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A methodology based on sound non-equilibrium thermodynamics principles is developed to estimate the extremum dissipation point for steady-state incompressible flow past a sphere at low Reynolds numbers. It is shown, that the extremum dissipation point appears at the point when both the shear stress and the pressure at the surface of the sphere are equal to zero. The Reynolds number and the position of the extremum dissipation flow past a sphere were further estimated with the aid of a mathematical model for pressure distribution on the sphere surface, accounting for both creeping and ideal flow. The parameters of the model were determined by comparison of the calculated pressure distribution at the surface with the available literature data. The conditions at which the separation angle and the extremum dissipation angle coincide were also investigated. It is believed that this work could be used to further elucidate the flow past a sphere. [ABSTRACT FROM AUTHOR]

Microchannels are small-scale channels with unique properties that make them useful in various fields, such as electronics, biomedical engineering, and chemical engineering. This research paper investigates the effect of microchannel geometry on fluid flow behavior at different values of the Reynolds number. A rectangular microchannel with a pattern of obstructions and water as the working fluid was used in this study. Computational fluid dynamics (CFD) simulations were used to investigate the impact of different channel geometrical configurations and different values of the Reynolds number on fluid flow behavior. The results showed that the channel geometrical configuration and the Reynolds number significantly affect fluid flow behavior. A geometry with increasing obstruction heights led to higher values of pressure drop than the geometry with decreasing obstruction heights. This study provides valuable insights into microchannel flow behavior and can be used for the development of optimized microchannel designs for diverse applications. [ABSTRACT FROM AUTHOR]

Most of the studies have expressed film thickness ( I i ) as a function of Weber number HT ht , capillary number HT ht , E tv s number HT ht , and inverse viscosity number HT ht where, Mo = Morton number HT ht . These are related as follows: HT ht Graph (1)where I i SP * sp is the non-dimensional film thickness, I i is the film thickness, I D i is the diameter of the conduit. [Extracted from the article]