## 4 Results and Discussion  
Firstly, in order to producea quick sketch of self-consistency and the impact trends of parameters, the analysis of variance is carried out to show the normal distribution plot of the residuals of 18 typical tested points (shown in Figure 3), which indicates self-consistency of the results. In Figure 3, the data show the normal probability distribution of residuals after an analysis of variance (ANOVA) of the tested results. The horizontal axis stands for the internally studentized residual, which is the quotient resulting from the division of a residual by an estimate of its standard deviation. The vertical axis stands for its corresponding normal possibility, which has exponential coordinates, hence, the normal distribution plot of residuals can show its self-consistency if the data lie in a neat straight line. The maximum deviation is below 10% with the correlation fitting based on RSM. The three-dimensional response surface is plotted into a polynomial correlation, with the highest order of two. Figure 4 shows the response surface plot with a fixed maximum Reynolds number of 800 for demonstration. From the response surfaces with fixed various parameters, it is noted that \(l/d_{h}\), as a geometrical parameter, has a negative influence on the Nusselt number. The rise of \(l/d_{h}\) leads to a dramatic weakening in the heat transfer performance. Along with the fact that the maximum Reynolds number and Valensi number both have a positive impact on the Nusselt number, more detailed experimental results are obtained with error bars indicating the uncertainty of acquired data, which is not higher than 5.8%. Figures 5-7 present the Nusselt number variations with six different \(l/d_{h}\) values when the Valensi numbers are 150, 200, and 250, respectively. These values are realized by the combination of three different lengths and two different hydraulic diameters, as listed in Table 1. It can be seen from the figures that, when the Reynolds number and Valensi number are both a controlled constant, the Nusselt number decreases as \(l/d_{h}\) is increased, reflected in the response surface illustrated in Figure 4. The oscillating-flow heat transfer performance will be significantly weakened when \(l/d_{h}\) is increased within the range discussed. Figure 4: Response surface with a fixed maximum Reynolds number of 800. Figure 3: Normal plot of residuals for 18 typical tested points. The results indicate that when the hydraulic diameter of the channel (roughly twice of the plate spacing) is constant, for the heat transfer with a smaller length (\(l/d_{h}\) is relatively small), the heat transfer performance of the parallel plates in oscillating helium flow is significantly better than that of heat exchangers with longer fins. It is assumed that the heat transfer process is enhanced by the entrance effect of oscillating flow. In addition, if the heat exchanger length is too large, being even longer than the peak-to-peak displacement of working fluid, part of the fluid particles will be trapped in the flow channel experiencing the reciprocating motion. As the \"trapped\" fluid has a temperature similar to that of the wall, the oscillating heat transfer will be relatively weak. From the view of the whole heat exchanger, it can be regarded that the central part of the heat transfer area doesn't play a role in the heat exchanger. Figure 5: Nusselt number variation with \(l/d_{h}\), \(Va=150\). Figure 6: Nusselt number variation with \(l/d_{h}\), \(Va=200\). Figure 7: Nusselt number variation with \(l/d_{h}\), \(Va=250\). a good role in the heat transfer process, which will lead to a lower Nusselt number of the oscillating flow inside the entire channel. With longer channels, there will be a larger area that has no effective heat transfer. Hence, for the heat exchanger types A and B, the obtained magnitudes have orders of B1 \(>\) B2 \(>\) B3 and A1 \(>\) A2 \(>\) A3. Numerical simulation by [PERSON] et al.