## 3 Results and Discussions
### The Effect of the Heat Exchanger Wall Temperature on the Flow Field
#### 3.2.2 The Effect of Wall Temperature on the Flow and Heat Transfer  
The effect of temperature on the flow and heat transfer is investigated by setting the heat exchanger wall temperatures to the values shown in Table 1. It should be noted that all comparisons to experiments were made using the model that applies the experimental temperature profiles of Figure 3 on the hot and cold plates (of course, except cases marked as \"adiabatic\" or \"dT = 0\"). However, for the sake of comparisons between numerical cases, \"flat\" temperature profiles were set up, as already mentioned in the introduction to Section 3.2. Figure 18 shows the comparison between the experimental and numerical velocity profiles for the flow at the location of 10 mm from the joint above the cold plate for comparable temperature gradients set up along the plates. The slight differences in the magnitude between the experimental and CFD data can be accounted for by the typical errors of particle image velocimetry (PIV), although it is worth mentioning that thermophoresis which affects \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Drive Ratio (\%)**} & **Working** & **Frequency** & **Mean Pressure** & \multicolumn{2}{c}{**Heat Exchanger Wall Temperature (\({}^{\circ}\)C)**} \\ \cline{3-6}  & **Medium** & **(Hz)** & **(bar)** & **Hot, \(T_{H}\)** & **Cold, \(T_{C}\)** \\ \hline \multirow{4}{*}{0.3} & \multirow{4}{*}{Nitrogen} & \multirow{4}{*}{13.1} & \multirow{4}{*}{1} & \multirow{4}{*}{100} & \multirow{4}{*}{30} \\  & & & & & 200 & 30 \\ \cline{1-1} \cline{5-6}  & & & & 100 & 30 \\ \cline{1-1} \cline{5-6}  & & & & 300 & 30 \\ \cline{1-1} \cline{5-6}  & & & & 300 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Wall temperature condition of the heat exchanger. seeding particles in the presence of temperature gradients [27] can also have an additional impact on the experimental data. Figure 16: Velocity profiles from computational fluid dynamics (CFD) model (black and grey lines) and the experiment (red and black symbol) for all 20 phases of a flow cycle. The heat exchanger walls are adiabatic. Figure 17: Vorticity contours within the channel with plates treated as adiabatic walls—comparison between the results from (**a**) the experiment of [PERSON] et al. [11] and (**b**) CFD. As shown in Figure 9a, buoyancy effects are observed in the experimental results. The heat supplied by the HHX causes reduced density of the fluid, which results in a buoyancy driven flow in the open area next to the HHX superimposed on the forced convection due to the flow being ejected from the channel by acoustic excitation as well as thermal expansion of the fluid travelling in the hot part of the channel. These temperature effects are likely contributors to the flow asymmetries observed in Figure 7b. These effects are also seen through a comparison of velocity profiles between the models with and without the temperature gradient imposed on the heat exchanger walls (cf., Figure 16 vs. Figure 18). The above asymmetry can be observed in two ways: Firstly, the whole structure of the velocity profile plotted in Figure 18 seems to be \"leaning\" to the left in comparison to Figure 16. This is clearly illustrated in Figure 19, where the presence of temperature makes the velocity profile of \(\phi\)9 and its counterpart in reversed flow, \(\phi\)19, \"lean\" to the left. Secondly, the maximum magnitude of velocity fluctuation extends further to the centreline when temperature effects are included in the model as seen in Figure 20a. In the absence of temperature effects (adiabatic wall condition shown in Figure 20 as dT = 0), the velocity profile is similar at both CHX and HHX. When the temperature effect is considered, the velocity profile at the HHX seems shifted up towards the centreline (\(y\) = 3 mm) and the magnitude of the velocity is larger compared to an equidistant location at the CHX.