An analytical model for the design of optimized heat exchangers for thermoacoustic systems

Abstract

A 1-D nonlinear model for the heat transport from the edge of a thermoacoustic stack to a heat exchanger is developed. This model is an extension of the previous study by [Gusev et al., J. of Sound and Vibration 235, (2000)] to the case of a finite dimension heat exchanger with a temperature difference between the stack and the heat exchanger plates. The model is based on a relaxation-time approximation for transverse heat transfer that allows for the calculation of the heat flux through an adiabatic gap, separating the stack and the heat exchangers. It shows the generation of temperature harmonics close to the edge of the plates that leads to nonlinear heat transport through the gap. The heat flux extracted by the hot side heat exchanger is calculated, taking into account viscous dissipation along the plates and reverse heat conduction toward the stack. An optimal set of geometrical and relaxation parameters for the heat exchanger is obtained. Results are compared with experimental measurements of temperature fluctuations behind the stack plates, and with the results of numerical simulations from the literature. [This work is supported by ANR (project MicroThermoAc NT05142101).]