A numerical investigation of a single highly confined bubble moving through a millimeter-scale channel in the absence of phase change is presented. The simulation includes thermal boundary conditions designed to match those of completed experiments. The channel is horizontal with a uniform-heat-generation upper wall and an adiabatic lower boundary condition. The use of a Lagrangian framework allows for the simulation of a channel of arbitrary length using a limited computational domain. The liquid phase is a low-Reynolds-number unsteady laminar flow, and the phase interactions are modeled using the Volume-of-Fluid method with full geometric reconstruction of the liquid/gas interface. Results are presented for two bubble sizes, two liquid flow rates, and two Prandtl numbers. The paper focuses on heat transfer in the rearward wake of the bubble. Nusselt numbers for the higher Prandtl number case are shown to follow a power law relationship with distance behind the bubble. Important dynamical structures include a pair of vortical structures at the rear of the bubble associated with cold fluid being brought near the wall and fluid jets oriented in the transverse direction to either side of the bubble.

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