Modeling and analysis of optical properties of nanoparticles and nanofluids for effective absorption of solar radiation and their heating

Abstract

This review presents a comprehensive analysis of the recent studies and advances related to optical properties of nanoparticles, their heating under solar irradiation and heat conversion, relevant equations and theoretical modeling approaches and application of nanofluids for direct absorption of solar radiation. A lot of papers including theoretical, numerical and experimental up-to-date works are reviewed and summarized carefully to give a panoramic overview of the role of the nanoparticles. Modern nanotechnology can produce various homogeneous and hybrid (core–shell) nanoparticles from different metals and materials which have unique optical and thermal properties. It was found that the application of nanoparticles selected on the basis of the presented analysis has shown remarkable properties and offers unique advantages over conventional fluids in optical absorption, thermo-physical and heating properties of nanofluids. This fact can play a crucial role in increasing the efficiency of solar energy harvesting.

1 Introduction

Sustainable energy generation is one of the most important challenges of our society today. Solar energy is the compatible permanent source of renewable energy with minimal environmental impact and a key item in renewable energy technologies because it provides a nearly unlimited availability, clean and safety energy [1]. The challenge lies in efficiently trapping and converting solar energy into thermal energy, and therefore, a method of efficient solar energy conversion and harvesting must be developed.

Solar absorbers and collectors are conventional devices for the absorption of solar radiation and its conversion into thermal energy of the working liquid [2, 3]. It was recently proposed to use direct absorption of solar energy by working fluid in the absorber volume for the increase in efficiency of solar energy trapping [4, 5]. But there is the problem with poor absorption properties of the typical working fluids (water, glycols, etc.).

The solar radiation spectra I_S present the complicated dependence on wavelength λ [6]. It can be approximately modeled by the radiation spectra of a perfectly black body with Planck distribution that is a function of wavelength λ and temperature T_S of radiation source [7]

$$I_{\text{S}} \,\sim\frac{{\pi hc^{2} }}{{\lambda^{5} \left( {\exp \left( {{\raise0.7ex\hbox{${hc}$} \!\mathord{\left/ {\vphantom {{hc} {\lambda kT_{\text{S}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\lambda kT_{\text{S}} }$}}} \right) - 1} \right)}}$$

(1)

where h and k are Plank and Boltzmann constants, respectively, and c is the light velocity.

The comparison of the solar irradiance (intensity) I_S on λ (1) and dependencies of extinction coefficient of water $\alpha_{\text{ext}}^{\text{W}}$ [8] shows that the value of maximal intensity I_S is approximately located in the interval of λ with minimal value of $\alpha_{\text{ext}}^{\text{W}}$ (see Fig. 1). So, the use of clear liquids based on water is difficult for effective absorption of solar energy.

Fig. 1

The dependence of radiation extinction coefficient by water (dashed, blue) and solar irradiance I_S (solid, orange) on radiation wavelength λ

To improve fluid optical properties, some nanostructures and nanoparticles (NPs) are added to working fluids that are directly exposed to incoming solar irradiance [4, 5, 9,10,11]. In recent years, it has been shown that mixing NPs in a fluid has a dramatic effect on its optical properties and considerably improves the optical and photothermal conversion properties of working transparent fluids with formation of nanofluids (NFs).

Important advances in nanotechnology led to production of different types of NPs with various structures, sizes and shapes [12,13,14], which have been demonstrated their great and immense potential. Optical properties of NFs are of great importance particularly for their use in volumetric direct absorbers. It is important because the selection of NPs can result in a significant improvement in the absorption of NFs in the ultraviolet (UV), visible (VIS) and infrared (IR) electromagnetic spectrum regions.

Optical properties of various types of NPs are actively investigated in recent years [13,14,15,16,17,18,19,20,21,22]. These investigations were concentrated on UV, VIS and near-IR spectral intervals for laser and optical sources and their applications. The investigations of NP optical properties have received additional impulse after the commencement of the NPs use for solar radiation absorption applications. It needs to investigate more wide spectral interval than it was investigated before with some specific requests on the NPs properties.

Successful applications of NPs for effective absorption of optical radiation are strongly connected with the so-called surface plasmon resonance of radiation on nanosphere and a NP absorbs and scatters radiation energy well at resonance wavelength [13,14,15,16,17,18,19,20,21,22]. The design of NPs with chosen and adjusted plasmonic and thermo-optical properties is possible by the selection of the materials, material composition and geometrical properties (sizes) of NP including the attempts to search for novel and better plasmonic NPs and the achievements of “ideal” optical characteristics [23,24,25].

It is possible to realize excellent optical properties of NPs on the basis of manipulation of NP plasmon resonance. But the essential information is now limited and separated results of the applications of various NPs do not present whole picture.

The selection of NPs optical properties should provide the maximal heating of NPs and NF. Effective maximal heating of both NP itself and the ambient fluid by solar radiation, the conversion of absorbed energy into thermal energy and intensive thermal energy transfer from NPs to NF are determined by high absorption and small scattering of radiation by NPs [13,14,15,16,17,18,19,20,21,22]. Radiation scattering is concurrent and parasitic process and leads to the following multiple processes of absorption and scattering and decreasing the absorption efficiency. Unfortunately, up-to-date publications represent critical missing data in the field of solar heating of NPs.

Novel approaches for solar energy conversion are presented below. The analysis of novel heating model has been presented that correctly describes the temperature dynamics of heating of NPs and fluid by solar radiation, and in particular, this model allows us to select appropriate optical properties of NPs. To date, the works in this area have been limited but their results demonstrate that selective solar-absorbing NPs can be designed and produced.

This review presents a comprehensive modern review of the optical properties of spherical metallic, oxide and metal core–its oxide shell NPs, placed in water, and solar thermal conversion of absorbed energy by NPs. This review is concentrated on the recent studies and achievements mostly during 2016–2018 years naturally taking into account the base papers from previous years. Carbon NPs, nanotubes, have been investigated and reviewed [26,27,28], and they are out of our review.

2 Optical properties of metallic nanoparticles

2.1 Analysis of optical properties of metallic nanoparticles

Among various NPs, metallic NPs are of special interest for solar energy applications because of their prominent plasmonic (absorption) and thermo-optical properties. The plasmonic and optical properties of metallic NPs were previously investigated for optical and laser applications in the narrow spectral interval 300–1000 nm [13,14,15,16,17,18,19,20,21,22,23,24,25]. Some of these results can be used for NP solar applications with serious limitations because of the absence of spectral interval 1000–2500 nm. Main parameters of the NP optical investigations [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50] for the purposes of solar applications, including NP metal, size, spectral interval and used methods of investigations, surrounding liquid, are presented in Table 1. Theoretical investigations of absorption, scattering, extinction and scattering indicatrices of radiation by various NPs have been carried out on the basis of Mie theory [29,30,31,32,33,34,35, 37, 38, 41,42,43, 46, 50], DDA [36] and FDTD [39] methods. Experimental investigations of NP optical properties used dark-field microspectrometer, optical and transmittance spectroscopy, etc.

Table 1 Optical properties of spherical metallic NPs

Au NPs were immersed in water and oil, maximal ranges of investigated diameters were d₀ = 5–250 nm, and spectral interval was 250–2500 nm [29,30,31,32,33,34,35,36,37,38,39]. It was found the shift of plasmon resonance wavelength to larger values of λ with increasing NP diameters. The estimation of the size distribution of the metallic NPs was obtained through the fitting of the extinction spectra via Mie theory [31]. The investigation of plasmonic absorption and scattering properties of metallic NPs in the spectral interval 250–2500 nm for NP radii r₀ = 25, 50, 75 nm has been carried out [30, 33, 37]. Spherical gold, aluminum, silver and copper NPs with diameters 20–140 nm were theoretically investigated for the wavelength range 300–1350 nm [38]. Comparative analysis has been performed for the absorption properties of noble metallic NPs (Au, Ag, Cu and Al) to determine suitable parameters for effective solar heating [39].

Experimental dark-field microspectrometer measured quantitative spectral scattering cross sections of Au NPs for comparison with computer results [29]. The link between optical properties and photothermal conversion efficiencies for gold NPs is theoretically and experimentally investigated [32,33,34,35,36]. The results indicate that the photothermal efficiencies of gold NPs are size tunable, and their variation can be correlated with the absorption/extinction ratios [32], and it is higher for gold NFs than that of pure water [34]. Good agreement of the modeling results was observed with the experimental data except spectral interval of 600–800 nm, which they attributed to the existence of large aggregates in the NFs. The optical properties and photothermal conversion efficiencies for Au NPs were experimentally (UV–VIS spectroscopy) and theoretically (DDA) investigated with good agreement between experimental and theoretical results [35, 36].

Ag NPs were immersed in water, therminol, DI water and EG, maximal ranges of investigated diameters were d₀ = 10–1000 nm, and spectral interval was 250–2500 nm (see Table 1). Experimental investigations of Ag NPs include the spectroscopic measurements of extinction coefficients over wavelengths that are important for solar energy (250–2500 nm) [40]. Transmittance of Ag NPs with nominal size of 35–1000 nm dispersed in base fluid has been measured, and the results reasonably well match the theoretical transmittance data [42]. It was noted that the effect of agglomeration played a significant role in determining the resulting transmittance of the silver NP suspensions. A combined numerical and experimental study has been conducted on a NF direct absorption collector utilizing silver NPs dispersed in deionizing water [43]. The optical properties measurement of NFs showed remarkable enhancement even at low particle concentration. The formation of plasmon high-order resonances (quadrupolar and more) with an increase in NP sizes up to 250 nm is very interesting possibility for the use of these features in solar absorption radiation [33, 41].

