Confined bubbly flows in millimeter-scale channels produce significant heat transfer enhancement when compared to single-phase flows. Experimental studies support the hypothesis that the enhancement is driven by a convective phenomenon in the liquid phase as opposed to sourcing from microlayer evaporation or active nucleation. A numerical investigation of flow structure and heat transfer produced by a single bubble moving through a millimeter-scale channel was performed in order to document the details of this convective mechanism. The simulation includes thermal boundary conditions emulating those of the experiments, and phase change was omitted in order to focus only on the convective mechanism. The channel is horizontal with a uniform-heat-generation upper wall and an adiabatic lower surface. A Lagrangian framework was adopted such that the computational domain surrounds the bubble and moves at the nominal bubble speed. The liquid around the bubble moves as a low-Reynolds-number unsteady laminar flow. The volume-of-fluid method was used to track the liquid/gas interface.

This paper reviews the central results of this simulation regarding wake heat transfer. It then compares the findings regarding Nusselt number enhancement to a reduced-order model on a two-dimensional domain in the wake of the bubble. The model solves the advective-diffusion equation assuming a velocity field consistent with fully developed channel flow in the absence of the bubble. The response of the uniform-heat-generation upper wall is included. The model assumes a temperature profile directly behind the bubble which represents a well-mixed region produced by the passage of the bubble.

The significant wake heat transfer enhancement and its decay with distance from the bubble documented by the simulation were captured by the reduced-order model. However, the channel surface temperature recovered in a much shorter distance in the simulation compared to the reduced-order model. This difference is attributed to the omission of transverse conduction within the heated surface in the two-dimensional model. Beyond approximately one bubble diameter into the bubble wake, the complex flow structures are replaced by the momentum field of the precursor channel flow. However, the properties and thickness of the heated upper channel wall govern the heat transfer for many bubble diameters behind the bubble.

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