## 3 Results and Discussion
### Heat Transfer Condition  
Finally, the wall heat transfer calculated from the CFD models is compared to the experimental data. Heat flux, \(q\), for all models is averaged over one cycle and the length of the heat exchanger, \(l\), and calculated as:  
\[q_{H,C}=\frac{1}{2\pi l}\int_{0}^{2\pi}\int_{0}^{l}-k\frac{dT}{dy}\bigg{|}_{wall }dxd\phi. \tag{17}\]  
Subscripts \(H\) and \(C\) refer to HHX and CHX, respectively. Here, the mean thermal conductivity, \(k\), is used to calculate the heat flux obtained from laminar, transition-SST and SST k-\(\omega\) models [22].  
Figure 19 shows that the heat flux predicted from the numerical models and experiments increases with an increase of the drive ratio (indeed, for easier comparisons with the literature, the drive ratio is replaced by the Reynolds number, but it is still easy to identify the four drive ratios). The Reynolds number is calculated as \(Re=\rho u_{m}D/\mu\) as already outlined in Section 2. The flow behaviour for drive ratios investigated in this paper has been shown to be well predicted using the SST k-\(\omega\) turbulence model and the transition-SST model. Therefore, the results shown in Figure 19 are based on the laminar and these two turbulent models.  
Figure 19: Heat fluxes at cold and hot heat exchangers: comparison between numerical and experimental results.  
Figure 18: The effect of the drive ratio on dimensionless mean flow viscous dissipation (**a**) and the enlarged view of the viscous dissipation at the end of plates (**b**).  
In general, judging from Figure 19, the numerical predictions of heat transfer at the HHX are reasonably well aligned with the experimental values for all drive ratios. Here, the lowest discrepancy between numerical predictions and experiment is around 24% for the lowest drive ratio of 0.30%. As the drive ratio increases, the discrepancy drops to 7%. On the other hand, for the CHX, the agreement seems reasonable for the three lower drive ratios, 0.30%, 0.45% and 0.65%, where the lowest discrepancy is around 31%, 4% and 30%, respectively. The disagreement becomes substantially worse for the highest drive ratio of 0.83%, where the smallest discrepancy between CFD and the experiment is around 97%.  
Of course, a judgement as to what constitutes reasonable agreement is somewhat arbitrary; however, the literature tends to agree that in complex flow cases like this, a discrepancy of around 30% is not unexpected. One also needs to remember that the experimental results were obtained from the acetone-based PLIF measurement technique with the stated temperature accuracy of \(\pm 16\) K, where calibration for the low temperature end of the range is particularly challenging. This may well explain the discrepancies between CFD and experiment that tend to be within 30% in the majority of cases, but in particular, also the case of the highest drive ratio for the CHX, which seems to be an experimental \"outlier\".  
It is also worth comparing in detail the CFD results themselves. It is clear that the results obtained from the turbulent models are consistently closer to the experiment than from the laminar model (although this improvement is dwarfed by the overall large gap between all numerical results and the experiment). In particular, the transition-SST model gives better predictions of heat flux for drive ratios of 0.45% and 0.65% compared to predictions from the laminar model. For the highest drive ratio of 0.83%, the use of the SST k-\(\omega\), instead of the laminar, model brings the discrepancy of 117% down to 97%.