Al NPs experimentally and theoretically have been investigated [30, 37,38,39,40, 44, 45]. Aluminum NPs show very strong extinction coefficient at shorter wavelength and peak at 0.3 nm [37, 44]. It should be noted join results for Ag and Al NFs. The Rayleigh scattering approach for these metal NFs has differences with experimental data, because of agglomeration of NPs as well as the formation of oxide layer in metallic NPs [40]. The same situation exists for Mie solution also because of agglomeration phenomenon [45].

The radiation transmission characteristics of Ni NPs have been investigated by spectroscopic measurement [46]. The radiation properties of the ionic liquid NFs containing Ni and Cu NPs were investigated by the experimental and theoretical (Rayleigh) methods [47]. The model fails to accurately predict the extinction coefficients in the wavelength below 1250 nm, especially for Ni and Cu NPs, due to their possible surface oxidation. The investigation of plasmonic absorption and scattering properties of metallic Ni NPs has been carried out [33, 37] for radiation wavelengths in the spectral interval 250–2500 nm for NP radii r₀ = 25, 50, 75 nm.

Cu NPs have attracted a lot of interests in recent years due to their interesting properties, low-cost preparation and many potential applications in solar energy absorption [30, 37,38,39, 47,48,49]. Transmission electron microscopy and UV–VIS spectrometry of the Cu NPs, immersed in polyethylene glycol (PEG), have been investigated [48]. The transmittance of water-based Cu NFs at different volume fractions over solar spectrum was measured by the UV–VIS–NIR spectrophotometer based on integrating sphere principle [49], and the transmittance decreases with increasing NP size, mass fraction and optical depth.

Optical properties Ti, Ni, Mo, Zn and Co NPs with the radii in the range from 25 to 75 nm were analyzed in the whole solar spectrum [33, 37]. Indicatrices of light scattering by homogeneous metallic Ti, Ni and Zn NPs with radii of r₀ = 50, 75, 100 nm are calculated numerically for wavelengths of λ = 300, 560 and 1000 nm [50]. It needs the selection of appropriate NPs for application in solar absorption on the basis of theoretical and experimental investigations.

2.2 Optical properties of selected metallic nanoparticles for solar absorption applications

Optical properties of selected metallic NPs are analyzed here for the purpose of their possible solar absorption applications. Optical properties of NPs are determined by efficiency factors of absorption K_abs, scattering K_sca and extinction K_ext = K_abs + K_sca [15] of radiation by an NP and parameter $P_{1} = K_{\text{abs}} /K_{\text{sca}}$, which describes the correlation between absorption and scattering of radiation by NP and characterizes the contribution of the absorption in the process of NP–radiation interaction [20]. The maximal absorption and minimal scattering of radiation by NP are realized if absorption factor K_abs has own maximum and parameter P₁ should be greater (or much greater) than 1, P₁ > 1 (or P₁ ≫ 1). It means that the maximal part of radiation will be absorbed by NP during the first act of photon interaction with NP. Moreover, the dependence of K_abs(λ) should be coordinated with the dependence of solar intensity I_S(λ). These facts will allow us to achieve maximal efficiency of solar radiation absorption by NPs and their heating. In the opposite case, when K_sca > K_abs and P₁ < 1, scattering of solar radiation by NP will dominated under absorption by NP and following multiple scattering by NPs will lead to redistribution of radiation intensity between NPs and surrounding medium and a significant decrease in NP heating. The variant with value P₁ ≈ 1 means approximately equal possibility for the use of a NP as absorber and scatterer simultaneously.

The investigation of optical properties of 12 metallic NPs has been conducted [30, 37]. Au, Ag, Pt, Ti, Zn, Ni, Mo and Pd NPs were chosen as possible agents for absorption of solar energy, and the results of comparative analysis of their optical properties [33] are presented here. These NPs are immersed in water, and all results for them are presented for the spectral interval 200–2500 nm, which contains approximately 99% of whole solar energy. The values of optical indexes of refraction and absorption of metals and surrounding water were used from [51, 52].

The dependencies of solar irradiance I_S (1), factor K_abs and parameter P₁ on the wavelength λ in the spectral interval 200–2500 nm for mentioned spherical homogeneous metallic NPs with the values of NP radii r₀ = 25, 50, 75 nm are presented in Figs. 2 and 3.

Fig. 2

Dependencies of solar irradiance I_S (a, c, e, g solid, orange, left axis), absorption efficiency factor K_abs of NP (a, c, e, g right axis) and parameter P₁ (b, d, f, h) on λ for Au (a, b), Pt (c, d), Ag (e, f), Pd (g, h) NPs with the radii r₀ = 25 (dotted, green), 50 (dashed, violet), 75 (dashed-dotted, red) nm. Horizontal solid line denotes the value P₁ = 1 [33]

Fig. 3

Dependencies of solar irradiance I_S (a, c, e, g solid, orange, left axis), absorption efficiency factor K_abs of NP (a, c, e, g right axis) and parameter P₁ (b, d, f, h) on λ for Zn (a, b), Ni (c, d), Mo (e, f), Ti (g, h) NPs with the radii r₀ = 25 (dotted, green), 50 (dashed, violet), 75 (dashed-dotted, red) nm. Horizontal solid line (black) denotes the value P₁ = 1 [33]

Au and Ag NPs are mostly investigated by different authors for solar thermal applications [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. The dependencies of efficiency factor K_abs on λ for Au and Ag NPs have typical plasmon resonance shapes with formation of one resonance maximum of $K_{\text{abs}}^{\hbox{max} }$ (Fig. 2). The factor K_abs sharply decreases up to ~ 10¹–10² times in comparison with its maximum $\, K_{\text{abs}}^{\hbox{max} }$, and Au and Ag NPs practically have insignificant absorption of solar radiation in IR region. Suitable values of P₁ ≥ 1 are realized for Au NPs for whole spectral interval 200–2500 nm only for r₀ = 25 nm. It means a sharp increase in radiation scattering by Au NPs with the increase in NP radius r₀. For Ag NPs, the values of P₁ ≥ 1 are realized for the narrow intervals of wavelengths and for all presented values of r₀.

Au and Ag NPs were widely used in experiments [29, 31, 32, 34,35,36, 40, 42, 43]. Chen et al. [35] experimentally studied the size-dependent optical properties of aqueous Au nanofluids synthesized via the one-step method. According to Fig. 4, the Au nanofluid with nanoparticle size of 25 nm showed the best absorbance characteristic compared to 33-nm- and 40-nm-sized particles since the 25-nm sample had the highest absorbance in the peak spectra intensity of solar radiation. These experimental results support the theoretical calculations in Fig. 2a for Au NPs. On the other hand, Au and Ag NPs do not show their real applicability for effective absorption of solar radiation, and therefore, they are not suitable for this purpose.

Fig. 4

Absorbance spectra of Au nanofluids with different nanoparticle sizes and solar radiation spectrum [35]

The dependencies of K_abs on λ for fixed values of r₀ have typical plasmon resonance shapes for all presented metallic NPs (Figs. 2, 3). An increase in r₀ leads to the formation following plasmon resonances—1 (for Ti, Ni NPs) and 2 (for Pt, Mo, Pd NPs) resonances for r₀ = 50 nm and the formation of 2 (for Pt, Ti, Ni, Pd NPs) and 3 (for Mo NP) resonances for r₀ = 75 nm. Some oscillation structures of the dependencies of K_abs on λ are formed with increasing r₀ for Zn NPs.

The significant decrease in K_abs is realized in the UV and IR spectral intervals, respectively, with the decrease and increase in λ accordingly. The increase in r₀ leads to the shifting of the placement of maximum $K_{\text{abs}}^{\hbox{max} }$ to bigger values of λ in VIS and IR regions and leads to a decrease in its value. It means the possibility to match the dependence of K_abs (λ) to the dependence I_S(λ) up to near close or practically overlapping of these ones. So, the absorption spectrum of metallic NPs is typically broadened with increasing r₀ and an NP can absorb a larger portion of the spectrum maintaining an absorption peak and leading to a further enhancement in the absorption efficiency.

Main feature of all presented dependencies of P₁(λ, r₀) is the decrease in P₁ with increasing r₀ for the whole spectral interval 200–2500 nm. It is interesting to note the values of P₁ ≥ 10–100 for mentioned NPs with r₀ = 25–75 nm in IR spectral interval. However, the value of P₁ with increasing r₀ can be smaller than 1 in some regions of solar spectrum or practically in whole solar spectrum.

On the other hand, the parameters P₁ for Ti and Ni NPs are bigger than 1, P₁ > 1, for r₀ = 25, 50, 75 nm for whole spectral interval 250–2500 nm. It means that Ti, Ni NPs are good absorbers of radiation in a wide range of UV, VIS and IR optical spectrum in comparison with other presented NPs.

In part 2, the results of the investigations [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49] have been reviewed. Comprehensive analysis of optical properties of eight metallic NPs with different radii in near-UV, VIS and IR radiation intervals has been carried out on the basis of the choice of the NP metal, radius r₀ and factor K_abs(λ) and coordination between the dependencies of factor of radiation absorption K_abs(λ) by NP and solar irradiance I_S(λ) and estimations of novel parameter P₁ with condition P₁ ≥ 1 for effective absorption of solar radiation. Metallic Ti, Ni NPs can be applied as perspective candidates for effective absorption of solar radiation.

