## 4 Application of Nanofluid in PTC
### Experimental Studies
[PERSON] et al. [49] experimentally investigated the effect of Al\({}_{2}\)O\({}_{3}\)/water nanofluid on thermal behavior of the PTC at 0.05-0.5 vol % of Al\({}_{2}\)O\({}_{3}\). They concluded that the thermal efficiency could be enhanced by 8.54% if the maximum volume fraction of 0.5% was applied. [PERSON] et al. [44] conducted an experiment in which he used a different base flow, ethylene glycol (EG) and dispersed MWCNT and SiO\({}_{2}\) in it up to 0.3% volume fraction. They reported that MWCNT/ethylene glycol is the most efficient fluid in term of higher thermal efficiency. The thermal enhancement of 30.4% and 14% was suggested by them for MWCNT/ EG and SiO\({}_{2}\)/ EG, respectively, comparing with EG as the base fluid. [PERSON] et al. [50] examined the effect of CeO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), and TiO\({}_{2}\) with water as a base flow on the performance of PTC. They used a variety of volume fraction ranging from 0.5 to 3 vol. %. They found that at 3% volume fraction, (CeO\({}_{2}\))/water nanofluid had the highest thermal efficiency enhancement by 27%, followed by alumina and titania nanofluid with 25% and 23% enhancement, respectively. [PERSON] et al. [51] experimentally studied the effect of Al\({}_{2}\)O\({}_{3}\) and Fe\({}_{2}\)O\({}_{3}\) nanoparticle dispersed in water with different weight fraction ranging from 0.2-0.3% and flow rates (1-2 L/min) on the thermal efficiency of the PTC in winter. It was concluded that at 2 L/min flow rate and 0.3 wt %, Al\({}_{2}\)O\({}_{3}\)/water and Fe\({}_{2}\)O\({}_{3}\)/water nanofluid application enhances the thermal efficiency by 13% and 11%, respectively. [PERSON] et al. [52] examined the effect of TiO\({}_{2}\)/water nanofluid at different volume fractions of 0.05-0.5% on PTC thermal performance. They reported that at 4 kg/min mass flow rate both convection heat transfer and thermal efficiency of PTC could be enhanced by 22.76% and 8.66%. [PERSON] et al. [53] experimentally investigated the effect of Al\({}_{2}\)O\({}_{3}\), CuO, and SiC mixed with water at 1-5 vol. % on the thermal and optical performance of the PTC at four different locations in Iran (Tehran, Yazd, Shiraz, and Tabriz). Shiraz was found to have the highest thermal efficiency resort to install the PTC. They also mentioned that the application of CuO/water nanofluid enhances the convection heat transfer by approximately 33% compared with water itself. Hence, as expected, CuO/water nanofluid is the best option for thermal efficiency enhancement. [PERSON] et al. [54] selected six working fluids including supercritical CO\({}_{2}\), Therminol VP-1, pressurized water, Al\({}_{2}\)O\({}_{3}\)/Therminol VP-1, CuO/Therminol VP-1, and Fe\({}_{3}\)O\({}_{4}\)/Therminol and conducted an experimental study to study their effect on the thermal efficiency of PTC. They concluded that application of pressurized water as working fluid might lead to highest efficiency enhancement at low temperatures. However, due to its application limits, it causes difficulty to use. Aside from pressurized water, Al\({}_{2}\)O\({}_{3}\)/Therminol VP-1, CuO/Therminol VP-1, and Fe\({}_{3}\)O\({}_{4}\)/Therminol application can lead to the efficiency enhancement of 0.22%, 0.18%, and 0.15%. This means that Al\({}_{2}\)O\({}_{3}\)/Therminol VP-1 nanofluid is the best working fluid to achieve the highest efficiency. [PERSON] et al. [55] conducted an experimental study on Ferrofluids (magnetic nanofluid) with 0.05% volume fraction with and without magnetic field presence. They found that if a magnetic field is applied, the thermal efficiency can be enhanced up to 25% compared to conventional PTC. [PERSON] et al. [56] investigated the effect of Al2O3/ water nanofluid with 1% and 3% volumetric concentration on the thermal efficiency of PTC experimentally. The results indicated that using 3% volumetric concentration of Al\({}_{2}\)O\({}_{3}\) can enhance the efficiency by approximately 28% (40.8% to 52.4%) compared to water as a base flow at incident angles varying from 20-30. Finally, [PERSON] et al.