The paper presents an analysis of the entropy generation in the bifurcation of a fluid-carrying tube in the presence of wall suction. The objective is to minimize the entropy generation rate due to the viscous flow within the tubes. Several simplifying assumptions are made to reduce the problem to a multi-objective optimization in 3 independent variables: the aspect ratio of the domain served by the flow, the diameter ratio of the primary and secondary branches, and the length of the secondary branch (the location of both the “source” of the fluid and the “sink”, i.e. the place of desired delivery of the fluid, being a datum). The wall suction is assumed to be proportional to the wetted area. For three different initial assumptions (constant Re, constant fluid velocity, constant fluid volume) it is shown that an “optimal shape” exists and is identified by the minimum entropy generation. But, this minimum is always higher than the value pertaining to the unsplit tube with no wall suction. The study demonstrates that, for a given design goal (i.e., for an assigned “function” the configuration is called to perform) Entropy Generation Minimization is a feasible “topological Lagrangian” for the bifurcation geometry.

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