3 Optical properties of homogeneous and core–shell nanoparticles

3.1 Analysis of optical properties of core–shell and homogeneous oxide nanoparticles

Recently, many research efforts have been focused on the investigation of spherical core–shell NPs because of their unique size-dependent physical and chemical properties [12,13,14, 20, 21, 53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72]. Core–shell NPs have great potential for various applications due to strongly enhanced surface plasmon resonance for absorption and tuning of absorption and scattering bands across the VIS and near-IR intervals of the optical spectrum by varying the core and shell materials (metals, oxides, semiconductors), their composition and the relative core size and shell thickness (see Table 2).

Table 2 Optical properties of core–shell NPs

Optical properties of material core and Au shell were investigated [53,54,55,56,57,58,59,60]. SiO₂, Fe₃O₄ [53], SiO₂ [54], Fe₃O₄ [55], Si, SiC [56, 57], Ag [58, 59], SiO₂, ZrO₂, TiO₂ [60] were used as core materials. Their results show next features and possibilities of the core–shell NPs use.

Increasing core size leads to shifting of the location of resonance wavelength and maximal values of optical factors to the larger values of wavelengths and decreasing their maxima [53]. It was found that plasmon resonance frequency can be precisely tuned by adjusting the Au layer thickness which allows us to control the absorption peak of the NF and to match with the incident solar spectrum [54]. It was estimated a redshift in the plasmon resonance peak up to hundreds or even close to 1000 nm to a more desirable NIR wavelengths [60] and from a wavelength of about 600 nm to around 1400 nm for core–shell NPs [56].

Optical properties of core–shell NPs were experimentally assessed using UV–VIS spectrophotometer and dynamic light scattering [55]. Simulation results based on extended Mie theory show the nonlinear dependencies of optical properties of core–shell silver–gold (and gold–silver) NPs on radiation wavelengths, core radii and shell thicknesses [58, 59]. It should be noted the theoretical [56] and experimental [57] investigations of optical properties of core–shell NPs with Si, SiC core and Ag, Cu, Al shell.

The metal core–its oxide shell NPs are very interesting for the improvement in and manipulation of the NP plasmon resonances. The formation of thin oxide shell with the thicknesses of about 5–10 nm on metallic NP can be achieved by different chemical [11] and physical [63] methods, as a result of natural oxidation of metal NPs in reactive ambience. The action of intensive optical (solar) radiation and following NP heating can promote the oxidation of surface layer of metallic NP and the formation of hybrid metallic core– its oxide shell NPs.

Zhang et al. [47] experimentally and theoretically investigated radiation properties of the ionic fluid and its NFs. It was experimentally found that optical absorption property of liquid can be significantly enhanced by dispersing a very low volume fraction of NPs in it. At the volume fraction of 10 ppm, the extinction coefficient of the NF containing the Ni NPs with an average size of 40 nm is higher than that of the one containing the Cu NPs with the similar average size, owing to their different complex refractive indexes. The extinction coefficients of ionic liquid NFs containing Ni, Cu and carbon-coated Ni (C/Ni) NPs were modeled based on Rayleigh approximation. Figure 5 shows that in the wavelength below 1200 nm, the model fails to accurately predict the extinction coefficients, especially for Cu and Ni NPs. This discrepancy has been explained due to possible surface oxidation of the metal NPs and changing optical and other properties of NPs. This fact has been also established in experimental investigation with metallic NPs [40]. The possibility of the formation of oxide shell on the metal NP surface should be taken into account for possible solar thermal applications of metallic NPs.

Fig. 5

Rayleigh scattering approximation of ionic nanofluids extinction coefficients with average sizes of 40 nm at volume fraction of 10 ppm [47]

Optical properties (efficiency factors of absorption, scattering and extinction) of core–shell NPs with metallic core and its oxide shell (Ag–Ag₂O, Al–Al₂O₃, Cu–Cu₂O, etc.) [60] and (Ni–NiO, Ti–TiO₂, Zn–ZnO, Mo–Mo₂O₃) [66, 67] have been numerically calculated on the basis of Mie theory for the purposes of solar radiation absorption. These results highlight the possibility of single core–shell Ti–TiO₂ and Ni–NiO NPs with radii of about 75–100 nm for effective application as perfect absorbers for solar radiation in the complete optical spectrum 200–2500 nm [64,65,66,67]. The angle-dependent light scattering indicatrices and scattering efficiency for core–shell NPs are discussed as a function of the core radius-and-shell thickness ratio and on their relative comparison [50, 61].

Synthesis, optical and plasmonic properties of core–hollow and material–shell NPs were investigated [68, 69]. Dependencies of optical properties of spherical two-layered NPs on parameters of gold core and some material shell are investigated [70]. Optical properties of Ag@TiO₂ and CdS@ TiO₂ core–shell nanostructures were investigated [71]. The implementation of single-particle absorption spectroscopy on strongly scattering plasmonic NPs has been presented [72].

Homogeneous oxide (Al₂O₃, SiO₂, CuO, ZnO, etc.) NPs were used in experimental and theoretical investigations of solar radiation absorption by NPs (see Table 3) [43, 50, 65, 67, 73,74,75,76,77,78,79,80].

Table 3 Optical properties of homogeneous oxide NPs

Optical properties of titania (TiO₂) and alumina (Al₂O₃) water-based NFs were investigated experimentally and theoretically in the spectral range 250–1100 nm [73]. It was supposed that titania NP may perform as a good solar irradiation absorber if it can be stabilized properly. Optical absorption measurements limited to 200–1300 nm were performed on several water-based NFs (Al₂O₃, CuO, TiO₂, ZnO, CeO₂ and Fe₂O₃) [74]. Experimental extinction coefficient in the spectral interval 250–1100 nm for magnetite NF Fe₃O₄ with NP sizes 15 nm was larger than the calculated values [43]. Optical properties of water-based NFs from MgO NPs with sizes 10 nm were investigated in the spectral interval 300–1500 nm [80]. The investigation of optical properties and radiation transfer of TiO₂ NFs with the consideration of scattering effects has been carried out [81].

NPs in NF have a great tendency to aggregate into large secondary agglomerate, due to their nanoscale size and high surface energy, even in the presence of the anti-agglomeration agent. Aggregation process and its effect on optical characteristics of the Al₂O₃ NFs were investigated using electron microscopy, dynamic light scattering and UV–VIS spectroscopy, and the results indicate that extinction coefficients of the NFs reduce rapidly with time within visible to near-IR region [75,76,77]. The effects of dispersants, mass fractions and NP materials on the radiation properties of NFs are analyzed [78]. The optical properties of CuO NF were investigated at the different temperatures [79].

The advantage of the applications of oxide NPs in thermal processes consists in their permanent properties during long time. On the other hand, the radiation absorption, scattering and extinction of homogeneous oxide TiO₂, NiO and Mo₂O₃ NPs have been investigated [65, 67]. These NPs have significant absorption only in the spectral interval 300–500 nm and show practical impossibility to use oxide TiO₂, NiO and Mo₂O₃ NPs for effective absorption of solar radiation in spectral interval 500–2500 nm containing ~ 75% of solar energy. These results are in contradiction with results [73], and they are discussed more widely in the next part.

3.2 Optical properties of selected homogeneous metallic, oxide and metallic core and its oxide shell nanoparticles

It is very interesting to compare the optical properties of homogeneous metallic, oxide and metallic core– its oxide shell NPs for solar radiation absorption. The matter is that preceding theoretical and experimental investigations [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81] did not reply on main question because of some contradictive results and conclusions what types of NPs from mentioned above can be used more properly for absorption of solar radiation. As it was mentioned before, optical properties of Ti, Ni NPs could be selected for achievement of maximal absorption of solar energy by NPs. On the other hand, it was established that oxide shell can be formed on the metallic NPs and with time flow the thickness of oxide shell can be significant and homogeneous oxide NP can be arisen from metallic NP.

That is why metallic Ti, Ni NPs, oxide TiO₂, NiO NPs and metal core and oxide shell Ti–TiO₂, Ni–NiO NPs were chosen for the following analysis for solar absorption applications on the basis of comparison of optical properties of various NPs in preceding parts.

Figures 6 and 7 present the dependencies of solar irradiance I_S, absorption efficiency factor K_abs and parameter P₁ for homogeneous Ti, TiO₂, core–shell Ti–TiO₂ NPs and accordingly Ni, NiO, Ni–NiO NPs with the radii r₀, r₁ = 50, 75, 100, 125 nm (the thickness of oxide shell is Δr₁ = 10 nm, r₁ = r₀ + Δr₁, r₀—core radius) on λ [65]. The radii of homogeneous NPs r₀ are equal to the radii r₁ = r₀+ ∆r₁ of core–shell NPs according to the correct comparison of the results for equivolume NPs. It was used refractive indices [82, 83] for oxides.

