Heat transfer characteristics of oscillating flow regenerator filled with circular tubes or parallel plates

Under assumption of small perturbation, linear thermoacoustic theory was applied to analyze heat transfer characteristics of compressible oscillating flow in two kinds of simple regenerators filled with circular tubes or parallel plates. Based on the cross-sectional oscillating velocity and temperature distributions, the exact expressions of Nusselt number were derived in complex notation. The Nusselt number is the function of Prandtl number, kinetic Reynolds number Reω and the third dimensionless variable, D. Here, the D is defined as the ratio of heat transfer capability aroused by mean temperature gradient and gas compressibility. Both the gas compressibility and mean temperature gradient effects were discussed and two corresponding Nusselt numbers were given. In particular, simpler expressions for these two Nusselt numbers were deduced for extreme values of Reω and D. Finally, combined effect of gas compressibility and non-zero mean temperature gradient on heat transfer characteristics were analyzed via D. The analysis shows that the mean temperature gradient gives predominant contribution to the heat transfer performance of oscillating flow regenerator.