Modeling of micro-scale thermoacoustics

Thermoacoustic phenomena, that is, onset of self-sustained oscillations or time-averaged fluxes in a sound wave, may be harnessed as efficient and robust heat transfer devices. Specifically, miniaturization of such devices holds great promise for cooling of electronics. At the required small dimensions, it is expected that non-negligible slip effects exist at the solid surface of the "stack"-a porous matrix, which is used for maintaining the correct temporal phasing of the heat transfer between the solid and oscillating gas. Here, we develop theoretical models for thermoacoustic engines and heat pumps that account for slip, within the standing-wave approximation. Stability curves for engines with both no-slip and slip boundary conditions were calculated; the slip boundary condition curve exhibits a lower temperature difference compared with the no slip curve for resonance frequencies that characterize micro-scale devices. Maximum achievable temperature differences across the stack of a heat pump were also calculated. For this case, slip conditions are detrimental and such a heat pump would maintain a lower temperature difference compared to larger devices, where slip effects are negligible.