Fig. 6

Dependencies of absorption factor K_abs and parameter P₁ of homogeneous Ti (a, b), TiO₂ (e, f) NPs and for core–shell Ti + TiO₂ (c, d), Δr₁ = 10 nm, NPs with r₀, r₁ = 50 (dashed, blue), 75 (dashed-dotted, red), 100 (dotted, green), 125 (solid, brown) nm (all curves are referred to right axis) and solar irradiance I_S (1, solid, orange, a–f all curves are referred to left axis) on wavelength λ. Horizontal solid line (black) denotes the value P₁ = 1 [65]

Fig. 7

Dependencies of absorption factor K_abs and parameter P₁ of homogeneous Ni (a, b), NiO (e, f) NPs and for core–shell Ni-NiO (c, d), Δr₁ = 10 nm, NPs with r₀, r₁ = 50 (dashed, blue), 75 (dashed-dotted, red), 100 (dotted, green), 125 (solid, brown) nm (all curves are referred to right axis) and solar irradiance I_S (1, solid, orange, a–f all curves are referred to left axis) on wavelength λ. Horizontal solid line (black) denotes the value P₁ = 1 [65]

The dependencies of K_abs(λ) for Ti, Ti–TiO₂ and Ni, Ni–NiO NPs with r₀, r₁ = 75 nm are very close to the dependence of I_S(λ) in whole spectral interval. The dependencies of K_abs on λ have been shifted to smaller values of wavelength for r₀, r₁ = 50 nm, and they have been shifted to larger values of wavelength for r₀, r₁ = 100, 125 nm in comparison with the location of I_S(λ) for r₀, r₁ = 75 nm.

The parameter P₁ is larger than 1, P₁ ≥ 1, in whole spectrum for Ti NPs with r₀ = 50, 75 nm but for Ni NPs only for r₀ = 50 nm. The increase in r₀ leads to the formation of wavelength region, where P₁ is smaller than 1 in some spectral intervals (see Figs. 6, 7). The value of P₁ is sharply increased up to P₁ ~ 10–20 with increasing λ in the deep infrared spectral interval. But the influence of this fact is decreased due to small part of solar energy concentrated in this spectral interval.

The presence of an oxide shell leads to an increase in absorption compared to scattering of radiation by two-layered Ti–TiO₂, Ni–NiO NPs in comparison with pure Ti, Ni NPs in the important spectral intervals 250–1000 nm and improves the possibility of Ti–TiO₂, Ni–NiO NPs applications with enhanced performance for energy absorption. The parameter is equal to P₁ ≥ 1 in whole interval 200–2500 nm for Ti–TiO₂ NPs with r₁ ≤ 100 nm and for Ni–NiO NPs with r₁ ≤ 75 nm.

The TiO₂ and NiO NPs have significant absorption only in the spectral interval 300–500 nm, and their values of K_abs are sharply decreased in the IR spectral interval λ > 700 nm up to ~ 3–4 order of value that means practically insignificant absorption of solar radiation by TiO₂ and NiO NPs in this spectral interval. In general, TiO₂ and NiO NPs are therefore not suitable for absorption in solar thermal applications because of extremely low absorption in VIS and IR regions of spectrum and their parameters P₁ ≪ 1. Analogous conclusions can be possibly made for other different pure oxide NPs, for example, for Al₂O₃, SiO₂, Mo₂O₃ NPs. It should be noted that pure oxide NPs were used in various experiments [43, 73,74,75,76,77,78], but without verification of the real use of them for solar effective absorption.

So, spherical Ti, Ti–TiO₂ NPs and in smaller degree Ni, Ni–NiO NPs with r₀, r₁ = 50–100 nm can be applied as possible candidates for effective absorption of solar radiation and can be used as good absorbers among other possible candidates.

3.3 Indicatrices of radiation scattered by homogeneous and core–shell nanoparticles

An NP absorbs and scatters the radiation incident on it. The radiation absorbed by an NP withdraws from the subsequent optical processes, and the scattered radiation propagates in a medium with NPs and participates in subsequent acts of absorption and scattering by NPs, etc. The scattering indicatrix shows the relative radiation intensity scattered by an NP in different directions in the range of variation of the scattering angles from 0° to 360°.

In the process of light–NP interaction absorption by NPs, scattering of radiation with indicatrices close to spherical is of interest. In this case, the scattered radiation will be uniformly distributed in all directions from the scattering NP and potentially be effectively absorbed by neighboring NPs. In the case of the dominant scattering of radiation by an NP into rear or front hemisphere, the scattering processes will emit radiation from the irradiated region of the NF and sharply reduce the efficiency of the final radiation absorption by NPs.

Figure 8 shows the scattering indicatrices of radiation with wavelengths λ = 300 (UV) nm, 560 (VIS) nm and 1000 (IR) nm for homogeneous Ti, TiO₂ NPs and two-layered Ti–TiO₂ NPs (shell thickness Δr₁ = 10 nm) with radii r₀, r₁ = 50, 75, 100 nm. Radiation propagates from left to right (from 180° to 0°).

Fig. 8

Scattering indicatrices of radiation with wavelengths λ = 300 nm (a, d, g), 560 nm (b, e, h), 1000 nm (c, f, i) for Ti NPs (a, b, c), TiO NPs (g, h, i) and Ti + TiO NPs, Δr₁ = 10 nm, with r₀, r₁ = 50 nm (dotted, blue), r₀ = 75 nm (solid, red), r₀ = 100 nm (dashed-dotted, green) (d, e, f). Radiation is propagated from left to right (from 180° to 0°) [50]

For all NPs with r₀, r₁ = 50, 100 nm and for λ = 300, 560 nm, the radiation scattering indicatrices are elongated forward in the direction of radiation propagation. The scattering of 560 and 1000 nm by NPs with r₀, r₁ = 75 nm looks like more spheroidal with approximate equal scattering toward rear and front directions. The increase in wavelength leads to a certain scattering increase in the rear hemisphere for λ = 1000 nm and for all NP sizes to more uniform distribution of radiation in space and almost symmetrical picture of the scattering indicatrix. This fact means that radiation will be scattered uniformly around NPs and this situation will be more appropriate for the use of solar radiation absorption by NF.

With increasing wavelength, the amount of scattered radiation decreases significantly, especially for small NP sizes. The scattering indicatrices of radiation with wavelengths λ = 300, 560, 1000 nm by Ni, NiO, Ni–NiO NPs show the same features presented higher.

In this part, results of optical properties of core–shell and homogeneous oxide NPs [53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80] have been reviewed. Comprehensive analysis of optical properties of homogeneous metallic Ti, Ni and oxide TiO₂, NiO NPs and core–shell Ti–TiO₂, Ni–NiO NPs has been carried out. Ti, Ni and core–shell Ti–TiO₂, Ni–NiO NPs can be applied as perspective candidates for effective absorption of solar radiation. Oxide TiO₂, NiO NPs cannot be used for effective absorption of solar radiation due to extremely low absorption in VIS and IR regions of spectrum. The increase in radiation wavelength leads to more uniform distribution of scattered radiation in space, and indicatrices look like more spheroidal with approximate equal scattering in rear and front directions.

4 Optical properties of nanoparticle systems and nanofluids

4.1 Analysis of optical properties of nanoparticle systems and nanofluids

Analysis of optical properties of NPs systems and NFs investigated and used in optical and solar radiation absorption applications is presented below. The extinction coefficients of NPs systems and NFs and optical transmission of the layer of NFs are investigated for the purposes of effective absorption, extinction of solar radiation and estimation of geometrical size of absorbers. Partially, this topic was reviewed in part 2 (see [42, 43, 45, 46, 49, 56, 58, 66, 67, 74, 80]).

A review of optical properties is presented for direct absorption of solar radiation [84]. Our review studies various NPs more widely and novel model of heating of NPs and surrounding fluid by solar radiation has been discussed. The extinction and absorption coefficients for metallic Au, Ag, Al NPs, oxide Fe₂O₃, CeO₂ NPs were investigated theoretically on the basis of Rayleigh and Mie approximations and experimentally on the basis of spectrophotometric and integrating sphere measurements.

A few theoretical investigations of optical properties of NPs and NFs have been carried out. Numerical investigation of the optical properties of plasmonic Au, Ag, Cu and Al NPs with radii 10–50 nm has been carried out for effective solar absorption [39]. A theoretical approach for calculation of the extinction coefficients of NFs with particle agglomeration is proposed based on diffusion limited cluster aggregation simulation and generalized multi-particle Mie solution method [89]. Mostly used models are presented along with their limitations and applications [87]. Lambert–Beer, Mie and Gans approaches and discrete dipole approximation (DDA) are employed for determination of the extinction coefficient and transmittance of Al, Ag NFs.

Experimental investigation of absorbance and transmittance in the spectral interval 200–2500 nm for different concentrations of Ag NPs, decorated graphene oxide nanosheets, has been carried out [88]. Experimental investigation of extinction coefficient of Al₂O₃–CuO binary NPs dispersed in ethylene glycol–water mixture has been carried out [62]. Extinction coefficients and transmittance of NFs from core/shell NP_S for efficient trapping of solar radiation have been investigated [56, 71]. Optical transmission measurements were performed on several water-based NFs of oxide NPs (Al₂O₃, CuO, TiO₂, ZnO, CeO₂ and Fe₂O₃) as a function of NPs concentration for application in direct absorption of solar energy [74]. Extinction coefficients and transmittance of NFs from oxide NP_S for efficient absorption of solar radiation have been investigated [73, 75].

The optical properties (absorption, transmittance and extinction coefficient) of NFs based on metal, metal oxide, etc. have been thoroughly reviewed in variation with particle size and shape, path length and volume fraction [86]. Optical solar absorption was increased with increasing NP size and volume concentration, and the transmittance of NFs has indirect relation with NP size, volume fraction.

