The role of unavoidable space between heat exchangers and stack inside a thermoacoustic standing wave generator is investigated. A two-dimensional Low Mach number viscous and heat conducting flow model of the active thermoacoustic cell, comprising heater and cooler separated by a stack made of parallel conducting plates, is described. Three different models of heat exchangers are implemented and compared. Ideal heat exchangers consist of a fluid zone with imposed temperature. The other two models are made up of stacks of horizontal plates, either with specified wall temperatures, in one model and with constant prescribed heat fluxes in the other. A multiple scale analysis allows for coupling the active thermoacoustic cell model with the flow inside the resonator, obtained as a solution to a linear acoustic formulation. When a large enough temperature difference is applied between the heat exchangers, initial pressure perturbations grow. Different resonant modes are amplified for different configurations, in the same way as in experimental observations.

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