Specific heat capacity of molten salt-based alumina nanofluid
© Lu and Huang; licensee Springer. 2013
Received: 18 April 2013
Accepted: 15 May 2013
Published: 21 June 2013
There is no consensus on the effect of nanoparticle (NP) addition on the specific heat capacity (SHC) of fluids. In addition, the predictions from the existing model have a large discrepancy from the measured SHCs in nanofluids. We show that the SHC of the molten salt-based alumina nanofluid decreases with reducing particle size and increasing particle concentration. The NP size-dependent SHC is resulted from an augmentation of the nanolayer effect as particle size reduces. A model considering the nanolayer effect which supports the experimental results was proposed.
KeywordsNanofluid Nanolayer Specific heat capacity (SHC) Molten-salt
where the subscripts nf, np, and f denote nanofluid, NP, and solvent, respectively, and cp, ϕ, and ρ are SHC, volume fraction, and density, respectively. In this work, we investigate SHCs of molten salt-doped with alumina NPs. The material selected is because of the fluid utilized as a heat storage medium in the solar-thermal power plants, and the SHC of it determines energy storage capacity in the power plants. Here, the effect of NP addition on the SHC of the molten salt and the underlying mechanisms were examined. Furthermore, a theoretical model supporting the experimental results was proposed.
Results and discussion
Figure 4b shows the SHCs of the 13-nm and 90-nm alumina NPs and bulk alumina at various temperatures. The SHCs of NPs were measured using model 7020 of EXSTAR while the values of the SHCs of the bulk alumina were taken from Ginnings and Furukawa . The SHCs of NPs and bulk alumina increases as temperature increases. Meanwhile, the SHC increases as particle size reduces and the SHC of 90 nm is approaching that of bulk alumina at high temperature. The size-dependent SHC of NPs has also been observed from previous studies [17, 18]. This increment of SHC with reducing particle size could be explained by the Debye model of heat capacity of solids, wherein the heat capacity increases as the Debye temperature reduces . The Debye temperature decreases with reducing particle size , resulting in an increased SHC.
Figure 4c shows the SHCs of solid salt and solid salt doped with 13-nm and 90-nm alumina NPs at 0.9, 2.7, and 4.6 vol.%, respectively (measured using model 7020 of EXSTAR). The effect of NP concentration on the SHC of the solid salt doped with NPs is not significant whereas the SHC decreases with increasing NP size. The NP-size-dependent SHC might be due to the fact that the larger NPs have a smaller SHC (see Figure 4b). Nevertheless, the effect of NP addition on the SHC of the nanofluid is pronounced (see Figure 4a).
The theoretical prediction using Equation 1 is also shown in Figure 5, where the values of cp,np are obtained from the temperature-averaged (290°C to 335°C) SHCs of the 13- and 90-nm alumina NPs shown in the Figure 4b (i.e., 1.30 and 1.10 kJ/kg-K, respectively). The red dash line and blue dash-dot line in Figure 5 are the theoretical predictions of Equation 1 for the nanofluids having 13- and 90-nm alumina NPs, respectively (where cp,13nm, cp,90nm, and cp,f are 1.30, 1.10, and 1.59 kJ/kg-K, respectively whereas ρnp and ρf are 3,970 and 1794 kg/m3, respectively). It is noted that the alumina NP density was taken from the value of the bulk alumina as an approximation. The existing model (Equation 1) predicts a slight decrease trend of the SHC of the nanofluid with increasing particle concentration since the SHCs of NPs are smaller than that of molten salt. This slight decrease tread is similar to that observed for the solid salt doped with NPs (see Figure 4c). Furthermore, the model (Equation 1) shows that the SHCs of nanofluids decrease with increasing particle size because smaller particles have larger SHC, which is in contrast to the experimental results for the nanofluid. In addition, the experimental results have a large difference from the model prediction of Equation 1, which has also been observed in previous studies [6, 9–12]. This indicates that there might be other mechanisms responsible for the large discrepancy.
The proposed mechanisms for the thermal conductivity enhancement are the following: (1) Brownian motion [19, 20]. It is argued that Brownian motion of NPs in the solvent could result in a microconvection effect that enhances heat transfer of the fluid; (2) Colloidal effect [21–23]. It says that heat transfer in nanofluids can be enhanced by the aggregation of NPs into clusters; (3) Nanolayer effect [24–26]. The solid-like nanolayer formed on the surface of the nanoparticle could enhance the thermal conductivity of the fluid . In light of these studies, we believe that some of these mechanisms might affect the SHC of nanofluid as well.
