# Preparation Techniques of TiO\({}_{2}\) Nanofluids and Challenges: A Review
## 3 Thermal Conductivity
\begin{table}
\begin{tabular}{c c c} \hline
**Researcher** & **Derived Model** & **Discussion** \\ \hline \multirow{2}{*}{[PERSON] and [PERSON] et al. [94]} & \multirow{2}{*}{\(k_{eff}=k_{f}\left[\frac{\left[2\alpha_{f}-2\right]}{\left[1+\frac{2\alpha_{f}-2 }{\alpha_{f}+2}\left(\alpha_{f}-k_{f}\right)\right]}{\left[1+\frac{2\alpha_{f} -2}{\alpha_{f}+2}\left(\alpha_{f}-k_{f}\right)\right](1+\beta)^{2}}\right]\)} & \multirow{2}{*}{Modified Maxwell model and included} \\  & & \\  & & \(k_{ff}=k_{f}\left[\frac{\left[2\alpha_{f}-2\right]}{\left[1-\gamma\right]+\left(1 +\beta\right)^{2}\left(1+2\right)\right]}\) & \\ \hline \multirow{2}{*}{[PERSON] et al. [95]} & \multirow{2}{*}{\(k_{eff}=k_{f}\left[1+\frac{\left[3\alpha_{f}\right]}{\frac{2\alpha_{f}}{ \alpha_{f}}}\right]\)} & \multirow{2}{*}{The developed comprehensive model} \\  & & & included the analyzer thickness, particle size, temperature, volume fraction and the \\  & & & interaction between adjacent nanoparticles. \\ \hline \multirow{2}{*}{[PERSON] et al. [96]} & \multirow{2}{*}{Model I: \(k_{sf}=k_{sf}\left[\left(\frac{\alpha_{f}}{\alpha_{f}}\right)\left(\frac{ \alpha_{f}}{\alpha_{f}}\right)^{1.33}\left(\frac{\alpha_{f}}{\alpha_{f}}\right) ^{0.38}\right]\)} & Model I: \(k_{sf}=k_{sf}\left[\left(\frac{\alpha_{f}+\left(-1\right)k_{sf}+\left(-1\right) \left(k_{sf}-k_{sf}\right)\right)\left(1+\beta\right)^{2}\right]\)} & Model II helped to visualize the percentage \\  & & & contribution of layer thickness, particle shape, Brownian motion to the enhancement in \\  & & thermal conductivity of nanofluids. \\ \hline \multirow{2}{*}{[PERSON] et al. [97]} & \multirow{2}{*}{\(k_{sf}=k_{sf}\left[\frac{k_{sf}+\left(-1\right)k_{sf}-\left(-k_{sf}-k_{sf} \right)\right)\left(\alpha_{f}-k_{sf}\right)\alpha_{f}}\)} & Considered the liquid layer thickness, \\  & & thermal conductivities of base fluid and \\  & & nanoparticles but not the interface between \\  & & particles and particle size. \\ \hline \multirow{2}{*}{Corcione [98]} & \multirow{2}{*}{\(k_{sf}=1+4.4R^{\Delta 4}\rho^{\Delta 4}\rho^{\Delta 66}\left(\frac{7}{\gamma_{m}} \right)^{10}\left(\frac{k_{sf}}{\alpha_{f}}\right)^{0.66}\)} & The empirical correlation of Corcione is \\  & & applicable with 1.86\% of standard deviation \\  & & error over a wide range of temperature \\  & & (294-324 K), nanoparticle diameter \\  & & (10-150 nm) and volume fraction (0.002-0.9) \\ \hline \end{tabular}
\end{table} 
Table 1: Thermal conductivity models. Figure 16: Thermal conductivity of TiO\({}_{2}\) nanofluid as a function of temperature from various studies. represented with the help of error bars. The upper and lower ends relatively show the maximum and minimum values of thermal conductivity against temperature values. From all of the above discussion following deductions can be drawn:  
* Thermal conductivity of TiO\({}_{2}\) nanofluids is directly related to the temperature. * The variation in particle concentration directly influences the thermal conductivity of the nanofluid. * The results obtained in different studies by using water as a base fluid showed better performance as compared to the ethylene glycol.