###### Abstract  
The oscillating-flow heat transfer performance in finned heat exchangers is one of the main factors affecting the working efficiency of regenerative heat engines and refrigerators. In addition to the working parameters, the geometrical parameters of finned heat exchangers are also major influencing factors. In the present study, the ratio of the heat exchanger length and hydraulic diameter is applied as an independent similarity criterion. An experimental study has been carried out with six different geometrical dimensions of finned heat exchangers with parallel plates, in order to analyze the impacts of fin length, plate spacing, and corresponding relative fluid displacement amplitude, under various working conditions. Based on 298 tested points, a comprehensive empirical correlation for the finned heat exchangers with parallel plates working in oscillating flow has been proposed, providing a relatively accurate prediction, with 98.6% of data in the \(\pm\)20% deviation and 83.9% of data in the \(\pm\)10% deviation, within the range discussed. oscillating flow; heat transfer; finned heat exchanger; empirical correlation 2017 7  
the heat transfer characteristics of oscillating gas in a circular copper tube heated by constant heat flux. The average Nusselt number was correlated with the dimensionless amplitude and frequency, obtaining a preliminary empirical correlation. In 2007, [PERSON] et al. [6] carried out a study on the heat transfer characteristics of the oscillating-flow heat exchanger, measuring the heat transfer in a finned-tube heat exchanger. [PERSON] and [PERSON] [7] obtained the temperature and velocity fields in a parallel plate channel heat exchanger, using the planar laser-induced fluorescence (PLIF) technique, combined with the particle image velocimetry (PIV). The relationship between the Nusselt number and the Reynolds number was thus obtained. Recently, [PERSON]'s group investigated the effect of fin length and fin spacing on the thermal performance of finned-tube heat exchangers [8]. The heat transfer rate can be predicted using the correlation between the heat transfer effectiveness, and the normalized fin spacing and fin length. In the past decade, researchers have been approaching a deeper understanding of the oscillating flow behaviors, using state-of-the-art techniques [9; 10; 11; 12; 13; 14]. [PERSON] et al. [15; 16] experimentally studied the influence of working conditions, as well as the compression-expansion effect, on the Nusselt number of finned heat exchangers. An empirical correlation of the Nusselt number, with the maximum Reynolds number and Valensi number, has been summarized. Following the analysis and optimization method, this work aims to introduce the geometrical parameters as major factors of the heat transfer performance prediction. It presents an empirical correlation for the finned heat exchanger working in oscillating flow, which comprehensively considers velocity amplitude, oscillating frequency, pressure ratio, and geometrical dimension during the heat transfer process. In the following discussion, the dimensionless parameters are defined as:  
\[Re_{\text{max}}=\frac{u_{A}d_{h}}{\
u}, \tag{1}\]  
\[Va=\frac{\omega\,{d_{h}}^{2}}{\
u}, \tag{2}\]  
\[Nu=\frac{hd_{h}}{k}, \tag{3}\]  
\[PR=\frac{p_{m1}+p_{A1}}{p_{m1}-p_{A1}}, \tag{4}\]  
where \(u_{A}\) and \(\omega\) are the velocity amplitude and angular frequency of the flow, respectively. \(h\) is the mean convective heat transfer coefficient. \(\
u\) and \(k\) are the kinetic viscosity and thermal conductivity of the fluid, respectively. \(d_{h}\) is the hydraulic diameter. For the cross-section shape of the flow channels in fin-type heat exchangers, the geometry primarily depends on the channel length \(l\) and hydraulic diameter \(d_{h}\). In the design of heat exchangers working in oscillating flow, the length direction, parallel to the direction of oscillating fluid, is constrained by the gas peak-to-peak displacement.