Nusselt numbers of laminar, oscillating flows in stacks and regenerators with pores of arbitrary cross-sectional geometry.

Though widely used in steady-flow heat transfer applications, the Nusselt number-a dimensionless heat transfer coefficient-has not been studied as thoroughly in oscillating flows and is therefore not generally used in thermoacoustic applications. This paper presents expressions for the Nusselt numbers of laminar oscillating flows within the pores of stacks and regenerators, 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. Results are shown for parallel plates, circular pores, rectangular pores, and within the boundary layer limit. It is shown that bulk temperature does not become infinite during an acoustic cycle and that the Nusselt number is a complex constant at all times. In addition, steady-flow Nusselt numbers are recovered when velocity and temperature profiles are like those in steady flows.