Solutions to the fully developed convection heat transfer problem in core annular flows

Heat transfer in circular pipes with two concentric regions (core annular flows) is a problem that arises in materials processing and the chemical industries. Examples of this problem include the flow of oil/water for a certain range of Reynolds numbers and flow through packed bed chemical reactors. In this work, the convection heat transfer problem is solved for a core-annular flow that is both thermally and hydrodynamically fully developed. Solutions are obtained for an outer surface of the pipe that is subjected to three different boundary conditions: uniform heat flux, constant wall temperature, and convective heat flux. The velocity and the temperature profiles are calculated analytically and Nusselt numbers are evaluated for the three cases. The analytical results are validated by comparison with the solutions for the single-phase fluid.