RELAXATION-TIME APPROXIMATION FOR ANALYTICAL EVALUATION OF TEMPERATURE FIELD IN THERMOACOUSTIC STACK

The problem of analytical description of temperature fields and heat fluxes in thermoacoustic devices (such as refrigerators and prime-movers) is discussed. It is demonstrated that for the precise analysis of the thermoacoustic process near the edges of the stacks and the heat exchangers, and also for the prediction of the heat fluxes between the stack and the heat exchangers, it is necessary to avoid the traditional “mean-field” approximation. In other words, on the spatial scale of the order of a particle displacement in the standing acoustic wave, hydrodynamical (advective) transport of heat cannot be described as a diffusional transport with an effective (depending on the acoustic wave power) diffusivity. In order to get insight into the non-linear phenomena, related to axial (along the stack) advective transport of heat, the simplified description of the transverse heat exchange between the gas and the stack (the relaxation-time approximation) has been adopted in the present investigation. The analytical descriptions obtained of the temperature distribution and of the heat flux predict, in particular, that in some cases the thermoacoustic heat flux between two stacks separated by an adiabatic gap can increase with the increasing width of the gap.