4.2 Optical properties of selected nanoparticle systems and nanofluids for effective absorption of solar radiation

A complex and extensive discussion of the selection of spherical metallic and metal–its oxide core–shell NPs and NFs containing these NPs is carried out below. It is interesting to determine the contribution of fluid (water) and NPs separately and totally in absorption, scattering and extinction of solar radiation in the whole spectral interval of 200–2500 nm [36, 37].

Figure 9 presents the dependencies of solar irradiance I_S on λ, the dependencies of the coefficients of scattering $\alpha_{\text{sca}}^{\text{W}}$ and absorption $\alpha_{\text{abs}}^{\text{W}}$ of radiation by water [7] and the calculated spectral coefficients of absorption $\alpha_{\text{abs}}^{\text{N}} = \pi N_{0} r_{0}^{2} K_{\text{abs}} (r_{0} ,\lambda )$ and scattering $\alpha_{\text{sca}}^{\text{N}} = \pi N_{0} r_{0}^{2} K_{\text{sca}} (r_{0} ,\lambda )$ of radiation by Ti NPs, Ti–TiO₂ NP systems with the radii r₀, r₁ = 50, 125 nm, NP concentrations N₀ = 1·10⁹ cm⁻³ and with r₀, r₁ = 75 nm and N₀ = 1·10⁹, 1·10¹⁰ cm⁻³.

Fig. 9

Dependencies of the coefficients of radiation absorption $\alpha_{\text{abs}}^{\text{N}}$ (solid, red 1, 2) and scattering $\alpha_{\text{sca}}^{\text{N}}$ (dashed, brown, 1, 2) by Ti (a, b) and Ti-TiO₂ (c, d), Δr₁ = 10 nm, NP systems with the radii r₀, r₁ = 50 (1), 125 (2) nm, N₀ = 1·10⁹ cm⁻³ (a, c) and with the radii r₀, r₁ = 75 nm, N₀ = 1·10⁹ (1), 1·10¹⁰ (2) cm⁻³ (b, d), the coefficients of absorption $\, \alpha_{abs}^{W}$ (3, solid, blue a–d) and scattering $\, \alpha_{sca}^{W}$ (3, dashed, blue a–d) radiation by water (all curves are referred to left axis) and solar irradiance I_S on λ (4, solid, orange, a–d, all curves are referred to right axis) [65, 66]

Optical coefficients for core–shell NP systems are determined the same expressions as for homogeneous NPs but with substitution r₀ to r₁. The influence of r₀, r₁ on optical properties of NFs is analyzed under constant values of N₀ = 1·10⁹ cm⁻³ (Fig. 9a, c). Radiation scattering by water is significant only in the UV spectral region 200–400 nm (see Fig. 9), and it is approximately equal to zero for λ > 500 nm.

Increasing r₀, r₁ of mentioned NPs from 50 nm till 125 nm leads to increasing spectral interval from ~ 200–900 nm till ~ 200–1200 nm in which radiation absorption by Ti and Ti–TiO₂ NPs dominates absorption by water $\alpha_{\text{abs}}^{\text{W}}$ for N₀ = 1·10⁹ cm⁻³. As a result, solar radiation absorption by NF in the presented spectral intervals is determined by dominated influence of NPs.

On the other hand, water is the dominating factor in radiation absorption in the spectral intervals λ > 900 (containing ~ 38% of whole solar radiation energy) or λ > 1200 (~ 20% solar energy) nm in comparison with NPs with r₀, r₁ = 50 nm and r₀, r₁ = 125 nm accordingly.

The radiation absorption coefficient for water $\alpha_{\text{abs}}^{\text{W}}$ sharply increases with the increase in λ and $\alpha_{\text{abs}}^{\text{W}}$ is larger than 10¹ cm⁻¹ in the spectral range λ > 1400 nm. Therefore, absorption of solar radiation in this interval is realized in water thin layer with the thickness of about ~ 1/$\alpha_{\text{abs}}^{\text{W}}$ ~ 10⁻¹–10⁻² cm, which prevents the realization of volumetric absorption of solar radiation. This is the main problem for the use of water or water-based fluid for volumetric absorption of solar radiation in spectral interval λ > 1400 nm.

The influence of the values of N₀ = 1·10⁹, 1·10¹⁰ cm⁻³ on optical properties of NFs is analyzed here under constant value r₀, r₁ = 75 nm (Fig. 9b, d). In the spectral intervals ~ 200–900 and ~ 200–1200 nm, solar radiation absorption by water is much smaller than radiation absorption by both types of NP systems with concentration N₀ = 1·10⁹ and 1·10¹⁰ cm⁻³ accordingly and solar radiation absorption is determined by the influence of NPs. However, in the spectral interval λ > 900 nm and λ > 1200 nm, water is the dominating factor in radiation absorption in comparison with mentioned NP systems.

Figure 10a–d shows the spectrum of the solar irradiance I_S(λ) on wavelength λ and the spectral dependencies of the coefficients of radiation extinction by water ($\alpha_{\text{ext}}^{\text{W}}$) and by the systems of Ti and Ti + TiO₂ NPs ($\alpha_{\text{ext}}^{\text{N}}$) with r₀, r₁ = 50, 125 nm at concentration of N₀ = 1·10⁹ cm⁻³ (a, c) and with r₀, r₁ = 75 nm for NP concentrations N₀ = 1·10⁹, 1·10¹⁰ cm⁻³ (b, d), the total coefficient of radiation extinction by NFs $\alpha_{\text{ext}}^{{}}$ = $\alpha_{\text{ext}}^{\text{N}}$ + $\alpha_{\text{ext}}^{\text{W}}$ with systems of Ti, Ti + TiO₂ NPs. Spectral dependence of radiation extinction by water $\alpha_{\text{ext}}^{\text{W}}$ on λ practically coincides with the dependence $\alpha_{\text{abs}}^{\text{W}}$(λ).

Fig. 10

Dependencies of the coefficients of radiation extinction $\alpha_{\text{ext}}^{\text{N}}$ (dashed-dotted, red) by Ti (a, b) and Ti–TiO₂ (c, d), Δr₁ = 10 nm, NP systems with the radii r₀, r₁ = 50 (1), 125 (2) nm, N₀ = 1·10⁹ cm⁻³ (a, c) and with radii r₀, r₁ = 75 nm, N₀ = 1·10⁹ (1), 1·10¹⁰ (2) cm⁻³ (b, d), coefficient of radiation extinction by water $\alpha_{\text{ext}}^{\text{W}}$(dashed-dotted, blue a–d) and total coefficient of radiation extinction $\alpha_{\text{ext}}^{{}}$ = $\alpha_{\text{ext}}^{\text{N}}$ + $\alpha_{\text{ext}}^{\text{W}}$ by NF (3, solid, brown), all curves are referred to left axis, and solar irradiance Is (4, solid, orange a–d, all curves are referred to right axis) [65, 67]

The extinction of solar radiation by water in the spectral ranges ~ 200–900 nm and ~ 200–1200 nm is smaller than that of Ti, Ti + TiO₂ NPs with r₀, r₁ = 50 nm and r₀, r₁ = 125 nm accordingly. As a result, the extinction of the radiation in the mentioned spectral ranges is determined by the dominant influence of the system of NPs and $\alpha_{\text{ext}}^{{}}$ ≈ $\alpha_{\text{ext}}^{\text{N}}$.

Water dominantly influences on the radiation extinction by NF in the spectral range λ > 900 nm and λ > 1200 nm, and NF extinction coefficient $\alpha_{\text{ext}}^{{}}$ is practically equal to $\alpha_{\text{ext}}^{\text{W}}$, $\alpha_{\text{ext}}^{{}}$ ≈ $\alpha_{\text{ext}}^{\text{W}}$ and for λ > 1400 nm $\alpha_{\text{ext}}^{\text{W}}$ ~ 10¹–10² cm⁻¹ [7]. The spectral interval λ ~ 1100–1300 nm is a transition zone from the dominant influence of NPs to the dominant influence of water on solar radiation absorption and extinction.

Consequently, the extinction of the solar radiation will occur in a thin layer of water with a thickness of about ~ 10⁻¹–10⁻² cm in the indicated interval. It is impossible to use the radiation absorption in the range of 1200–2500 nm by an NF based on water for volumetric absorption of radiation or moreover to use additional absorbers (NPs).

Analogous theoretical and experimental investigation of the radiation absorption characteristics of a Ni nanoparticle suspension was carried out by spectroscopic transmission measurement [46]. Ni nanoparticles having average diameter of 4.9 nm were dispersed in alkyl naphthalene with volume fraction of 0.001 (N₀ = 110¹⁶ cm⁻³). Figure 11 shows measured absorption coefficients of the Ni nanoparticle suspension and the base fluid, and analytically predicted absorption coefficient of a cloud of nanoparticles. The absorption coefficient of a particle cloud of Ni nanoparticles was calculated by the Mie scattering theory under the assumption of independent scattering.

Fig. 11

Calculated absorption coefficient for a Ni nanoparticle cloud compared with the experimental data [46]

The absorption cross section of a Ni nanoparticle increases toward the shorter wavelength range. As outlined in Fig. 11, the radiation characteristics predicted by the Mie theory showed good agreement between the model and optical measurements with the increase in absorption coefficient due to nanoparticle suspension in visible and near-infrared wavelengths in which most solar radiation energy is included. The base fluid was transparent and the absorption coefficient was relatively low from visible wavelengths to around 1.6 μm, whereas the absorption coefficient of the nanoparticle suspension was significantly larger than that of the base fluid. At the same time, absorption coefficient of the suspension in the infrared region remains the same as one of the base fluid. Enhancement of solar radiation absorption using a nanoparticle suspension has been demonstrated.

