Investigation of heat transfer in turbulent nanofluids using direct numerical simulations

A numerical study has been performed by using a combined Euler and Lagrangian method on the convective heat transfer of Cu and ${\text{Al}}_2{\text{O}}_3$ nanofluids under the turbulent flow conditions. The effects of volume fraction of nanoparticles, nanoparticle sizes, and nanoparticle material are investigated. The mechanism of convective heat transfer enhancement in nanofluids has also been investigated, by studying the influence of particle dispersion and two-way interaction between fluid and particle temperature. The results show significant enhancement of heat transfer of nanofluids. The numerical data are compared with the correlation data of the experiments and reasonably good agreement is achieved.

Figure 1

Temporal evolution of $k_{\text{max}}\eta$ and $k_{\text{max}}{\eta }_{\theta }$ along time is shown in the plot. Values of $k_{\text{max}}\eta$ and $k_{\text{max}}{\eta }_{\theta }$ are always greater than one, thus ensuring accurate resolution of small scale structures and accurate interpolation of fluid velocities.

Figure 2

Effective Nusselt number of Cu(100)/DIW and ${\text{Al}}_2{\text{O}}_3\left(100\text{nm}\right)/\text{DIW}$ nanofluids are plotted at different volume fractions. Effective Nusselt number is observed to increase with the increase of the volume fraction of nanofluids.

Figure 3

Contours of instantaneous velocity vector, deformation tensor $II$ and square temperature gradient $G_i^2$ are shown for Cu(100 nm)/DIW nanofluids at different volume fractions. (a) Cu(100 nm)/DIW nanofluid at $\Phi =0.5\%$; (b) Cu(100 nm)/DIW nanofluid at $\Phi =0.1\%$; (c) Cu(100 nm)/DIW nanofluid at $\Phi =1.0\%$. Change in the values of $II$ with the change of the volume fraction of nanofluids is observed to be negligible. However, the contour plot of $G_i^2$ shows a significant increase in its values as the volume fraction of nanofluids increases.

Figure 4

Distribution of $G_i^2$ and the terms in the $G_i^2$ evolution equation; $P_{c2}$, dissipation and dissipation are shown for (a) Cu(100 nm)/DIW nanofluids at $\Phi =0.1\%$; (b) Cu(100 nm)/DIW nanofluid at $\Phi =0.5\%$; (c) Cu(100 nm)/DIW nanofluid at $\Phi =1.0\%$. The contour of $G_i^2$ shows a significant increase in its values at volume fraction of 1.0%.

Figure 5

Distribution of $G_i^2$ and the negative and positive terms of $P_{c3}$ are shown for (a) Cu(100 nm)/DIW nanofluids at $\Phi =0.1\%$; (b) Cu(100 nm)/DIW nanofluid at $\Phi =0.5\%$; (c) Cu(100 nm)/DIW nanofluid at $\Phi =1.0\%$. Distribution of positive value of $P_{c3}$ is very small and is not significantly influenced by the change of the volume fraction. However, the negative value of $P_{c3}$ is found to be significantly increased with the increase of the volume fraction of nanofluids.

Figure 6

Effective Nusselt number of Cu/DIW and ${\text{Al}}_2{\text{O}}_3/\text{DIW}$ nanofluids, for 0.5% volume fraction, are plotted at different particle sizes. Effective Nusselt number is observed to decrease with the increase of particle diameter.

Figure 7

Contours of instantaneous velocity vector, deformation tensor $II$ and square temperature gradient $G_i^2$ are shown for 0.5% volume fraction of Cu/DIW nanofluids at different particle diameters. (a) Cu(75 nm)/DIW nanofluid at $\Phi =0.5\%$; (b) Cu(100 nm)/DIW nanofluid at $\Phi =0.5\%$; (c) Cu(150 nm)/DIW nanofluid at $\Phi =0.5\%$. Change in the values of $II$ with the change of the particle diameter is observed to be negligible. However, the contour plot of $G_i^2$ shows a significant increase in its values as the volume fraction of nanofluids increases.

Figure 8

Distribution of $G_i^2$ and the terms in the $G_i^2$ evolution equation; $P_{c2}$, dissipation and dissipation are shown for (a) Cu(75 nm)/DIW nanofluid at $\Phi =0.5\%$; (b) Cu(100 nm)/DIW nanofluid at $\Phi =0.5\%$; (c) Cu(150 nm)/DIW nanofluid at $\Phi =0.5\%$. The contour of $G_i^2$ shows a significant decrease in its values for the particle diameter of 150 nm. However, this decrease in the values of $G_i^2$ is not due to the production term $P_{c2}$. The magnitude of $P_{c2}$ is not influenced by the increase of the particle diameter.

Figure 9

Distribution of $G_i^2$ and the negative and positive terms of $P_{c3}$ are shown for (a) Cu(75 nm)/DIW nanofluid at $\Phi =0.5\%$; (b) Cu(100 nm)/DIW nanofluid at $\Phi =0.5\%$; (c) Cu(150 nm)/DIW nanofluid at $\Phi =0.5\%$. Distribution of positive value of $P_{c3}$ is very small and is not significantly influenced by the change of the particle size. However, the negative value of $P_{c3}$ is found to be significantly decreased with the increase of the particle diameter.

Figure 10

Distribution of $G_i^2$ and the negative and positive terms of $P_{c3}$ are shown for (a) Cu(75 nm)/DIW nanofluid at $\Phi =0.5\%$; (b) ${\text{Al}}_2{\text{O}}_3\left(75\text{nm}\right)/\text{DIW}$ nanofluid at $\Phi =0.5\%$. Distribution of positive value of $P_{c3}$ is very small and is not significantly influenced by the change of the particle size. However, the negative value of $P_{c3}$ is found to be significantly increased for Cu/DIW nanofluids when compared to that of ${\text{Al}}_2{\text{O}}_3/\text{DIW}$ nanofluids.