We describe numerical solutions of the flow-field generated by heat sources distributed continuously over a spherical surface that is rising at a fixed speed in a viscous fluid. This is a model for small, highly curved flames of the type that can be supported by very lean hydrogen/air mixtures (flame-bubbles). Heat swept into the wake behind the sphere generates finite disturbances at downstream infinity, and the boundary conditions there should be chosen accordingly. We compare results obtained in this way with results generated by imposing uniform conditions (Dirichlet or Neumann) at the downstream boundary.

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