Publications on optical properties of homogeneous metallic and core–shell systems NPs and NFs [46, 56, 62, 71,72,73,74,75, 84,85,86,87,88,89,90,91] have been reviewed in this part. The optical properties of NFs in near-UV, VIS and IR radiation intervals are determined by the total action of optical properties of water (fluid) and NPs system. The absorption and extinction of radiation by a system of NPs and the surrounding fluid are complementary and, at the same time, competitive processes in the absorption and extinction of solar radiation by NFs. Light absorption conditions for NFs include dominant radiation absorption by NPs with selected properties and concentrations compared to the solar absorption by water in the spectral intervals 200–900 (200–1200) nm. These results allow us to evaluate the characteristics of NP systems and NFs with selected values of N₀, r₀, r₁, types of NPs and the NF layer thickness as effective volumetric absorber.

5 Heating of nanoparticle system and surrounding fluid by solar radiation

5.1 Analysis of the properties of nanoparticle systems and nanofluids

Properties of NP systems and NFs were investigated in optical and solar radiation absorption and their heating applications during previous years [34, 92,93,94,95,96,97,98,99,100]. The photothermal conversion efficiency (PTE) of gold NFs has been investigated both experimentally and theoretically under natural solar irradiation conditions [34, 100]. The PTE of gold NFs was found to be much higher than that of pure water and increased nonlinearly with the NP concentration [100].

The thermal simulation of suspended SiO₂/Ag NPs showed a uniform temperature rise under solar irradiation and exhibits a higher photothermal performance [101]. Optical nanostructures can control the optical absorption and are therefore being investigated for solar thermal applications with design of optical nanostructures [104]. The photothermal conversion efficiency of CuO/Ag plasmonic NF is higher than that of CuO NF under the same conditions and is proportional to NPs concentration [105]. The photothermal conversion performance of six commonly used materials (Ag, Fe, Zn, Cu, Si, Al₂O₃) in direct absorption solar collectors was experimentally investigated under a focused simulated solar flux of 12 Suns [106]. It should be noted that the processes of radiation absorption by NPs and NFs, their heating and thermal conversion were investigated insufficiently, but the results of these processes will determine the success of NP solar applications.

5.2 Heating of nanoparticle system and surrounding fluid by solar radiation

The main goal of solar light-to-thermal energy conversion is to achieve maximum value of NP and fluid temperatures under solar radiation action. The heating of NPs is determined by their absorption of solar radiation and simultaneously by heat transfer (thermal conduction) from NPs to ambient fluid and its heating, including also absorption of solar radiation by fluid. Novel model of NPs and NFs heating by solar radiation is analyzed below in detail.

The absence of temperature gradient and uniform irradiation by solar radiation inside absorber volume, and mono-dispersed system of NPs with one NP size are used as assumptions for the simplification of system of equations. The heating of NPs and fluid is described by next system of equations taking into account all made assumptions [97]

$$\rho_{0} c_{0} V_{0} \frac{{{\text{d}}T_{0} }}{{{\text{d}}t}} = \pi_{0} r_{0}^{2} \int\limits_{{\lambda_{1} }}^{{\lambda_{2} }} {I_{\text{S}} \left( \lambda \right)K_{\text{abs}} \left( {r_{0} ,\lambda } \right)} {\text{d}}\lambda {-}J_{\text{C}} S_{0,}$$

(2)

$$c_{\text{m}} \rho_{\text{m}} \frac{{\partial T_{\text{m}} }}{\partial t} = N_{0} J_{\text{C}} S_{0} + \int\limits_{{\lambda_{1} }}^{{\lambda_{2} }} {\alpha_{\text{abs}}^{\text{W}} \left( \lambda \right)I_{\text{S}} \left( \lambda \right)} {\text{d}}\lambda$$

(3)

with the initial conditions:

$$T_{0} \left( {t = 0} \right) = T_{\infty } ,T_{\text{m}} \left( {t = 0} \right) = T_{\infty }$$

(4)

where ρ₀, c₀ and c_m, ρ_m are density and heat capacity of NP material and ambient fluid (water) accordingly [108], S₀ = 4πr ²₀ is the surface area, V₀ = 4/3πr ³₀ is the volume of spherical NP of radius r₀, T₀ is the NP temperature uniformed over its volume, T_m is the surrounding medium temperature, T_∞ is the initial NP and surrounding medium temperatures, the wavelengths λ₁, λ₂ mean the boundaries of optical spectrum under consideration and J_C is the loss energy density flux from NP surface due to heat conduction. N₀, I_S, K_abs(λ),$\alpha_{\text{abs}}^{\text{W}}$ are denoted before.

The value of J_C at NP surface is determined by quasi-stationary solution of heat conduction equation in spherical case [20] taking into account the heating of fluid with temperature T_m = T_m(t).

$$J_{\text{C}} = \frac{{k_{\text{m}} }}{{r_{0} }}\left( {T_{0} - T_{\text{m}} } \right)$$

(5)

where k_m is a constant thermal conduction coefficient of fluid [109]. The expression:

$$q_{\text{abs}} = \pi r_{0}^{2} \int\limits_{{\lambda_{1} }}^{{\lambda_{2} }} {I_{\text{S}} \left( \lambda \right)K_{\text{abs}} \left( {r_{0} ,\lambda } \right)} {\text{d}}\lambda$$

(6)

will be used further and q_abs can be viewed as integral of power of solar irradiance absorbed by NP.

Solar radiation extinction (absorption) in the spectral interval 200–1200 nm is determined by dominated influence of the NPs system in water. Solar radiation absorption by water is much smaller than radiation absorption by NPs (see part 4), and $\alpha_{\text{abs}}^{\text{W}}$ can be neglected in Eq. (3). As a result of this simplification, the solutions for T₀, T_m from (2–5) have the forms [107]:

$$T_{0} = T_{\infty } + \frac{{{\text{q}}_{\text{abs}} N_{0} }}{c\rho }t - \frac{{{\text{q}}_{\text{abs}} \left( {c_{\text{m}} \rho_{\text{m}} } \right)^{2} }}{{4k_{\text{m}} \pi r_{0} \left( {c\rho } \right)^{2} }}\left[ {\exp \left\{ { - \frac{t}{{\tau_{\text{m}} }}} \right\} - 1} \right]$$

$$T_{\text{m}} = T_{\infty } + \frac{{{\text{q}}_{\text{abs}} N_{0} }}{c\rho }t + \frac{{{\text{q}}_{\text{abs}} c_{\text{m}} \rho_{\text{m}} N_{0} c_{0} \rho_{0} V_{0} }}{{4k_{\text{m}} \pi r_{0} \left( {c\rho } \right)^{2} }}\left[ {\exp \left\{ { - \frac{t}{{\tau_{\text{m}} }}} \right\} - 1} \right]$$

(7)

$c\rho = c_{\text{m}} \rho_{\text{m}} + 4\pi r_{0}^{3} c_{0} \rho_{0} N_{0} /3$ is the heat capacity of the heterogeneous NF. The characteristic time τ_m = $\frac{{c_{0} \rho_{0} r_{0}^{2} c_{\text{m}} \rho_{\text{m}} }}{{3k_{\infty } c\rho }} = \tau_{0} \frac{{c_{\text{m}} \rho_{\text{m}} }}{c\rho }$ determines the dependencies of temperatures T₀ and T₁ on time t. The values of τ_m are accordingly equal to  ≈ 3.710⁻⁹, 1.510⁻⁸ s for r₀ = 50, 100 nm. The use of core–shell NPs leads to analogous solutions with some deviations in designations.

The dependence of NP overheating ΔT = T₀− T_m relatively water temperature T_m on time t [see (7)] is determined

$$\Delta T = T_{0} {-}T_{\text{m}} = \frac{{{\text{q}}_{\text{abs}} c_{\text{m}} \rho_{\text{m}} }}{{4k_{\text{m}} \pi r_{0} c\rho }}\left[ {1 - \exp \left\{ { - \frac{t}{{\tau_{\text{m}} }}} \right\}} \right]$$

(8)

The dependence of normalized NP overheating ΔT_n by solar radiation on time t is equal

$$\Delta T_{\text{n}} = \Delta T/\frac{{{\text{q}}_{\text{abs}} c_{\text{m}} \rho_{\text{m}} }}{{4k_{\text{m}} \pi r_{0} c\rho }} = 1 - \exp \left\{ { - \frac{t}{{\tau_{\text{m}} }}} \right\}$$

(9)

Conversion of light energy starts with photo-induced generation of energy-rich electrons and ultrafast electron dynamics in NPs [102]. The dependencies of ΔT_n for Ti NPs with r₀ = 50, 100 nm, immersed in water, are presented in Fig. 12a. The increase in ΔT_n begins from time instant t ~ 10⁻⁹, 10⁻¹⁰ s, and ΔT_n achieves own maximal value of ΔT_n = 1 at t ~ 10⁻⁸, 10⁻⁷ s for r₀ = 50, 100 nm accordingly. After achievement of maximal NP overheating relatively fluid, the equivalence has been established between absorption radiation energy by NP and heat loss from NP by heat conduction.

