional fluids produces an enhancement of the thermal conductivity in the host liquids [1; 2; 3]. According to their potential applications in the heat transfer field, NFs have been a subject of intensive investigations [4; 5; 6; 7; 8; 9]. Over the past two decades, significant amount of experimental data has been gathered on the thermal conductivity enhancement capabilities of metallic and oxide nanoparticles, carbon nanofibers, and carbon nanotubes in these traditional fluids. Comprehensive recent reviews and studies about thermal conductivity enhancement and heat transfer characteristics of NFs were presented in the literature [10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. Many parameters affected the thermal conductivity of the resultant NFs: the kind of nanoparticles, shape and diameter of the particles, particle volume concentrations, temperatures, type of the base fluid, acidity (pH) of the base fluid, preparation techniques, and clustering [2; 6; 20]. Several theoretical models and mechanisms have been proposed in the literature for explaining the measured thermal conductivity of NFs using various assumptions [11; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. However, reported works on theoretical and experimental investigations to understand the science and mechanisms behind the thermal conductivity enhancement of NFs continue to be controversial and far from comprehensive [31; 32]. [PERSON] and [PERSON] [23; 33] concluded that the hydrodynamic effect of the Brownian motion of nanoparticles causes an enhancement in the thermal conductivity of the NFs and was a crucial factor regarding the mechanism governing the thermal behaviors. Contradicting this, [PERSON] et al. [34] suggested that the nanoparticles' Brownian motion had a negligible effect on the extraordinary thermal transport properties of NFs. [PERSON] and co-workers concluded that the nanofluids' thermal conductivity was described by effective medium theory, where aggregation of the particles causes an enhancement ofthe nanofluids' thermal conductivity. Furthermore, experimental studies showed that the nanofluids' thermal conductivity increased with the decrease of the particle size [35; 36; 37; 38; 39], while other studies reported the opposite conclusions, where the thermal conductivity increased with the increase of particle size [40; 41; 42; 43; 44; 45; 46].  
Recently, [PERSON] et al. [47] and [PERSON] and [PERSON] [48] studied the dependence of NFs' thermal conductivity on the nanoparticles' material. They argued and showed that the thermal conductivity of NFs has a direct connection with the density of the nanoparticles' material, even though they did not focus their attention on the value of the nanoparticles' thermal conductivity.  
Most of the theoretical models for thermal conductivity of NFs embedded with nanoparticles fail to fit the experimental data, maybe because of the lack of nanoparticle thermal conductivity data [49; 50; 51; 52; 53]. Practically, however, measuring thermal conductivity for individual nanoparticles is very difficult. Therefore, the objective of this work was to calculate the thermal conductivity of nanoparticles dispersed in EG and water by using the Prasher analytical model [54]. Afterward, the analytical formula that was given by [PERSON] and [PERSON] [55] and the Yu and Choi model [56] were used to verify the obtained values of nanoparticles' thermal conductivity.