Flow pattern construction-based tubular heat transfer intensification using calculus of variations

The flow pattern construction-based optimization approach was applied to tubular heat transfer intensification. As the first step in the optimization, the flow pattern was constructed from the thermodynamic point of view, with the heat transfer entropy generation set as the optimization objective and the viscous dissipation set as the constraint. The necessary conditions for the conditional extremum were determined to constitute a CFD model for the flow pattern construction. The hydrodynamic and heat transfer characteristics of the constructed optimal flow pattern are shown to be significantly different from those of the ordinary flow pattern. In particular, a flow structure containing multiple vortices appeared in the optimal flow pattern to improve the heat transfer performance. The second step of the proposed optimization was to design the internal geometric structure of the heat transfer tube to construct a real flow pattern that produces a larger heat transfer rate. The results of the geometry optimization indicate that porous inserts arranged near the tube wall can be a useful strategy for practical heat transfer intensification.