Fig. 12

The temporal dependencies of normalized NP overheating ΔT_n [see (9), green] for Ti NPs with r₀ = 50 (1), 100 (2) nm immersed in water (a) and of the temperatures T₀ (dashed, red) of Ti NPs system with r₀ = 100 nm, N₀ = 1·10⁹ (1), 1·10¹⁰ (2) cm⁻³ and T_m (solid, blue) of surrounding water [see (10)], which are heated by solar radiation [107]

For solar radiation action, the condition t ≫ τ_m is obeyed and the dependencies of temperatures T₀, T_m (7) are transformed:

$$\begin{aligned} & T_{0} \approx T_{\infty } + \frac{{{\text{q}}_{\text{abs}} N_{0} }}{c\rho }t + \frac{{{\text{q}}_{\text{abs}} \left( {c_{\text{m}} \rho_{\text{m}} } \right)^{2} }}{{4k_{\text{m}} \pi r_{0} \left( {c\rho } \right)^{2} }} \\ & T_{\text{m}} \approx T_{\infty } + \frac{{{\text{q}}_{\text{abs}} N_{0} }}{c\rho }t - \frac{{{\text{q}}_{\text{abs}} c_{\text{m}} \rho_{\text{m}} N_{0} c_{0} \rho_{0} V_{0} }}{{4k_{\text{m}} \pi r_{0} \left( {c\rho } \right)^{2} }} \\ \end{aligned}$$

(10)

The temperatures T₀ and T_m increase in time t due to the condition of absence of heat loss outside the irradiated volume, and this solution is applicable for period of time till thermal energy loss out of absorber volume is negligible. The temperatures T₀, T_m are proportional to the NP concentration N₀.

Stationary overheating of NPs in comparison with fluid T₀−T_m for t ≫ τ_m is constant during the radiation action [see also ΔT (8)]:

$$\Delta T = T_{0} - T_{\text{m}} = \frac{{{\text{q}}_{\text{abs}} c_{\text{m}} \rho_{\text{m}} }}{{4k_{\text{m}} \pi r_{0} c\rho }}$$

(11)

Figure 12b presents the temporal dependencies of the temperatures T₀ of the Ti NPs system with r₀ = 100 nm, N₀ = 1·10¹⁰, 1·10⁹ cm⁻³ and T_m of surrounding water (10), which are heated by solar radiation.

The heating of the NPs by solar irradiation, their intensive heat exchange with the surrounding water and following its heating starts after characteristic time t ~ τ_m ≈ 1.5·10⁻⁸ s (see Fig. 12a) from irradiation commencement. The energy release in NPs and their heat exchange lead to the increase in the temperatures T₀ and T_m in time with small difference between them due to intense heat exchange of NPs with surrounding water.

It should be taken into account that thermal energy of volume unit of surrounding water at initial temperature T_∞ = 273 K is equal to E_m∞ = c_mρ_mT_∞ = 1.14·10³ J/cm³ and it is much larger than the thermal energy E_0∞ = N₀c₀ρ₀V₀T_∞ = 3.13·10⁻² J/cm³ of Ti NP system with high values of r₀ = 100 nm and N₀ = 1·10¹⁰ cm⁻³.

Due to this reason, remarkable heating of water commences only from the moment t ~ 1 s after radiation action, when the value of thermal energy transferred from NP system to water till this moment is sufficient to increase water temperature T_m because of great difference between heat capacities of fluid and NP system mentioned above. Temperatures T₀ and T_m achieve the value of about ~ 283 K (T_∞ = 273 K) at t ~ 100 s for N₀ = 1·10¹⁰ cm⁻³, r₀ = 100 nm. The results in Fig. 12a, b are presented for Ti NPs, but their important features are applicable for various NPs with analogous values of NP and NF parameters.

It should be noted that the temporal linear dependence of T₀, T_m has been experimentally established [109,110,111] for initial period of heating, which confirms the dependencies (10). The temperature curves are shown in Fig. 13, which clearly shows that Au NPs had good photothermal conversion capability under the xenon lamp radiation [109]. There was a temperature limitation for Au NPs, which was depended on the shape and size of Au NPs, the radiation intensity and the ambient temperature. Under the intense and long enough illumination, the process of temperature changed consisted of the following procedures: (i) temperature increased with time; (ii) Au NPs reached their own photothermal conversion limitation, taking into account the heat losses, and had constant conversion efficiency, but the temperature still increased and (iii) the temperature became constant when the absorption and dissipation of energy reached equilibrium. In the process of (ii) and (iii), the rate of rise in temperature slowed down until reaching the point of energy balance. The temperature change in Au NPs with different sizes could be calculated by Eq. (10) during the process (i), when temperature increased with time.

Fig. 13

Temperature changes with time for Au NFs from two different groups G1 (a) and G2 (b) under 1.5 kW m⁻² illumination [109]

As it was mentioned above, water is the dominating factor in solar radiation absorption in the spectral interval 1200 < λ<2500 nm and absorption of solar radiation in whole spectral interval 200–2500 nm will be realized in thin water layer with the thickness of about 1/ $\alpha_{\text{abs}}^{\text{W}}$ ~ 10⁻¹–10⁻² cm. The NPs, placed in this thin layer, undergo by solar radiation with the wavelengths in the spectrum 200–2500 nm. NPs located in the deep layers with the depth larger than $1 /\alpha_{\text{abs}}^{\text{W}}$ absorb radiation only in the spectral interval ~ 200–1200 nm penetrating in deep water layers.

Figure 14 presents the dependencies of q_abs, q_abs/πr₀ on r₀ for homogeneous Ti, Au NPs and q_abs, q_abs/πr₁ on r₁ for core–shell Ti–TiO₂ NPs for two different cases—(a) for NPs placed in surface layer irradiated with wavelengths in the interval 200–2500 nm, (b) for NPs in the deep layers of water volume irradiated with 200–1100 nm. Figure 14 is transformed from Figs. 3 and 4 [97]. Results for Au NPs are presented for comparison. The expression of q_abs determines the energy release in NPs (10), the rate of NPs and NF heating, the quantitative values and temporal dependencies of T₀, T_m (7–11). The combinations of q_abs/πr₀ and q_abs/πr₁ determine the value of NP overheating in comparison with fluid ΔT, ΔT_n (8, 9) and also the influence on temporal dependencies T₀, T_m on t (7, 10).

Fig. 14

The dependencies of q_abs (solid, red), P₁ (dashed, brown) on r₀, r₁ accordingly, horizontal solid lines (black) denote the value of P₁ = 1 (a, b) and the dependencies of q_abs/πr₀, q_abs/πr₁ on r₀, r₁ (solid, red c, d) accordingly for homogeneous Ti (1), Au (3) NPs and for core–shell Ti-TiO₂ (2), Δr₁ = 10 nm, NPs in the spectral intervals 200–1100 nm (a, c) and 200–2500 nm (b, d)

The difference in the values of q_abs for various Ti and Ti–TiO₂ NPs with the radii r₀, r₁ ≥ 50 nm is not very significant. The values of q_abs and q_abs/πr₀ for Au are significantly smaller than these ones for Ti and Ti-TiO₂ for r₀, r₁ > 50 nm. It is connected with the different optical properties of these NPs. It means that Au NPs can be used for absorption of solar radiation with comparative efficiency of Ti and Ti–TiO₂ NPs only in the range of r₀ ≤ 50 nm. The values of q_abs and q_abs/πr₀, q_abs/πr₁ for Ti and Ti–TiO₂ NPs in the spectral interval 200–2500 nm are larger than those in the interval 200–1100 nm.

Parameter P₁ for NP determines the correlation between integral absorbed and scattered solar radiation by NP

$$P_{ 1} = \frac{{q_{\text{abs}} }}{{q_{\text{sca}} }}$$

(12)

$q_{\text{sca}}^{{}} = \pi r_{0}^{2} \int_{{\lambda_{1} }}^{{\lambda_{2} }} {I_{\text{S}}^{{}} \left( \lambda \right)} K_{\text{sca}} \left( {r_{0} ,\lambda } \right){\text{d}}\lambda$ is the integral of solar radiation power scattered by NP and analogous expression q_sca for system of core–shell NPs with r₁. Parameters P₁ for Ti and Ti–TiO₂ NPs decrease from the values of about ~ 10 for r₀, r₁ = 25 nm till the values of about ~ 1 with increasing r₀, r₁ till r₀, r₁ = 125 nm.

The increase in r₀, r₁ leads to the increase in q_abs and q_abs/πr₀, q_abs/πr₁, but to the decrease in P₁, and taking into account their opposite influence, the maximal absorption efficiency could be achieved by appropriate selection of these parameters for various NPs.

The results of heating of homogeneous metallic and core–shell systems NPs and fluid [92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111] have been reviewed in this part. In general, next set of parameters determines the effective absorption and heating of NPs and fluid (NFs)—q_abs, r₀ (r₁), N₀, cρ, c_mρ_m, k_m, P₁ [see (10–12)]. These results highlight the possibility for effective application of homogeneous Ti and core–shell Ti–TiO₂ NPs with the radii of about 75–125 nm as effective absorbers of solar radiation and NF heaters.

It should be noted two problems that influence on thermal processes in NFs.

In general, NPs can initially have different sizes and the NP system is polydisperse one. In addition, even in the case of the initial monodisperse NP system, when all NPs have the same radii, various processes can occur in NF. NPs have a great tendency to collide and aggregate into larger clusters [75,76,77]. These also include the change in NPs size due to mechanical interaction between themselves and with the absorber walls, as well as the change (decrease) in NP sizes in high-temperature NFs due to evaporation and other processes [108].

