Abstract
General expressions for the Nusselt numbers of laminar oscillating flows within the pores of stacks and regenerators are derived from thermoacoustic theory developed by Rott and Swift. These expressions are based on bulk (velocity-weighted, cross-sectionally averaged) temperature, rather than the cross-sectionally averaged temperature. Two cases are considered: flow with oscillating pressure and no external temperature gradient, and oscillating velocity within an external temperature gradient and negligible pressure oscillations. These expressions are then applied to parallel plates, circular pores, rectangular pores, and within the boundary layer limit. Steady-flow Nusselt numbers are recovered when the thermal penetration depth is at least as great as the hydraulic radius of the pore. In addition, temperature and flow profiles within this regime are like those of steady flows.
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