Particle aggregation was observed when both the solid salt and the molten salt were doped with NPs as shown in Figures 2 and 3. The sizes of the clusters formed from the aggregated NPs are both on the order of 1 μm in the solid salt and molten salt (see Figures 2 and 3). However, the SHC of the solid salt doped with NPs is close to that of solid salt alone whereas the SHC of the molten salt doped with NPs is apparently different from that of molten salt. Furthermore, the NP size effect shows reverse trends in these two cases: the SHC of solid salt increases as NP size reduces (see Figure 4c) whereas the SHC of molten salt doped with NPs decreases as NP size reduces (see Figure 4a). This indicates that the observed large discrepancy between the SHCs of nanofluid and molten salt does not result from the particle aggregation effect. In addition, Ishida and Rimdusit  have also shown that the SHC is a structure-insensitive property, provided that formation of different degrees of network do not affect the SHC of the composite. Furthermore, since SHC is not a transport property, the microconvection effect caused by Brownian motion of NPs should not play a significant role in the SHC of the nanofluid. Thus, we conjectured that the nanolayer effect might be the only important factor among these three mechanisms affecting the SHC of the nanofluid. Accordingly, a theoretical model considering the nanolayer effect on the SHC was proposed. Since the solid-like nanolayer formed on the surface of NP is at a thermodynamic state between solid salt and molten salt , the value of the SHC of the nanolayer should lay between those of the solid salt (1.04 kJ/kg-K) and the molten salt (1.59 kJ/kg-K). In other words, the nanolayer has a lower SHC than that of the molten salt. Further, the thermal properties of the nanolayer (e.g., thermal conductivity and SHC) could vary with different combinations of NPs and base fluids, since the structure of the nanolayer is dependent on the interaction of molecules . In addition, Lin et al.  also found that the nanolayer structure is size-dependent, resulting in a size-dependent thermal conductivity.
where ρf and ρnp are solvent density and NP density, respectively.
Using Equation 5, one can obtain the SHC of the nanofluid (cp,nf) at any mass fraction (α’) from the measured SHC of the nanofluid (cp,m) at a certain mass fraction (α) for a given NP size. The predictions using Equation 5 for the SHCs of the nanofluids at various concentrations having 13-nm alumina NPs (red solid line) and 90-nm alumina NPs (blue dash line) based on the measured SHCs at 4.6 vol.%, along with the experimental results, are also shown in Figure 5. As Figure 5 shows, the predictions from the proposed model agree well with the experimental results.
The large difference between the predictions of Equations 5 and 1 is from the result of the nanolayer effect on the SHC. This could be better understood by looking at the third term in the numerator of Equation 4. Since the weight of nanolayers (Wlayer’) increases as particle concentration increases, it results in a further reduced SHC, provided that the nanolayer has a lower SHC than that of molten salt. Furthermore, the increase of SHC with increasing particle size is also a result of the nanolayer effect. For a given NP concentration, the nanolayer effect increases as particle size reduces since the number of particle increases with reducing particle size. Thus, one observes a decreased SHC as particle size reduces, and particle concentration increases because of the augmentation of the nanolayer effect.
In conclusion, we have explored the SHC of the molten salt-based alumina nanofluid. The NP size-dependent SHC in the nanofluids had never been reported before and cannot be explained by the current existing model. We found that the reduction of the SHC of nanofluid when NP size reduces is due to the nanolayer effect, since the nanolayer contribution increases as particle size reduces for a given volume fraction. A theoretical model taking into account the nanolayer effect on the SHC of nanofluid was proposed. The model supports the experimental results in contrast to the existing model. The findings from this study are advantageous for the evaluation of the application of nanofluids in thermal storage for solar-thermal power plants.
Specific heat capacity
Scanning electron microscope
Energy dispersive spectrometer
Differential scanning calorimetry.
The authors would like to thank Dr. C-W Tu and Dr. S-K Wu of the Industrial Technology Research Institute and Prof. Chuanhua Duan of Boston University for the helpful discussion about the heat capacity of the nanofluid. The authors would also like to acknowledge the Green Energy and Environmental Laboratory of the Industrial Technology Research Institute for the use of their equipment for the heat capacity measurement. The funding support for this study is from the National Science Council of Taiwan (Grant no. NSC 101-2623-E-009 -001-ET).
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