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The heat transfer characteristics of regenerator in regenerative coolers such as pulse tube and Stirling coolers is important. Various methodologies of characterizing the Nusselt number between the regenerator matrix and working fluid have been established and applied. However, most of the existing formulas are based on the results of steady-state flow or low-frequency oscillating flow. In this paper, a tube model with finite wall thickness is built to investigate the Nusselt number in a regenerator under different flow conditions. The results indicate that within the Valensi number range typically used in coolers, the Nusselt number of oscillating and steady flow are numerically similar. But under extremely high Valensi numbers, significant differences are observed. This paper will generalize the variation features of the Nusselt number with the Valensi number in a simplified regenerator. Moreover, the applicability of the conventional theories under high Valensi numbers will be evaluated.
