## 3 Results and Discussions
### Investigation of the Effect of the Initial Fluid Temperature on Flow and Heat Transfer  
The current CFD study deals with flow fields with relatively high imposed temperature gradients which results in difficulties to achieve numerically a temperature field similar to that obtained from the experiment. A possible way of bringing these close to each other, within a reasonable computational time, was through setting an appropriate initial fluid temperature in the model. Three approaches were investigated and these are discussed below. Their outcomes are illustrated for phase \(\phi\)1 in Figure 9; the experimental data shown in Figure 9a are compared against CFD data in Figure 9b-d.  
First, the model was initialised with a uniform fluid temperature, \(T_{i}=300\) K. The model was iterated until it reached 70 flow cycles which is equivalent to 5 s of real time. Figure 9b shows that the resulting temperature field is still dominated by the low temperature of the initial 300 K. On the other hand, the experimental data in Figure 9a show that the average fluid temperature is considerably higher due to the fact that the experimental data was collected after the flow has conveniently settled  
Figure 8: Temperature profiles for HHX and CHX—comparison between experimental (EXP) and computational (CFD) results at the location 15 mm from the joint (above the HHX and CHX plates). in the steady oscillatory state. At that stage, the heat has been accumulated in the system giving rise to the mean temperature of the flow. For the computational model with initial temperature of 300 K, a significant amount of computational time and effort would be required if a similar heat accumulation as in the experiment were to be achieved. Second, the model was initialised with a uniform fluid temperature close to the mean temperature from the experiments, \(T_{i}=360\) K and was similarly iterated for 70 cycles. Although the resulting temperature field in Figure 9c is closer to the experimental results, the effect of natural convection in the open area next to the CHX is not visible in the computational result. In addition, the temperature of the fluid within the channel of the CHX reduces from the initial high temperature to a lower temperature due to the cooling effect at that location. The reason for the mismatch is not clear, especially as the wall of the heat exchanger is already modelled following the temperature measured by the thermocouples as reported in the experimental work [17]. However, it is possible that additional features need to be introduced into the model such as heat losses (the modelled resonator is adiabatic, in reality there are considerable heat losses), heat accumulation, or heat leakages. The known issues of experimental temperature uncertainties need to be borne in mind too. The third approach tried to improve the predictions of natural convection observed experimentally at the plate ends by initialising the model with an approximate temperature field estimated from the experimental results (\(T_{i}\approx T(x,y_{r})\)). The resulting temperature contour after 70 cycles is shown in Figure 9d. The effect of the initialisation temperature seems to dominate the temperature field especially at the open area next to the plates. In the area between the plates of the heat exchanger, the wall temperature seems to control the temperature within the area. Figure 10 shows the effect of initial temperatures on the velocity amplitudes at a location 1 mm away from the joint above the cold plate. Evidently, a higher mean temperature of 360 K results in a slightly higher amplitude of the velocity, especially during the second half of the cycle. This may suggest that the experimental temperature field is affected by the accumulation of heat within the investigated area since raising the initial temperature from 300 to 360 K brings the solution closer to the experimental results. The same observation can be made for all locations along the heat exchanger plate as illustrated in Figure 10b.