Next problem is in the significant influence of NPs on physical and hydrodynamical properties of NFs in comparison with pure fluid. Last investigations of thermo-physical, rheological and heat transfer properties of NFs for solar thermal applications are presented [112,113,114,115,116,117,118]. An investigation into the thermo-physical and rheological properties of NFs for solar thermal applications was carried out [112, 113]. It was reviewed metal oxide NFs including formulation, thermo-physical properties, mechanisms and heat transfer performance [114]. The investigation of the transfer mechanisms in NFs has been carried out [115,116,117,118], including investigation of convective heat transfer of NFs, characterization of heat transfer (thermal conductivity) characteristics and thermo-physical properties of NFs and their applications.

These features influence on heating and thermal processes in NF, and it is necessary to carry out investigations further and to take into account the possible polydispersity and influence of NPs on NF when exposed to intense solar radiation.

6 Applications of nanoparticles and nanofluids in solar thermal technologies

Results of optical properties of NPs and heating of NPs by solar radiation can be used in various solar thermal technologies, thermal devices, solar absorption thermal collectors and other possible applications.

General problems and challenges of NPs applications in solar thermal collectors are in the increase in their efficiency of absorption and conversion of solar energy. The overviews of application of NPs and NFs in solar thermal collector and its challenges were presented [119,120,121,122,123,124,125] for the purpose to improve the performance of solar collectors.

Recent advances in optical nanostructures design and fabrication, using very specific technology, such as integrating nitrogen-doped graphitic carbon with Au NPs for excellent solar energy absorption properties [123], and applications of NFs for solar/thermal energy conversion are reviewed [124, 125]. A review of economic feasibility and world scenario of solar water heating systems has been presented [122], and the importance of harvesting of solar radiation has been underlined.

The solar water heating systems are one of the most common applications of solar energy utilization. Such systems include flat plate and volumetric absorption solar collectors. Applications of NPs and NFs in flat plate solar collectors are investigated [126,127,128,129,130], including experimental evaluation of flat plate solar collector [127]. Effect of titanium dioxide/water NF use on thermal performance of the flat plate solar collector has been investigated [128]. Experimental and numerical investigations of the effect of Al₂O₃/TiO₂–H₂O NFs on thermal efficiency of the flat plate solar collector have been carried out [129].

The use of NPs and NFs in direct absorption solar collectors is real challenge and very perspective for the performance of solar energy harvesting. Direct absorption solar collectors show great potential for efficient conversion of sunlight to thermal energy. Applications of NPs and NFs in direct solar absorption collectors are investigated and reviewed [5, 8, 40, 76, 126, 131,132,133,134]. Part of these investigations was reviewed before. Recent investigations investigated applicability of various NPs for direct absorption solar collectors, including alumina NF and ZnO–Au composite hierarchical particles dispersed in oil-based NFs [76, 131]. The optimization problems of a direct absorption solar collector with blended plasmonic NFs and effect of plasmonic nanoshell-based NF on efficiency of direct solar thermal collector were discussed [132, 133]. The use of various NPs in flat plate and direct absorption solar collectors leads to increasing their thermal efficiency up to 10–15% in comparison with their collectors without NPs [126,127,128,129,130,131,132,133,134].

The last time the production of steam in thermal collectors under solar irradiation is very interesting field and a few investigations on this topic have been carried out [111, 135,136,137,138]. Steam production is essential for a wide range of applications, and currently, there is a discussion if steam could be generated on top of heated NPs in a solar receiver. But in reality steam generation is mainly caused by localized boiling around the heated NPs and vaporization in the superheated region due to highly non-uniform temperature and radiation energy distribution. Steam generation under sun action and photothermal heating enabled by plasmonic NFs have been investigated taking into account the volumetric solar heating, direct solar steam generation and comparative study on solar evaporation via NPs.

Applications of NPs for solar chemical technologies are investigated the last time [139,140,141,142,143,144,145]. Many exciting possibilities exist to exploit the extremely large surface area-to-volume ratio of NPs to effect chemical reactions. These can be either thermo-chemical in nature, where the absorption of concentrated sunlight causes high temperatures that drive the reactions, or photocatalytic, where the NPs serve as photocatalysts for splitting water, waste remediation or other purposes. The review of experimental investigation on directly irradiated particles solar reactors has been presented [139]. Great interest is connected with the problems of photocatalysis with solar energy, including sunlight-responsive photocatalyst based on TiO₂ for wastewater treatment [144] and photocatalytic water disinfection under solar irradiation by Ag@TiO₂ core–shell structured NPs [145].

An important problem of water desalination is discussed [146] with application of recent freshwater augmentation techniques.

The novel performance and environmental effects of conventional and nanofluid-based thermal photovoltaics has been discussed [149].

The applications of NPs in various solar cells can be used for increasing cells efficiency and are discussed in [147,148,149,150,151,152,153,154,155,156]. General problems of the NPs use in solar cells are investigated [147,148,149,150,151,152] taking into account quantum-sized nanomaterials for solar cell applications [147], possible strategies and recent results in plasmonic enhanced solar cells [148], optimized TiO₂ NPs packing for photovoltaic applications [150], performance enhancement of photovoltaic cells by changing configuration and using Al₂O₃ NPs [151] and influence of the Cu₂ZnSnS₄ NPs size on solar cell performance [152].

Hybrid solar cells from Sb₂S₃ NP ink [153], device performance enhancement of polymer solar cells by NP self-assembly [154], plasmonic effect of gold NPs in organic solar cells [155] and novel synergistic combination of Al/N Co-doped TiO₂ NPs for highly efficient dye-sensitized solar cells [156] were investigated and discussed.

For perovskite solar cells, NPs are used for the boosting efficiency of hole conductor-free cells by incorporating NiO NPs into carbon electrodes [157] and cobalt-doped nickel oxide NPs as efficient hole transport materials for low-temperature processed cells [158]. It is important that conversion efficiency of cells is improved to 14.5% [158] in comparison with previous investigations.

It should be noted that various NP applications in thermal solar technology can be used for the development of innovation devices or increasing efficiency existed technologies.

7 Conclusions

The present review is intended to bring the recent NP and NF optical properties and to summarize the latest thermal conversion and heating studies together with their application for direct absorption of solar radiation in order to facilitate the researchers and to realize the research potential in the field of NF-based absorber systems. This review can be considered as an important link between the optical properties of NPs and NFs and efficiency of NPs heating by solar energy. The results of systematic studies of all these characteristics have been presented as a prerequisite for the successful realization of the potential of selected NPs for solar thermal applications.

As commonly used working pure fluids are weak absorbers over the UV and VIS intervals of the solar spectrum, the addition of NPs has been proved to enhance the absorption characteristics of the base fluid. NPs offer the potential of improving the radiation properties of liquids, leading to a significant increase in the efficiency of thermal conversion of solar energy.

Although solar radiation absorption and thermal conversion by NPs and NFs are actively investigated in recent years, only a limited amount of the nearly unlimited potential combinations of NP structures, materials and sizes has been explored (as can be seen in the selected studies given in Tables 1, 2 and 3). Additionally, little progress has been made toward the development of NP heating approaches.

Initially, an overview of the optical properties of metallic, oxide and hybrid core–shell NPs and characterization techniques is presented in this review. The latest numerical and experimental works and recent developments in the field of direct radiation absorption are summarized and discussed. This review provides a vital set of optical property data to enable further development of promising candidates for broadband and spectrally selective NF solar absorbers. Eventually, the present challenges and future possible directions are outlined.

An overview of the results of NP solar heating and thermal conversion is presented. Novel solar heating approaches have been formulated for NPs and NFs, which can be applied for effective conversion of solar radiation. Novel parameters q_abs and P₁ are introduced for the description of input solar energy in NP, which can be viewed as integral absorbed solar power, and the correlation between absorption and scattering of radiation by NP accordingly.

Presented discussions highlight the possibility to use metallic Ti and core–shell Ti–TiO₂ NPs as perspective absorbers of solar radiation and heating of NPs and NFs in the spectral interval 200–2500 nm. Ti and Ti–TiO₂ NPs are available in the nanotechnology market and can be used for solar experiments. Furthermore, it is expected that the utilization of plasmonic Ni NPs, their core–shell structures and other NPs with controllable and broadband absorption properties over the entire solar spectrum attracts more attention.

There is also a need to optimize the NPs and NFs optical properties to ensure maximum thermal performance of the volumetric solar absorbers. Selection of suitable NPs includes the choice of their structure (homogeneous, core–shell, etc.), materials (metal, oxide, etc.), concentrations, sizes (their radii, thicknesses of oxide shells), optical indexes of absorption and refraction of NP material and surrounding medium, etc. and fluid (optical, thermo-physical, etc.) parameters for effective absorption of solar radiation and their effective heating. NPs and NFs with the selected characteristics can realize their effective heating by solar radiation for solar thermal energy applications. These results are highlighting the use of established remarkable approaches that can improve current solar thermal technologies in near future.

The prominent advantage of this review in comparison with others is the right connection of optical properties of selected NPs with novel approach of NP heating and thermal conversion of solar radiation for achievement of maximal heating of NPs and NF. Overall, these results show great potential for the use of selected NPs and NFs in direct absorption solar thermal systems, and this is important for their further development and improvement. From the other side, further researches are required in the following experimental investigations to search more appropriate NPs for effective absorption and their heating and to enhance the efficiency of solar absorbers over the next several coming years.