## 3 Results and Discussions
### The Effect of Gravity and Device Orientation on Flow and Heat Transfer  
The orientations of the resonator, relative to the gravity field, investigated in this study are schematically illustrated in Figure 25 (the three pairs of plates are for illustration only--all ten pairs are included in the model as before). The direction of the gravity field is modelled accordingly following the orientation. 0\({}^{\circ}\) corresponds to the horizontal layout in the figure, 90\({}^{\circ}\) indicates the hot plates above the cold plates, and 270\({}^{\circ}\) indicates the hot plates below the cold plates. The case with gravity switched off (g = 0) is also considered for reference. Experimental temperature profiles shown in Figure 3 are applied at the cold and hot plates in the models. Figure 26 shows the effect of gravity and device orientation (tilt angle 0\({}^{\circ}\), 90\({}^{\circ}\), and 270\({}^{\circ}\)) on the velocity profile plotted 15 mm from the joint above the cold and hot plates for selected phases \(\phi\)9 and \(\phi\)19. In order to differentiate between the data for the cold and hot channels, the lines for the velocity profiles at the hot channel are assigned a \"diamond\" symbol at the top end of the lines. The effect of gravity can be seen by comparing cases assigned as \"g, 0\({}^{\circ}\)\" (presented by solid-lines) and \"g = 0\" (presented by dashed-lines). For phase \(\phi\)9 (Figure 26b), the comparison shows that gravity has little effect on the flow structure in the horizontal orientation. However, the effect of gravity is seen to be larger at \(\phi\)19. Comparison between the magnitude of the velocity between \(\phi\)9 and \(\phi\)19 for both \"g, 0\({}^{\circ}\)\" and \"g = 0\" shows that the temperature-driven buoyancy flow seems to cause a stronger asymmetry  
Figure 24: Axial velocity at the middle of the channel along the hot (HHX) and cold (CHX) heat exchangers; temperature profiles assumed “flat”. Figure 25: Illustration of the thermoacoustic device orientation. Red and blue plates symbolise hot and cold heat exchangers, respectively. between the first and second parts of the flow cycle. The temperature-driven flow due to gravity seems to significantly assist the flow at \(\phi 19\) and slightly resist the flow at \(\phi 9\). For an orientation other than horizontal, the gravity field affects the flow depending on the direction of flow and the relative locations of the HHX and CHX. At an orientation of \(90^{\circ}\) (presented by the dashed-dotted lines), the cold plate is located below the hot plate resulting in a reduced velocity magnitude during \(\phi 9\) of the flow cycle, because the buoyancy effects are resisting the flow. As the flow reverses (shown as \(\phi 19\)), the buoyancy effect is helping the flow. As a result, the velocity magnitude becomes bigger than that at the first half of the cycle. Conversely, when the device is at an orientation of \(270^{\circ}\) (presented by the dotted-lines), the temperature-driven buoyancy effect assists the flow at \(\phi 9\) (Figure 26b), resulting in a higher velocity amplitude and hence a greater fluid displacement between the plates. At \(\phi 19\) (Figure 26a), the flow reverses and the temperature-driven buoyancy effect is resisting the flow. Consequently, the velocity amplitude within the channel is lower than that in the first part of the cycle. For all device orientations, the velocity amplitude within the hot channel is always bigger than that at the cold channel. This is a logical consequence of the temperature-dependent density as previously discussed. The effect of gravity and device orientation on the wall heat transfer is shown in Figure 27. The heat flux is averaged over the length of the heat exchanger and is calculated using Equation (8). The effect of gravity is less pronounced in the CHX compared to the HHX. This is in accordance with the effect of buoyancy driven flow, which is more pronounced at the HHX compared to the CHX.