GENERALIZED REYNOLDS-NUMBER FOR THE FLOW OF POWER-LAW FLUIDS IN CYLINDRICAL DUCTS OF ARBITRARY CROSS-SECTION

The pressure drop prediction requires the generalization of the Reynolds number for laminar flow of pseudoplastic fluids in cylindrical ducts. This generalized Reynolds number is now well established for very simple cross-sections, such as circular tubes or infinite parallel plane plates. To our knowledge, there is no generalization available for other cross-sections due to the complexity of the velocity profiles. The aim of this paper is to propose a generalized Reynolds number for cylindrical ducts of arbitrary cross-section. This new Reynolds number involves only one geometrical parameter, which can be easily determined theoretically or experimentally. This Reynolds number was successfully compared with definitions found in the literature. Moreover, this generalized Reynolds number seems to be in good agreement with experimental studies carried out in plate heat exchangers.