## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Reference** & **Phase** & **Size (nm)** & **Fraction (\%)** & **Temperature (\({}^{\circ}\)C)** & **Method** \\ \hline
[12] & n/a & 38.4 & 0–4.3 vol & Room temperature & THW \\
[13] & \(\gamma\) & 28 & 2.4–5.5 vol & 24 & SS \\
[14] & n/a & 20 & 0–40 wt & 10–50 & THW \\
[15] & n/a & 43 & 0–3 vol & Room temperature & THW \\
[16] & n/a & 38 & 0.3–3 vol & n/a & THW \\
[17] & n/a & 33 & 0–4 vol & 5–40 & THW \\
[18] & n/a & 11, 17, 150 & 1–4 vol & 21–71 & THW \\
[19] & n/a & 36 & 2–10 vol & 27.2–35.7 & SS \\
[20] & n/a & 80, 150 & 1 vol & 20–60 & THW \\
[21] & n/a & 10 & 1–8 vol & 30–50 & THW \\
[22] & n/a & 38.4 & 0–4 vol & 21–51 & TO \\
[23] & n/a & 43 & 1–3 vol & 20–50 & THW \\
[24] & \(\gamma\) & 13 & 0.1–3 vol & 25–52 & THW \\
[25] & n/a & 11, 45, 150 & 0–3 vol & 20–50 & THW, TO \\
[26] & \(\gamma\) & 13 & 1.2–4.3 vol & 32–67 & THW \\
[27] & n/a & 36, 47 & 0–18 vol & 20–48 & THW \\
[28] & \(\gamma\) & 25 & 2–3 vol & 15–45 & THW \\
[29] & n/a & 13 & 0.5 vol & 10–50 & THW \\
[30] & n/a & 40 & 0.1–20 vol & 25–65 & NF \\
[31] & n/a & \(\sim\)50 & 0.1–2 vol & 20–60 & THW \\
[32] & n/a & 11, 20, 40 & 0–10 vol & 23 & THW \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of research on thermal conductivity of Al\({}_{2}\)O\({}_{3}\)-water nanofluids. THW: transient hot-wire, SS: steady-state, TO: temperature oscillation, NF: nano-flash. In [29], the authors evaluated experimentally the effect of the ultrasonication time (from 0 to 5 h) using 0.5 vol% of nanoparticles and temperatures from 10 to 50 \({}^{\circ}\)C. In this case, a slight increase in thermal conductivity was observed for sonication times larger than 1 h and up to the 5 h tested. Also, in [29], higher values of thermal conductivities were obtained in comparison to [30]. Again, as in [28], an increase in thermal conductivity was obtained when the time increased from 1 to 2 h.  
According to [34], seven phases of alumina (transition alumina) are available, denoted by the following Greek symbols: gamma (\(\gamma\)), delta (\(\delta\)), eta (\(\eta\)), theta (\(\theta\)), kappa (\(\kappa\)), rho (\(e\)) and chi (\(\chi\)). In addition to this, they showed that the formation sequence of the different phases is a strong function of the raw materials used at the beginning and the way in which they are formed. ref. [35] shows that the surface area per gram of nano-powder depends on the phase (alpha: specific surface \(>\) 10 m\({}^{2}\)/gr, average particle size of 40 nm; gamma: specific surface \(>\) 40 m\({}^{2}\)/gr, average particle size of 15 nm). According to [36], phase transformations of alumina reduce the specific surface area of the nanoparticles. This result is associated with a structural collapse and decrease in the amount of surface electron-acceptor or electron-donor sites. However, as stated by [37], in spite of the high scientific interest in these nanoparticles, little is known yet about the physicochemical properties of their several morphological variations, which remain largely unexplored until now. Table 1 also summarizes the phase of the alumina nanoparticles used in different experimental studies. In four cases, the \(\gamma\)-phase was used, while, in the rest of works, the phase was not specified. The literature review presented allows for concluding that some experimental studies evaluating the impact of nanoparticle concentration, sonication time and temperature on the thermal conductivity of nanofluids containing water and alumina are available. In the special case of theta-phase alumina, no research has been found in the open literature. In the present work, the effect of these three independent parameters on the thermal conductivity of a nanofluid composed of water and this alumina phase is experimentally evaluated. For the first time, a sonication time as high as 16.5 h has been used.